Table of contents for issues of American Mathematical Monthly

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Volume 107, Number 1, January, 2000
Volume 107, Number 2, February, 2000
Volume 107, Number 3, March, 2000
Volume 107, Number 4, April, 2000
Volume 107, Number 5, May, 2000
Volume 107, Number 6, June / July, 2000
Volume 107, Number 7, August / September, 2000
Volume 107, Number 8, October, 2000
Volume 107, Number 9, November, 2000
Volume 107, Number 10, December, 2000
Volume 108, Number 1, January, 2001
Volume 108, Number 2, February, 2001
Volume 108, Number 3, March, 2001
Volume 108, Number 4, April, 2001
Volume 108, Number 5, May, 2001
Volume 108, Number 6, June / July, 2001
Volume 108, Number 7, August / September, 2001
Volume 108, Number 8, October, 2001
Volume 108, Number 9, November, 2001
Volume 108, Number 10, December, 2001
Volume 109, Number 1, January, 2002
Volume 109, Number 2, February, 2002
Volume 109, Number 3, March, 2002
Volume 109, Number 4, April, 2002
Volume 109, Number 5, May, 2002
Volume 109, Number 6, June / July, 2002
Volume 109, Number 7, August / September, 2002
Volume 109, Number 8, October, 2002
Volume 109, Number 9, November, 2002
Volume 109, Number 10, December, 2002
Volume 110, Number 1, January, 2003
Volume 110, Number 2, February, 2003
Volume 110, Number 3, March, 2003
Volume 110, Number 4, April, 2003
Volume 110, Number 5, May, 2003
Volume 110, Number 6, June / July, 2003
Volume 110, Number 7, August / September, 2003
Volume 110, Number 8, October, 2003
Volume 110, Number 9, November, 2003
Volume 110, Number 10, December, 2003
Volume 111, Number 1, January, 2004
Volume 111, Number 2, February, 2004
Volume 111, Number 3, March, 2004
Volume 111, Number 4, April, 2004
Volume 111, Number 5, May, 2004
Volume 111, Number 6, June / July, 2004
Volume 111, Number 7, August / September, 2004
Volume 111, Number 8, October, 2004
Volume 111, Number 9, November, 2004
Volume 111, Number 10, December, 2004
Volume 112, Number 1, January, 2005
Volume 112, Number 2, February, 2005
Volume 112, Number 3, March, 2005
Volume 112, Number 4, April, 2005
Volume 112, Number 5, May, 2005
Volume 112, Number 6, June / July, 2005
Volume 112, Number 7, August / September, 2005
Volume 112, Number 8, October, 2005
Volume 112, Number 9, November, 2005
Volume 112, Number 10, December, 2005
Volume 113, Number 1, January, 2006
Volume 113, Number 2, February, 2006
Volume 113, Number 3, March, 2006
Volume 113, Number 4, April, 2006
Volume 113, Number 5, May, 2006
Volume 113, Number 6, June / July, 2006
Volume 113, Number 7, August / September, 2006
Volume 113, Number 8, October, 2006
Volume 113, Number 9, November, 2006
Volume 113, Number 10, December, 2006
Volume 114, Number 1, January, 2007
Volume 114, Number 2, February, 2007
Volume 114, Number 3, March, 2007
Volume 114, Number 4, April, 2007
Volume 114, Number 5, May, 2007
Volume 114, Number 6, June / July, 2007
Volume 114, Number 7, August / September, 2007
Volume 114, Number 8, October, 2007
Volume 114, Number 9, November, 2007
Volume 114, Number 10, December, 2007
Volume 115, Number 1, January, 2008
Volume 115, Number 2, February, 2008
Volume 115, Number 3, March, 2008
Volume 115, Number 4, April, 2008
Volume 115, Number 5, May, 2008
Volume 115, Number 6, June / July, 2008
Volume 115, Number 7, August / September, 2008
Volume 115, Number 8, October, 2008
Volume 115, Number 9, November, 2008
Volume 115, Number 10, December, 2008
Volume 116, Number 1, January, 2009
Volume 116, Number 2, February, 2009
Volume 116, Number 3, March, 2009
Volume 116, Number 4, April, 2009
Volume 116, Number 5, May, 2009
Volume 116, Number 6, June / July, 2009
Volume 116, Number 7, August / September, 2009
Volume 116, Number 8, October, 2009
Volume 116, Number 9, November, 2009
Volume 116, Number 10, December, 2009


American Mathematical Monthly
Volume 107, Number 1, January, 2000

           Phillip A. Griffiths   Mathematics at the Turn of the
                                  Millennium . . . . . . . . . . . . . . . 1--14
                 C. W. Groetsch   The Commandant's Corollary . . . . . . . 15--23
                  Jerome Reiter   Using Statistics to Determine Causal
                                  Relationships  . . . . . . . . . . . . . 24--32
                     James Case   Paradoxes Involving Conflicts of
                                  Interest . . . . . . . . . . . . . . . . 33--43
                  J. E. McClure   Start Where They Are: Geometry as an
                                  Introduction to Proof  . . . . . . . . . 44--52
              Jerzy Tyszkiewicz   A Simple Construction for Tournaments
                                  with Every k Players Beaten by a Single
                                  Player . . . . . . . . . . . . . . . . . 53--54
                   Maria Suzuki   Alternative Formulations of the Twin
                                  Prime Problem  . . . . . . . . . . . . . 55--56
              Alexander Russell   An Easy Reduction of an Isoperimetric
                                  Inequality on the Sphere to Extremal Set
                                  Theory . . . . . . . . . . . . . . . . . 57--59
           Peter Malcolmson and   
                     Frank Okoh   Rings without Maximal Ideals . . . . . . 60--61
             Thomas R. Hagedorn   A Proof of a Conjecture on Egyptian
                                  Fractions  . . . . . . . . . . . . . . . 62--63
              S. S. Demidov and   
                   A. Shenitzer   The Evolution of \ldots Two Letters by
                                  N. N. Luzin to M. Ya. Vygodskii  . . . . 64--82
                   Catalin Zara   Problem 10774  . . . . . . . . . . . . . 83--83
                 Hadi Salmasian   Problem 10775  . . . . . . . . . . . . . 83--83
                    Yongge Tian   Problem 10776  . . . . . . . . . . . . . 83--83
                    Zafar Ahmed   Problem 10777  . . . . . . . . . . . . . 83--83
               Paul Bateman and   
                Dennis Eichhorn   Problem 10778  . . . . . . . . . . . . . 83--83
                   Andrei Jorza   Problem 10779  . . . . . . . . . . . . . 83--83
                  Kiran Kedlaya   Problem 10780  . . . . . . . . . . . . . 84--84
          John P. Robertson and   
            GCHQ Problems Group   Elliptic Curves to the Rescue: 10612 . . 84--86
          George E. Andrews and   
        John Henry Steelman and   
                 G. L. Body and   
                  D. Callan and   
              R. J. Chapman and   
                  K.-W. Lau and   
                J. T. Lewis and   
           J. H. Lindsey II and   
                    G. Lord and   
             J. G. Merickel and   
 Anchorage Math Solutions Group   Rogers--Ramanujan Partitions: 10627  . . 86--86
          George E. Andrews and   
                Kee-Wai Lau and   
                 G. L. Body and   
                  D. Callan and   
              R. J. Chapman and   
                    G. Lord and   
             H.-J. Seiffert and   
                  D. Zeilberger   Partitions and Pentagonal Numbers: 10628 86--87
              Frank Schmidt and   
                 Peter Mork and   
                D. Beckwith and   
                  D. Callan and   
              D. J. Chapman and   
                    G. Lord and   
             C. C. Rousseau and   
                P. Simeonov and   
                 J. H. Steelman   Interrupted Partitions: 10629  . . . . . 87--88
               David Callan and   
           Robin J. Chapman and   
          J. H. Lindsey, II and   
                       D. Huang   The Value of Primitive Words: 10636  . . 88--89
               Marcin Mazur and   
                Roy Barbara and   
                J. Anglesio and   
              R. J. Chapman and   
              N. Lakshmanan and   
                J. Melville and   
                    G. Peng and   
          C. R. Pranesachar and   
            GCHQ Problems Group   Quadrilaterals in an Isosceles Triangle:
                                  10653  . . . . . . . . . . . . . . . . . 89--91
             Michael Golomb and   
        GCHQ Problems Group and   
            G. D. Chakerian and   
              R. J. Chapman and   
           J. H. Lindsey II and   
              O. P. Lossers and   
                   A. Nijenhuis   Points That Form Simplices of Equal
                                  Volume: 10685  . . . . . . . . . . . . . 91--91
                  John P. Pratt   Book Review: \booktitleMapping Time: The
                                  Calendar and Its History., by E. G.
                                  Richards . . . . . . . . . . . . . . . . 92--99
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 100--102
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
             Thomas R. Hagedorn   Notes: a Proof of a Conjecture on
                                  Egyptian Fractions . . . . . . . . . . . ??
            Peter Malcomson and   
                     Frank Okoh   Notes: Rings Without Maximal Ideals  . . ??
                  John P. Pratt   \em Mapping Time: The Calendar and Its
                                  History, by E. G. Richards . . . . . . . ??
              Alexander Russell   Notes: An Easy Reduction of an
                                  Isoperimetric Inequality on the Sphere
                                  to Extremal Set Theory . . . . . . . . . ??
                   Maria Suzuki   Notes: Alternative Formulations of the
                                  Twin Prime Problem . . . . . . . . . . . ??
              Jerzy Tsyzkiewicz   Notes: a Simple Construction for
                                  Tournaments With Every $k$ Players
                                  Beaten by a Single Player  . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 2, February, 2000

         James A. Donaldson and   
             Richard J. Fleming   Elbert F. Cox: An Early Pioneer  . . . . 105--128
          Bennett Eisenberg and   
              Rosemary Sullivan   Crofton's Differential Equation  . . . . 129--139
               Allen J. Schwenk   What is the Correct Way to Seed a
                                  Knockout Tournament? . . . . . . . . . . 140--150
                     Ali Enayat   $ \delta $ as a Continuous Function of
                                  $x$ and $ \epsilon $ . . . . . . . . . . 151--155
                 Frank R. Pfaff   A Commutative Multiplication of Number
                                  Triplets . . . . . . . . . . . . . . . . 156--162
              Carsten Thomassen   The Rendezvous Number of a Symmetric
                                  Matrix and a Compact Connected Metric
                                  Space  . . . . . . . . . . . . . . . . . 163--166
                  Tamas Erdelyi   On the Equation a(a + d)(a + 2d)(a + 3d)
                                  = x$^2$  . . . . . . . . . . . . . . . . 166--169
                    Gerd Herzog   On Nonlinear Summability . . . . . . . . 170--171
                   Florian Luca   The Anti-Social Fermat Number  . . . . . 171--173
                   Anatole Beck   A Fractal Example in Ordinary
                                  Differential Equations . . . . . . . . . 174--175
                 Leonard Smiley   Problem 10781  . . . . . . . . . . . . . 176--176
               Douglas Iannucci   Problem 10782  . . . . . . . . . . . . . 176--176
                    Wu Wei Chao   Problem 10783  . . . . . . . . . . . . . 176--176
           Alberto Facchini and   
              Francesco Barioli   Problem 10784  . . . . . . . . . . . . . 176--176
                 Emeric Deutsch   Problem 10785  . . . . . . . . . . . . . 176--176
                     Leroy Quet   Problem 10786  . . . . . . . . . . . . . 177--177
            Juan Arias-de-Reyna   Problem 10787  . . . . . . . . . . . . . 177--177
               Warren Koepp and   
              Robin Chapman and   
           J. H. Lindsey II and   
             NSA Problems Group   On the Intersection of Z$^n$ with a
                                  Hyperplane: 10639  . . . . . . . . . . . 177--177
        Michael A. Filaseta and   
              Allen Stenger and   
                  D. Callan and   
                      Z. Franco   When a Multiple of $ \pi / 2 $ is Close
                                  to an Integer: 10640 . . . . . . . . . . 177--179
                   J. Gross and   
                G. Trenkler and   
             S.-O. Troschke and   
          William F. Trench and   
                  D. Callan and   
                   G. Wahba and   
              R. J. Chapman and   
               L. M. DeAlba and   
           J. H. Lindsey II and   
            IUTS Problems Group   A Property of Some Normal Matrices:
                                  10645  . . . . . . . . . . . . . . . . . 179--180
               Marcin Mazur and   
                  Kit Hanes and   
                J. Anglesio and   
               M. Benedicty and   
                S. B. Ekhad and   
              N. Lakshmanan and   
               A. Nijenhuis and   
                    J. H. Smith   Tangent Lines and Collinear Points:
                                  10673  . . . . . . . . . . . . . . . . . 180--181
                Wu Wei Chao and   
               Michael Reid and   
           F. Bellot Rosado and   
              R. J. Chapman and   
                  D. Donini and   
                S. B. Ekhad and   
              N. Lakshmanan and   
              O. P. Lossers and   
               A. Nijenhuis and   
               P. E. Nuesch and   
                  C. G. Petalas   Incenters and Excenters: 10693 . . . . . 182--184
               Gerald Heuer and   
        Kenneth F. Andersen and   
             P. Fitzsimmons and   
                   K. Heuer and   
                  S. S. Kim and   
           J. H. Lindsey II and   
              O. P. Lossers and   
            K. Poelladennou and   
                K. Schiling and   
                L. Scribani and   
                P. Simeonov and   
        GCHQ Problems Group and   
             NSA Problems Group   A Square Game: 10696 . . . . . . . . . . 184--184
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                   Anatole Beck   Notes: a Fractal Example in Ordinary
                                  Differential Equations . . . . . . . . . ??
                     Ali Enayat   As a Continuous Function of $x$ and
                                  \ldots . . . . . . . . . . . . . . . . . ??
           Tamas Erdélyi   Notes: On the Equation $ a (a + d)(a + 2
                                  d)(a + 3 d) = x2 $ . . . . . . . . . . . ??
                    Gerd Herzog   Notes: On Nonlinear Summability  . . . . ??
                   Florian Luca   Notes: The Anti-Social Fermat Number . . ??
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . ??
              Francis Edward Su   Book Review: \booktitleCake-Cutting
                                  Algorithms: Be Fair If You Can, by Jack
                                  Robertson and William Webb . . . . . . . 185--188
              Carsten Thomassen   Notes: The Rendezvous Number of a
                                  Symmetric Matrix and a Compact Connected
                                  Metric Space . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 3, March, 2000

              Andrew M. Gleason   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for Distinguished Service to Paul
                                  R. Halmos  . . . . . . . . . . . . . . . 193--194
             Chris Freiling and   
              Robert Hunter and   
             Cynthia Turner and   
             Russell C. Wheeler   Tiling with Squares and Anti-Squares . . 195--204
                Luis Verde-Star   Solving Linear Differential-like
                                  Equations  . . . . . . . . . . . . . . . 205--218
                   Garry Helzer   Special Relativity with Acceleration . . 219--237
               Bjorn Poonen and   
    Fernando Rodriguez-Villegas   Lattice Polygons and the Number $ 12 $   238--250
                 Tom Sibley and   
                     Stan Wagon   Rhombic Penrose Tilings Can be
                                  $3$-Colored  . . . . . . . . . . . . . . 251--253
                Ming-Chang Kang   Cubic Fields and Radical Extensions  . . 254--256
                     Lee Badger   Generating the Measures of $n$-Balls . . 256--258
                     Omar Hijab   The Volume of the Unit Ball in C$^n$ . . 259--259
          Michael D. Hirschhorn   Partial Fractions and Four Classical
                                  Theorems of Number Theory  . . . . . . . 260--264
                Sung S. Kim and   
                    Kil H. Kwon   Smooth $ (C^\infty) $ but Nowhere
                                  Analytic Functions . . . . . . . . . . . 264--266
                Detlef Laugwitz   Comments on the Paper ``Two Letters by
                                  N. N. Luzin to M. Ya. Vygodskii''  . . . 267--276
               Howard M. Taylor   Problem 10788  . . . . . . . . . . . . . 277--277
                  Robin Chapman   Problem 10789  . . . . . . . . . . . . . 277--277
                  Jean Anglesio   Problem 10790  . . . . . . . . . . . . . 277--277
                   Antal Fekete   Problem 10791  . . . . . . . . . . . . . 277--277
          Harold G. Diamond and   
             Ferrell S. Wheeler   Problem 10792  . . . . . . . . . . . . . 278--278
                   Florian Luca   Problem 10793  . . . . . . . . . . . . . 278--278
             David S. Hough and   
               Rodica E. Simion   Problem 10794  . . . . . . . . . . . . . 278--278
               David Callan and   
                  Knut Dale and   
                  Ivar Skau and   
        John Henry Steelman and   
 GCHQ Problem Solving Group and   
                 J. C. Binz and   
              R. J. Chapman and   
                  F. Herzig and   
                 A. Kundgen and   
                  R. Martin and   
                J. H. Nieto and   
                O. A. Saleh and   
                    S. Byrd and   
              E. Schmeichel and   
                  I. Sofair and   
                        M. Vowe   An Identity Involving Derangements:
                                  10643  . . . . . . . . . . . . . . . . . 278--279
             Emeric Deutsch and   
         John H. Lindsey II and   
        Michael H. Andreoli and   
                R. A. Agnew and   
              R. J. Chapman and   
                M. P. Cohen and   
            M. N. Deshpande and   
                M. D. Ernst and   
                   E. Hertz and   
                L. R. Ivory and   
                  W. Janous and   
                G. Keselman and   
               R. G. Mosier and   
                J. H. Nieto and   
                 R. Pinkham and   
                S. D. Sarti and   
                P. Simeonov and   
               W. R. Smythe and   
                 A. Stadler and   
             J. H. Steelman and   
               W. F. Trench and   
                 J. T. Ward and   
              M. Woltermann and   
Anchorage Math Solutions Group and   
            GCHQ Problems Group   How Far Does the First Element
                                  Dominate?: 10649 . . . . . . . . . . . . 279--280
               David Callan and   
              Robin Chapman and   
           J. H. Lindsey II and   
               J. Parkinson and   
               V. Schindler and   
                P. Simeonov and   
            GCHQ Problems Group   Analysis of a French Inheritance Law:
                                  10652  . . . . . . . . . . . . . . . . . 280--281
              Mihaly Bencze and   
               Dan Saracino and   
              Allen Stenger and   
               S. Amghibech and   
                J. Anglesio and   
                   R. Bauer and   
                  A. Siegel and   
                D. M. Bloom and   
                 G. L. Body and   
                  D. Callan and   
              R. J. Chapman and   
                    K. Ford and   
               S. M. Gagola and   
                N. Gauthier and   
              W. V. Grounds and   
                T. Hagedorn and   
              R. T. Koether and   
                 N. Komanda and   
             R. N. Krishnan and   
                  K.-W. Lau and   
           J. H. Lindsey II and   
              L. E. Mattics and   
                 C. A. Minh and   
             H. N. Ozsoylev and   
             C. Y. Yildirim and   
             P. G. Poonacha and   
              N. R. Sanjeev and   
                 C. Popescu and   
               J. Robertson and   
            H. -J. Sieffert and   
              J. O. Shallit and   
               N. C. Singer and   
                 A. Stadler and   
                 D. C. Terr and   
                T. V. Triff and   
                 T. Trimble and   
               P. Trojovsky and   
Anchorage Math Solutions Group and   
        GCHQ Problems Group and   
             NSA Problems Group   A Recurrence Generating Multiples of
                                  Primes: 10655  . . . . . . . . . . . . . 281--282
       James C. Owings, Jr. and   
           Jeremy E. Dawson and   
           Robin J. Chapman and   
           Darryl K. Nester and   
                R. A. Agnew and   
                  J. Beebee and   
                  D. Callan and   
           R. Garcia-Pelayo and   
               V. Hernandez and   
                  J. Martin and   
                 J. Hickman and   
                   D. Jones and   
                  S. S. Kim and   
                  O. Krafft and   
                M. Schaefer and   
                   G. Letac and   
           J. H. Lindsey II and   
              O. P. Lossers and   
            K. Poelladennou and   
               K. Schilling and   
                 M. Shemesh and   
        GCHQ Problems Group and   
             NSA Problems Group   A Sum of Chebyshev Inequalities: 10687   282--283
        Hassan Ali Shah Ali and   
         John H. Lindsey II and   
        GCHQ Problems Group and   
             NSA Problems Group   Extrema for Constrained Elementary
                                  Symmetric Functions: 10694 . . . . . . . 283--283
               Jose L. Diaz and   
        Tewodros Amdeberhan and   
               Erik I. Verriest   A Rational Identity: 10697 . . . . . . . 283--284
                Abram Kagan and   
              Colin Mallows and   
                Larry Shepp and   
             John H. Lindsey II   Bernoulli Component of a Sum: 10699  . . 284--284
              Jean Anglesio and   
               Shalosh B. Ekhad   Four More Distinguished Points of a
                                  Triangle: 10703  . . . . . . . . . . . . 285--285
              Gerald B. Folland   Book Review: \booktitle[untitled]  . . . 286--291
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 292--294
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                     Lee Badger   Notes: Generating the Measures of
                                  $n$-Balls  . . . . . . . . . . . . . . . ??
                 Harold P. Boas   \em Graphica 1. The Imaginary Made Real:
                                  The Images of Michael Trott; \em
                                  Graphica 2. The Pattern of Beauty: The
                                  Art of Igor Bakshee  . . . . . . . . . . ??
                     Omar Hijab   Notes: The Volume of the Unit Ball in $
                                  {C}^n $  . . . . . . . . . . . . . . . . ??
          Michael D. Hirschhorn   Notes: Partial Fractions and Four
                                  Classical Theorems of Number Theory  . . ??
                Ming-chang Kang   Notes: Cubic Fields and Radical
                                  Extensions . . . . . . . . . . . . . . . ??
                 Tom Sibley and   
                     Stan Wagon   Notes: Rhombic Penrose Tilings Can Be
                                  $3$-Colored  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 4, April, 2000

            Michael C. Sullivan   Knot Factoring . . . . . . . . . . . . . 297--315
           Robert S. Strichartz   Evaluating Integrals Using
                                  Self-Similarity  . . . . . . . . . . . . 316--326
                 Joel L. Weiner   How Helical Can a Closed, Twisted Space
                                  Curve be?  . . . . . . . . . . . . . . . 327--333
                   Chi-Kwong Li   Norms, Isometries, and Isometry Groups   334--340
            Francesc Aguilo and   
          Miguel Angel Fiol and   
              Maria Lluisa Fiol   Periodic Tilings as a Dissection Method  341--352
            Rajendra Bhatia and   
                 Chandler Davis   A Better Bound on the Variance . . . . . 353--357
                   J. N. Ridley   An Elementary Proof on Location of Zeros 357--360
                Neil Calkin and   
                Herbert S. Wilf   Recounting the Rationals . . . . . . . . 360--363
              Stephen E. Wright   A Note on Positively Spanning Sets . . . 364--366
                 Emeric Deutsch   Problem 10795  . . . . . . . . . . . . . 367--367
               Floor van Lamoen   Problem 10796  . . . . . . . . . . . . . 367--367
               Paul Bateman and   
                   Jeffrey Kalb   Problem 10797  . . . . . . . . . . . . . 367--367
                  Edward Neuman   Problem 10798  . . . . . . . . . . . . . 367--367
              Curtis Herink and   
                 Gary Gruenhage   Problem 10799  . . . . . . . . . . . . . 367--367
               Douglas Iannucci   Problem 10800  . . . . . . . . . . . . . 368--368
            Paul R. Pudaite and   
                     Glen Ellyn   Problem 10801  . . . . . . . . . . . . . 368--368
         Richard P. Stanley and   
          Richard Ehrenborg and   
             Stephen Gagola and   
              R. J. Chapman and   
               J. H. Lindsey II   Pairs with Equal Squares: 10654  . . . . 368--368
             Emeric Deutsch and   
               David Callan and   
                    M. Beck and   
                D. Beckwith and   
                    W. Bohm and   
              R. F. McCoart and   
            GCHQ Problems Group   Another Type of Lattice Path: 10658  . . 368--370
                 Erwin Just and   
                  A. Berele and   
                  J. Bergen and   
              K. A. Kearnes and   
                   G. Marks and   
                     G. P. Wene   A Sufficient Condition for
                                  Commutativity: 10661 . . . . . . . . . . 370--370
             Emeric Deutsch and   
               Harris Kwong and   
          Cecil C. Rousseau and   
             Paul K. Stockmeyer   A Formula for the Pell Sequence: 10663   370--371
             Zoltan Sasvari and   
        Jerrold W. Grossman and   
                   Sung Soo Kim   Avoiding Uncountably Many Subsets: 10667 371--372
                John Isbell and   
           Stephen Schanuel and   
     Stephen M. Gagola, Jr. and   
                 Mowaffaq Hajja   Fixed Points of Iterated Cyclic
                                  Difference Operators: 10676  . . . . . . 372--373
           Clark Kimberling and   
                  Peter Yff and   
                   Vasile Mihai   Another Set of Concurrent Cevians: 10678 373--373
             James G. Propp and   
               Keith A. Kearnes   An Application of Sperner's Theorem:
                                  10679  . . . . . . . . . . . . . . . . . 374--374
                 Kevin Ford and   
                    Kee-Wai Lau   Asymptotics of a Recurrent Sequence:
                                  10682  . . . . . . . . . . . . . . . . . 374--375
                D. W. Brown and   
                      John Cobb   A Countable Hausdorff Space with the
                                  Fixed Point Property: 10705  . . . . . . 375--376
             Zoltan Sasvari and   
             John H. Lindsey II   An Estimate for the Normal Distribution:
                                  10709  . . . . . . . . . . . . . . . . . 376--377
           David P. Bellamy and   
             Felix Lazebnik and   
                  Ray Redheffer   Characterizing Solutions to Simple
                                  Differential Equations: 10729  . . . . . 377--377
               Julian F. Fleron   Book Review: \booktitle[untitled]  . . . 378--384
               Thomas W. Cusick   Book Review: \booktitle[untitled]  . . . 384--386
                  Roger A. Horn   Editor's Endnotes  . . . . . . . . . . . 387--387
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 5, May, 2000

                 Andrew Browder   Topology in the Complex Plane  . . . . . 393--401
                   Keith Kendig   Is a 2000-Year-Old Formula Still Keeping
                                  Some Secrets?  . . . . . . . . . . . . . 402--415
               Joseph B. Keller   Optimal Running Strategy to Escape from
                                  Pursuers . . . . . . . . . . . . . . . . 416--421
              Michael Frame and   
             Brenda Johnson and   
                  Jim Sauerberg   Fixed Points and Fermat: a Dynamical
                                  Systems Approach to Number Theory  . . . 422--428
              Laurent Bartholdi   Lamps, Factorizations, and Finite Fields 429--436
               Raymond T. Boute   Zeroless Positional Number
                                  Representation and String Ordering . . . 437--444
             Kevin Broughan and   
                        Nan Zhu   An Integer Programming Problem with a
                                  Linear Programming Solution  . . . . . . 444--446
                Terence Jackson   A Short Proof That Every Prime $ p
                                  \equiv 3 \pmod 8 $ Is of the Form $ x^2
                                  + 2 y^2 $  . . . . . . . . . . . . . . . 447--447
         Jean-Paul Allouche and   
                 Michel Cosnard   The Komornik--Loreti Constant Is
                                  Transcendental . . . . . . . . . . . . . 448--449
                        Liu Wen   A Nowhere Differentiable Continuous
                                  Function . . . . . . . . . . . . . . . . 450--453
               Jacques Tits and   
                 John Stillwell   Symmetry . . . . . . . . . . . . . . . . 454--461
               Doru Caragea and   
                    Viviana Ene   Problem 10802  . . . . . . . . . . . . . 462--462
                Stephen Penrice   Problem 10803  . . . . . . . . . . . . . 462--462
       Achilleas Sinefakopoulos   Problem 10804  . . . . . . . . . . . . . 462--462
                   Antal Fekete   Problem 10805  . . . . . . . . . . . . . 462--462
            Hassan Ali Shah Ali   Problem 10806  . . . . . . . . . . . . . 462--462
          Marc Deléglise   Problem 10807  . . . . . . . . . . . . . 463--463
               Enrico Valdinoci   Problem 10808  . . . . . . . . . . . . . 463--463
             Paul Deiermann and   
                 Rick Mabry and   
                  Alain Tissier   Intersecting Curves: 10712 . . . . . . . 463--464
  Juan-Bosco Romero Marquez and   
          Heinz-Jurgen Seiffert   A Cute Characterization of Acute
                                  Triangles: 10713 . . . . . . . . . . . . 464--464
          Roger Cuculi\`ere and   
                 Albert Stadler   Successful Bootstrapping: 10715  . . . . 465--466
               Marcin Mazur and   
              Robin Chapman and   
             Petr Lison\vek and   
           Robert B. Israel and   
              Murray S. Klamkin   Rigid and Very Rigid Tetrahedra: 10717   466--467
           Daniel A. Sidney and   
National Security Agency Problems Group   Integrals and Sines: 10721 . . . . . . . 468--469
               Donald Knuth and   
               Darin Stephenson   The Probability of Being in a State:
                                  10726  . . . . . . . . . . . . . . . . . 469--470
             Walther Janous and   
               Enrico Valdinoci   The Best Constant in an Inequality:
                                  10730  . . . . . . . . . . . . . . . . . 470--470
               Allen C. Hibbard   Book Review: \booktitle[untitled]  . . . 471--474
                    Mic Jackson   Book Review: \booktitle[untitled]  . . . 474--478
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 479--481
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 6, June / July, 2000

          Edward R. Scheinerman   When Close Enough is Close Enough  . . . 489--499
                K. Robin McLean   Loops of Regular Polygons  . . . . . . . 500--510
         Arthur T. Benjamin and   
           Gregory M. Levin and   
              Karl Mahlburg and   
              Jennifer J. Quinn   Random Approaches to Fibonacci
                                  Identities . . . . . . . . . . . . . . . 511--516
                 D. Borwein and   
              J. M. Borwein and   
                    P. Marechal   Surprise Maximization  . . . . . . . . . 517--527
                    Pei Yuan Wu   Polygons and Numerical Ranges  . . . . . 528--540
                   Pavel Pudlak   Proofs as Games  . . . . . . . . . . . . 541--550
          Wlodzimierz Kuperberg   Holey Coronas A Solution of the
                                  Grunbaum--Shephard Conjecture on Convex
                                  Isohedral Tilings  . . . . . . . . . . . 551--555
                      Dan Romik   Stirling's Approximation for $ n! $: The
                                  Ultimate Short Proof?  . . . . . . . . . 556--557
              Richard Ehrenborg   The Hankel Determinant of Exponential
                                  Polynomials  . . . . . . . . . . . . . . 557--560
         Arthur T. Benjamin and   
               Matthew T. Fluet   What's Best? . . . . . . . . . . . . . . 560--562
                     Doug Engel   A Celtic Magnecurve Problem  . . . . . . 563--565
                 David Beckwith   Problem 10809  . . . . . . . . . . . . . 566--566
      Juan-Bosco Romero Marquez   Problem 10810  . . . . . . . . . . . . . 566--566
                     Phil Tracy   Problem 10811  . . . . . . . . . . . . . 566--566
           Yehuda Pinchover and   
                   Simeon Reich   Problem 10812  . . . . . . . . . . . . . 566--566
                   Fred Richman   Problem 10813  . . . . . . . . . . . . . 567--567
               Razvan Satnoianu   Problem 10814  . . . . . . . . . . . . . 567--567
         Barbara S. Bertram and   
                  Otto G. Ruehr   Problem 10815  . . . . . . . . . . . . . 567--567
             Emeric Deutsch and   
              Ira M. Gessel and   
                   David Callan   Permutation Parameters with the Same
                                  Distribution: 10634  . . . . . . . . . . 567--568
             David Beckwith and   
            Tiberiu V. Trif and   
                 Dan C. Popescu   A Series Involving Numbers of
                                  Factorizations: 10669  . . . . . . . . . 568--569
                   David Newman   A Recurrence inside a Generating
                                  Function: 10681  . . . . . . . . . . . . 569--570
Western Maryland College Problems Group   A Western Maryland Integral: 10708 . . . 570--572
             Bogdan Suceava and   
       Achilleas Sinefakopoulos   A Six Point Circle: 10710  . . . . . . . 572--573
               Sung Soo Kim and   
                     K. P. Hart   Partitioning the Interval into Closed
                                  Sets: 10733  . . . . . . . . . . . . . . 573--573
                   David Aldous   Book Review: \booktitle[untitled]  . . . 574--576
                  Michael Frame   Book Review: \booktitle[untitled]  . . . 576--580
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 7, August / September, 2000

         Charles S. ReVelle and   
              Kenneth E. Rosing   Defendens Imperium Romanum: a Classical
                                  Problem in Military Strategy . . . . . . 585--594
            Bruce C. Berndt and   
               Robert A. Rankin   The Books Studied by Ramanujan in India  595--601
                Rajendra Bhatia   Pinching, Trimming, Truncating, and
                                  Averaging of Matrices  . . . . . . . . . 602--608
                    Gerald Beer   When is a Family of Sets a Family of
                                  Bounded Sets?  . . . . . . . . . . . . . 609--614
             David S. Moore and   
                 George W. Cobb   Statistics and Mathematics: Tension and
                                  Cooperation  . . . . . . . . . . . . . . 615--630
       Jonathan Pakianathan and   
               Krishnan Shankar   Nilpotent Numbers  . . . . . . . . . . . 631--634
                Tom Jenkyns and   
                    Eric Muller   Triangular Triples from Ceilings to
                                  Floors . . . . . . . . . . . . . . . . . 634--639
                 Rodney Nillsen   Normal Numbers without Measure Theory    639--644
            M. M. Postnikov and   
                  Abe Shenitzer   The Problem of Squarable Lunes . . . . . 645--651
                 Emeric Deutsch   Problem 10816  . . . . . . . . . . . . . 652--652
                 Walther Janous   Problem 10817  . . . . . . . . . . . . . 652--652
                    Cezar Joita   Problem 10818  . . . . . . . . . . . . . 652--652
                    Olaf Krafft   Problem 10819  . . . . . . . . . . . . . 652--652
                 M. Mirzavaziri   Problem 10820  . . . . . . . . . . . . . 652--652
             Gerard J. Foschini   Problem 10821  . . . . . . . . . . . . . 653--653
               Jeffrey Lagarias   Problem 10822  . . . . . . . . . . . . . 653--653
          Jerrold R. Griggs and   
           Darryl K. Nester and   
                   Sung Soo Kim   The Asymptotics of the Birthday Problem:
                                  10665  . . . . . . . . . . . . . . . . . 653--654
                 Marius Cavachi   A Powerful Property: 10674 . . . . . . . 654--654
               Harm Derksen and   
                  Jeremy Dawson   A Characterization of Min or Max: 10677  654--655
              C. R. Pranesachar   Equicevian Points of a Triangle: 10686   656--657
                Wu Wei Chao and   
                Plamen Simeonov   When Quadrilaterals Have Inscribed
                                  Circles: 10698 . . . . . . . . . . . . . 657--658
           Floor van Lamoen and   
                     J. C. Binz   Beyond the De Longchamps Point: 10734    658--659
           Radu Theodorescu and   
            Jonathan M. Borwein   Moments of the Poisson Distribution:
                                  10738  . . . . . . . . . . . . . . . . . 659--659
             Stepan Tersian and   
                  Richard Bagby   A Definite Integral: 10746 . . . . . . . 659--660
                   Colm Mulcahy   Book Review: \booktitle[untitled]  . . . 661--663
            Jerrold W. Grossman   Book Review: \booktitle[untitled]  . . . 664--668
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 669--671
                      Anonymous   Lester R. Ford Awards for 1999 . . . . . 672--672
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 8, October, 2000

              Steven L. Lee and   
                 Gilbert Strang   Row Reduction of a Matrix and A = CaB    681--688
             S. Allen Broughton   Constructing Kaleidoscopic Tiling
                                  Polygons in the Hyperbolic Plane . . . . 689--710
                 Daniel K. Biss   A Generalized Approach to the
                                  Fundamental Group  . . . . . . . . . . . 711--720
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixtieth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 721--732
              Joseph A. Gallian   Putnam Trivia for the 90s  . . . . . . . 733--735
                  Oleg Pikhurko   On Envy-Free Cake Division . . . . . . . 736--738
                 Tom M. Apostol   Calculating Higher Derivatives of
                                  Inverses . . . . . . . . . . . . . . . . 738--741
               Holly Carley and   
                         Xin Li   The Modulus of Polynomials with Zeros at
                                  the Roots of Unity . . . . . . . . . . . 742--748
         Vladimir Rako\vcevi\'c   On the Norm of Idempotent Operators in a
                                  Hilbert Space  . . . . . . . . . . . . . 748--750
               Guang Yuan Zhang   A Simple Proof of a Theorem of Block and
                                  Hart . . . . . . . . . . . . . . . . . . 751--751
              George E. Andrews   Problem 10823  . . . . . . . . . . . . . 752--752
                     Ho-joo Lee   Problem 10824  . . . . . . . . . . . . . 752--752
                    Carl Miller   Problem 10825  . . . . . . . . . . . . . 752--752
Félix Martínez-Giménez   Problem 10826  . . . . . . . . . . . . . 752--752
                    Ulrich Abel   Problem 10827  . . . . . . . . . . . . . 752--752
                 David Beckwith   Problem 10828  . . . . . . . . . . . . . 753--753
                 Walther Janous   Problem 10829  . . . . . . . . . . . . . 753--753
               David Callan and   
             David Beckwith and   
 Anchorage Math Solutions Group   Periodic Points and Forests: 10666 . . . 753--754
             Harry Tamvakis and   
             Joseph J. Rushanan   Splitting Triple Products by Sign: 10683 754--754
            Donald E. Knuth and   
              Vaughan Pratt and   
                  O. P. Lossers   The Real Numbers, Algebraically: 10689   755--755
              H. W. Lenstra and   
National Security Agency Problems Group   Restricting the Order of Elements in a
                                  Group: 10684 . . . . . . . . . . . . . . 755--755
          Glenn G. Chappell and   
                  Robin Chapman   Ordering the Integers Using Specified
                                  Differences: 10692 . . . . . . . . . . . 756--756
              Iliya Bluskov and   
               Albert Nijenhuis   A Useful and Surprising Limit: 10695 . . 756--757
              Oscar Ciaurri and   
                 G. E. Bilodeau   Variation on the Mean Value Theme: 10739 757--757
         Athanasios Kalakos and   
            Michel Bataille and   
                 David M. Wells   A Differential Equation with Many
                                  Solutions: 10747 . . . . . . . . . . . . 757--758
              Gh. Costovici and   
              Kenneth Schilling   Conditions Ensuring Convergence: 10752   758--759
           Douglas Iannucci and   
               Brian D. Beasley   A Cosine Formula: 10756  . . . . . . . . 759--759
                     H. Burgiel   Book Review: \booktitle[untitled]  . . . 760--763
            Shirley B. Pomeranz   Book Review: \booktitle[untitled]  . . . 763--766
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 9, November, 2000

             R. Bruce Mattingly   Even Order Regular Magic Squares Are
                                  Singular . . . . . . . . . . . . . . . . 777--782
                Manjul Bhargava   The Factorial Function and
                                  Generalizations  . . . . . . . . . . . . 783--799
                  Jason Jeffers   Lost Theorems of Geometry  . . . . . . . 800--812
                   Walter Rudin   Sums of Squares of Polynomials . . . . . 813--821
               Edward B. Burger   Diophantine Olympics and World
                                  Champions: Polynomials and Primes Down
                                  Under  . . . . . . . . . . . . . . . . . 822--829
              Serge Tabachnikov   A Four Vertex Theorem for Polygons . . . 830--833
                Glyn Harman and   
                    Kam C. Wong   A Note on The Metrical Theory of
                                  Continued Fractions  . . . . . . . . . . 834--837
             Peter Kravanja and   
                  Ann Haegemans   Multidimensional Analytic Deflation  . . 837--841
                 Tom M. Apostol   Irrationality of The Square Root of Two
                                  -- A Geometric Proof . . . . . . . . . . 841--842
                    Anindya Sen   Fundamental Theorem of Algebra -- Yet
                                  Another Proof  . . . . . . . . . . . . . 842--843
                Walter Felscher   Bolzano, Cauchy, Epsilon, Delta  . . . . 844--862
               Floor van Lamoen   Problem 10830  . . . . . . . . . . . . . 863--863
          George E. Andrews and   
                   P. Paule and   
                       A. Riese   Problem 10831  . . . . . . . . . . . . . 863--863
                Donald E. Knuth   Problem 10832  . . . . . . . . . . . . . 863--863
          Charles Vanden Eynden   Problem 10833  . . . . . . . . . . . . . 863--863
                   Sung Soo Kim   Problem 10834  . . . . . . . . . . . . . 864--864
               Anna Dyubina and   
             Pierre de la Harpe   Problem 10835  . . . . . . . . . . . . . 864--864
                 Jon A. Wellner   Problem 10836  . . . . . . . . . . . . . 864--864
                 Leroy Quet and   
                  Robin Chapman   Bernoulli, Stirling, and Stirling: 10700 864--865
      William G. Spohn, Jr. and   
               Jeremy E. Dawson   Neighborly Pythagorean Triples: 10704    865--866
             James G. Propp and   
                Tiberiu V. Trif   Deriving a Perfect Square: 10706 . . . . 866--867
            C\ualin Popescu and   
       Achilleas Sinefakopoulos   Inequalities Involving Altitudes and
                                  Exradii: 10759 . . . . . . . . . . . . . 867--868
                 Leroy Quet and   
                  O. P. Lossers   A Convoluted Recursion: 10762  . . . . . 868--868
              Ray Redheffer and   
                  Robin Chapman   All Solutions in the Unit Cube: 10764    868--869
Szilárd András and   
            Ronald A. Kopas and   
     Heinz-Jürgen Seiffert   Symmetric Inequalities for x$^x$ and
                                  x$^{x 2}$ : 10766  . . . . . . . . . . . 869--870
                  Steve Kennedy   Book Review: \booktitle[untitled]  . . . 871--874
                Marion D. Cohen   Book Review: \booktitle[untitled]  . . . 874--876
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 877--878
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 107, Number 10, December, 2000

         Carolyn Eschenbach and   
                 Frank Hall and   
            Rohan Hemasinha and   
           Stephen Kirkland and   
               Zhongshan Li and   
               Bryan Shader and   
             Jeffrey Stuart and   
                   James Weaver   Properties of Tournaments among
                                  Well-Matched Players . . . . . . . . . . 881--892
   M. A. Hernández Cifre   Is There a Planar Convex Set with Given
                                  Width, Diameter, and Inradius? . . . . . 893--900
                 John Konvalina   A Unified Interpretation of the Binomial
                                  Coefficients, the Stirling Numbers, and
                                  the Gaussian Coefficients  . . . . . . . 901--910
            Stefan Treatman and   
                Cameron Wickham   Constructible Approximations of Regular
                                  Polygons . . . . . . . . . . . . . . . . 911--922
               David M. Bradley   Using Integral Transforms to Estimate
                                  Higher Order Derivatives . . . . . . . . 923--931
                Reid Barton and   
                    Keith Burns   A Simple Special Case of Sharkovskii's
                                  Theorem  . . . . . . . . . . . . . . . . 932--933
                William Watkins   The Quadratic Residues -1 and -3 . . . . 934--934
                    Gerd Herzog   Polynomials Solving Dirichlet Boundary
                                  Value Problems . . . . . . . . . . . . . 934--936
                   Karl Dilcher   An Extension of Fermat's Little Theorem,
                                  and Congruences for Stirling Numbers . . 936--940
               Floor van Lamoen   Morley Related Triangles on the
                                  Nine-Point Circle  . . . . . . . . . . . 941--945
Árpád Bényi and   
            Pawel Szeptycki and   
                 Fred Van Vleck   Archimedean Properties and Parabolas . . 945--949
                     Ho-joo Lee   Problem 10837  . . . . . . . . . . . . . 950--950
Florian S. Pârvânescu   Problem 10838  . . . . . . . . . . . . . 950--950
           Beresford N. Parlett   Problem 10839  . . . . . . . . . . . . . 950--950
             Jiansheng Yang and   
                    Shulin Zhou   Problem 10840  . . . . . . . . . . . . . 950--950
                     Erwin Just   Problem 10841  . . . . . . . . . . . . . 950--950
                  Bruce Reznick   Problem 10842  . . . . . . . . . . . . . 950--950
             Kent D. Boklan and   
              John P. Robertson   The Maximum Length of a Powerful
                                  Arithmetic Progression: 10702  . . . . . 951--951
                   Andrew Vince   Problem 10843  . . . . . . . . . . . . . 951--951
                John Isbell and   
            Julio Kuplinsky and   
                   Leon Mattics   A Union of Proper Subspaces?: 10707  . . 951--952
              Jean Anglesio and   
             Volkhard Schindler   Two Triangles with Common Vertex,
                                  Incenter, and Centroid: 10719  . . . . . 952--954
             Mowaffaq Hajja and   
               Peter Walker and   
               Danny Arrigo and   
              Xiaoshen Wang and   
                    Zafar Ahmed   A Cubic Spherical Integral: 10771  . . . 954--955
      William C. Waterhouse and   
                  Steve Butcher   Nonconstant Functions with Derivative
                                  Zero: 10772  . . . . . . . . . . . . . . 956--956
                Zafar Ahmed and   
                Peter M. Jarvis   A Family of Integrals: 10777 . . . . . . 956--957
              Kiran Kedlaya and   
                   Marcin Mazur   Incircle Partnerships: 10780 . . . . . . 957--958
             Paul Deiermann and   
                     Rick Mabry   Intersecting Curves: 10712 . . . . . . . 958--958
                Marion D. Cohen   Book Review: \booktitle[untitled]  . . . 959--963
                 J. David Logan   Book Review: \booktitle[untitled]  . . . 964--967
                  Roger A. Horn   Editor's Endnotes  . . . . . . . . . . . 968--969
                      Anonymous   Volume Information . . . . . . . . . . . 970--980
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 108, Number 1, January, 2001

                   W. E. Kirwan   Mathematics Departments in the 21st
                                  Century: Role, Relevance, and
                                  Responsibility . . . . . . . . . . . . . 1--9
               David Garber and   
                    Boaz Tsaban   A Mechanical Derivation of the Area of
                                  the Sphere . . . . . . . . . . . . . . . 10--15
                David J. Aldous   Reorganizing Large Web Sites . . . . . . 16--27
                 Dean Alvis and   
                 Michael Kinyon   Birkhoff's Theorem for Panstochastic
                                  Matrices . . . . . . . . . . . . . . . . 28--37
          Chaim Goodman-Strauss   Compass and Straightedge in the Poincaré
                                  Disk . . . . . . . . . . . . . . . . . . 38--49
                 Eric Schechter   Constructivism Is Difficult  . . . . . . 50--54
                  Ira M. Gessel   The Smith College Diploma Problem  . . . 55--57
          William C. Waterhouse   Cochran's Theorem for Rings  . . . . . . 58--59
                 Andrew Simoson   The Tumbling Tetrahedron . . . . . . . . 59--63
                 David Eppstein   Tangent Spheres and Triangle Centers . . 63--66
                       Marc Noy   Acyclic and Totally Cyclic Orientations
                                  in Planar Graphs . . . . . . . . . . . . 66--68
                Takayuki Furuta   The Hölder--McCarthy and the Young
                                  Inequalities Are Equivalent for Hilbert
                                  Space Operators  . . . . . . . . . . . . 68--69
                 John Stillwell   Modular Miracles . . . . . . . . . . . . 70--76
                 Nick MacKinnon   Problem 10844  . . . . . . . . . . . . . 77--77
                Ciprian Demeter   Problem 10845  . . . . . . . . . . . . . 77--77
         Józef Przytycki   Problem 10846  . . . . . . . . . . . . . 77--77
              Robin Chapman and   
             Kimmo Eriksson and   
                Richard Stanley   Problem 10847  . . . . . . . . . . . . . 77--77
           Kenneth B. Stolarsky   Problem 10848  . . . . . . . . . . . . . 77--77
                  Richard Bagby   Problem 10849  . . . . . . . . . . . . . 78--78
                Wolfdieter Lang   Problem 10850  . . . . . . . . . . . . . 78--78
           David M. Bradley and   
          Steven Levandosky and   
                        A. Meir   Series and Integral Trial Conditions:
                                  10642  . . . . . . . . . . . . . . . . . 78--79
                Fred Galvin and   
           Stephen C. Locke and   
               Sung Soo Kim and   
                   David Callan   A Generalization of Hall's Theorem:
                                  10701  . . . . . . . . . . . . . . . . . 79--80
               Florian Luca and   
             Francis B. Coghlan   Can Two Consecutive Numbers Both Be
                                  Perfect?: 10711  . . . . . . . . . . . . 80--81
                   Jet Wimp and   
                 Thomas Hermann   A Determinant with Polynomial Entries:
                                  10714  . . . . . . . . . . . . . . . . . 81--81
Michael L. Catalano-Johnson and   
                Daniel Loeb and   
                    John Beebee   A Cubical Gift: 10716  . . . . . . . . . 81--82
               Sung Soo Kim and   
               Mark D. Meyerson   When a Sum of Functions Is Increasing:
                                  10768  . . . . . . . . . . . . . . . . . 82--82
                Wu Wei Chao and   
                 Daniele Donini   Concurrent Lines in a Cyclic
                                  Quadrilateral: 10783 . . . . . . . . . . 83--83
                 Leroy Quet and   
              Reiner Martin and   
                  Otto G. Ruehr   A Zeta Function Series: 10786  . . . . . 84--84
               Doron Zeilberger   Book Review: \booktitle[untitled]  . . . 85--86
              John Guckenheimer   Book Review: \booktitle[untitled]  . . . 87--89
            William G. McCallum   Book Review: \booktitleCalculus
                                  Mysteries and Thrillers, by R. Grant
                                  Woods; How to Ace Calculus: The
                                  Streetwise Guide ~by Colin Adams; Joel
                                  Hass; Abigail Thompson . . . . . . . . . 90--93
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 94--96
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 2, February, 2001

                 Henry L. Alder   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award to Manuel P. Berriozábal for
                                  Distinguished Service to Mathematics . . 97--99
             Duane DeTemple and   
               Matthew Hudelson   Square-Banded Polygons and Affine
                                  Regularity . . . . . . . . . . . . . . . 100--114
                   Peter D. Lax   Change of Variables in Multiple
                                  Integrals II . . . . . . . . . . . . . . 115--119
            Adam Korányi   Around the Finite-Dimensional Spectral
                                  Theorem  . . . . . . . . . . . . . . . . 120--125
                William Mueller   Reform Now, before It's Too Late!  . . . 126--143
         H. Turgay Kaptano\uglu   In Praise of $ y = x^\alpha \sin (1 / x)
                                  $  . . . . . . . . . . . . . . . . . . . 144--150
           Jean B. Lasserre and   
      Konstantin E. Avrachenkov   The Multi-Dimensional Version of $
                                  \int^b_a x^p \, d x $  . . . . . . . . . 151--154
             Sibylle Zeller and   
              Maximilian Thaler   Almost Sure Escape from the Unit
                                  Interval under the Logistic Map  . . . . 155--158
  Robert Geretschläger and   
                 Walther Janous   Generalized Rearrangement Inequalities   158--165
                Seannie Dar and   
                    Shay Gueron   A Weighted Erd\Hos--Mordell Inequality   165--168
                Jan J. Dijkstra   A Four-Point Set That Cannot Be Split    168--170
                 David Beckwith   Problem 10851  . . . . . . . . . . . . . 171--171
                C\ualin Popescu   Problem 10852  . . . . . . . . . . . . . 171--171
                 Stevo Stevi\'c   Problem 10853  . . . . . . . . . . . . . 171--171
                    Wu Wei Chao   Problem 10854  . . . . . . . . . . . . . 171--171
            Ernesto Bruno Cossi   Problem 10855  . . . . . . . . . . . . . 171--171
                   Andrei Jorza   Problem 10856  . . . . . . . . . . . . . 172--172
              Harold G. Diamond   Problem 10857  . . . . . . . . . . . . . 172--172
             Emeric Deutsch and   
          Murray S. Klamkin and   
                Denis Constales   Counting the Solutions: 10540  . . . . . 172--173
             David M. Bloom and   
         Stephen M. Gagola, Jr.   Dirichlet Knew It All along: 10718 . . . 174--174
         Richard F. McCoart and   
                   Lyle Ramshaw   More Balls in Urns: 10722  . . . . . . . 174--176
      Christopher J. Hillar and   
     Heinz-Jürgen Seiffert   Two Sums That Are Congruent Modulo p:
                                  10723  . . . . . . . . . . . . . . . . . 176--176
               Andrei Jorza and   
                  O. P. Lossers   Maximum of a Polynomial on the Unit
                                  Circle: 10779  . . . . . . . . . . . . . 177--177
               Antal Fekete and   
                    Gary Martin   Squared Series Yielding Integers: 10791  177--178
              Edward Newman and   
                        Li Zhou   A Mean Inequality: 10798 . . . . . . . . 178--178
             Robert A. Fontenot   Book Review: \booktitle[untitled]  . . . 179--182
          Doris Schattschneider   Book Review: \booktitle[untitled]  . . . 182--188
                     Ben Herbst   Book Review: \booktitle[untitled]  . . . 188--190
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 3, March, 2001

                   Frank Morgan   Proof of the Double Bubble Conjecture    193--205
                Paul R. Wolfson   The Crooked Made Straight: Roberval and
                                  Newton on Tangents . . . . . . . . . . . 206--216
                   David Spring   Solution of a Calculus Problem on
                                  Minimal Volume . . . . . . . . . . . . . 217--221
               Dirk Huylebrouck   Similarities in Irrationality Proofs for
                                  $ \pi $, $ \ln 2 $, $ \zeta (2) $, and $
                                  \zeta (3) $  . . . . . . . . . . . . . . 222--231
                Lidia Aceto and   
               Donato Trigiante   The Matrices of Pascal and Other Greats  232--245
              Graham Byrnes and   
               Grant Cairns and   
                   Barry Jessup   Leftovers from the Ham Sandwich Theorem  246--249
               Patrick Martinez   Some New Irrational Decimal Fractions    250--253
           Pantelis A. Damianou   Monic Polynomials in Z[x] with Roots in
                                  the Unit Disc  . . . . . . . . . . . . . 253--257
                 Egon Scheffold   Pythagorean Triples of Polygonal Numbers 257--258
             Hans J. H. Tuenter   A Symmetry of Power Sum Polynomials and
                                  Bernoulli Numbers  . . . . . . . . . . . 258--261
                       Paul Yiu   Heronian Triangles Are Lattice Triangles 261--263
                  Vl. P. Vizgin   On the Emotional Assumptions without
                                  Which One Could Not Effectively
                                  Investigate the Laws of Nature . . . . . 264--270
                Donald E. Knuth   Problem 10858  . . . . . . . . . . . . . 271--271
                  Roland Bacher   Problem 10859  . . . . . . . . . . . . . 271--271
                 Emeric Deutsch   Problem 10860  . . . . . . . . . . . . . 271--271
                   Sung Soo Kim   Problem 10861  . . . . . . . . . . . . . 271--271
                    Wu Wei Chao   Problem 10862  . . . . . . . . . . . . . 271--271
                     Leroy Quet   Problem 10863  . . . . . . . . . . . . . 272--272
                C\ualin Popescu   Problem 10864  . . . . . . . . . . . . . 272--272
               Vasile Mihai and   
             Michael Woltermann   The Smoothest and Roughest Permutations:
                                  10725  . . . . . . . . . . . . . . . . . 272--273
              Jean Anglesio and   
                  O. P. Lossers   Periods from Sums of Powers: 10727 . . . 273--273
            M. N. Deshpande and   
             John H. Lindsey II   The Total Length of Short Cycles of a
                                  Random Permutation: 10732  . . . . . . . 273--274
        Hassan Ali Shah Ali and   
National Security Agency Problems Group   Getting the Same Weighted Average Two
                                  Ways: 10737  . . . . . . . . . . . . . . 274--274
                 Tim Keller and   
              Javier Cilleruelo   Squares with Four Equal Digits in an
                                  Even Base: 10741 . . . . . . . . . . . . 275--275
        Juan Arias-de-Reyna and   
                  Robin Chapman   The Square of a Random Determinant:
                                  10787  . . . . . . . . . . . . . . . . . 275--277
          Harold G. Diamond and   
             Ferrell S. Wheeler   A Convolution Formula for the Dickman
                                  Function: 10792  . . . . . . . . . . . . 277--278
              Curtis Herink and   
             Gary Gruenhage and   
            GCHQ Problems Group   Finite Subcovers for Open Covers with
                                  Exact Cardinality: 10799 . . . . . . . . 278--278
               Susan G. Staples   Book Review: \booktitle[untitled]  . . . 279--280
              George E. Andrews   Book Review: \booktitle[untitled]  . . . 281--285
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 286--288
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 4, April, 2001

                Rajendra Bhatia   Linear Algebra to Quantum Cohomology:
                                  The Story of Alfred Horn's Inequalities  289--318
                       R. Shail   A Proof of Thébault's Theorem . . . . . . 319--325
            John H. Hubbard and   
             Samer S. Habre and   
                Beverly H. West   The Convergence of an Euler
                                  Approximation of an Initial Value
                                  Problem Is Not Always Obvious  . . . . . 326--335
                 Garret Sobczyk   The Missing Spectral Basis in Algebra
                                  and Number Theory  . . . . . . . . . . . 336--346
             Rachel W. Hall and   
             Kre\vsimir Josi\'c   The Mathematics of Musical Instruments   347--357
               Holger Schellwat   A Simple Slide Rule for Finite Fields    358--360
          Razvan Alin Satnoianu   A General Method for Establishing
                                  Geometric Inequalities in a Triangle . . 360--364
                J. M. Aldaz and   
                   A. Bravo and   
        S. Gutiérrez and   
                        A. Ubis   A Theorem of D. J. Newman on Euler's $
                                  \phi $ Function and Arithmetic
                                  Progressions . . . . . . . . . . . . . . 364--367
                        Liu Wen   A Counterexample for the Two-Dimensional
                                  Density Function . . . . . . . . . . . . 367--368
              N. S. Astapov and   
                   N. C. Noland   The Remarkable Tetron  . . . . . . . . . 368--370
                 David Beckwith   Problem 10865  . . . . . . . . . . . . . 371--371
               Jerry Kazdan and   
                   Herbert Wilf   Problem 10866  . . . . . . . . . . . . . 371--371
          Oscar Ciaurri Ramirez   Problem 10867  . . . . . . . . . . . . . 371--371
            M. N. Deshpande and   
              A. V. Kharashikar   Problem 10868  . . . . . . . . . . . . . 371--371
                    Lenny Jones   Problem 10869  . . . . . . . . . . . . . 372--372
         Hugh L. Montgomery and   
          Ulrike M. A. Vorhauer   Problem 10870  . . . . . . . . . . . . . 372--372
                Donald E. Knuth   Problem 10871  . . . . . . . . . . . . . 372--372
             Titu Andreescu and   
               Gilbert N. Lewis   Preserving the Sum of Three Cubes: 10728 372--373
        Gustavus J. Simmons and   
        John Henry Steelman and   
 GCHQ Problem Solving Group and   
                  O. P. Lossers   A Congruence for Pascal Triangular
                                  Matrices: 10735  . . . . . . . . . . . . 373--374
                  Mizan R. Khan   An Optimization with a Modular
                                  Constraint: 10736  . . . . . . . . . . . 374--375
      Charles Vanden Eynden and   
            Jerrold W. Grossman   Distinguishing between the Partite Sets
                                  of a Bipartite Graph: 10740  . . . . . . 375--375
                 Emre Alkan and   
            Stephen Gagola, Jr.   The Maximal Property for Finite Groups:
                                  10742  . . . . . . . . . . . . . . . . . 375--376
            C\ualin Popescu and   
                  O. P. Lossers   Comparing a Sum over Quadratic Residues
                                  and Nonresidues: 10743 . . . . . . . . . 376--377
                    Jiro Fukuta   Not Quite a Theorem on Quadrilaterals:
                                  10755  . . . . . . . . . . . . . . . . . 377--378
   Achilleas Sinefakopoulos and   
                 Daniele Donini   Cirumscribing an Inscribed
                                  Quadrilateral: 10804 . . . . . . . . . . 378--378
                Arthur M. Hobbs   Book Review: \booktitle[untitled]  . . . 379--381
                       Eli Maor   Book Review: \booktitle[untitled]  . . . 382--385
                Harsh V. Pittie   Book Review: \booktitle[untitled]  . . . 386--387
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 5, May, 2001

                 Constance Reid   The Alternative Life of E. T. Bell . . . 393--402
            Peter Lindqvist and   
                    Jaak Peetre   Two Remarkable Identities, Called Twos,
                                  for Inverses to Some Abelian Integrals   403--410
               Judy Kennedy and   
         Sahin Koçak and   
                 James A. Yorke   A Chaos Lemma  . . . . . . . . . . . . . 411--423
               Robert E. Greene   Real Analyticity: From Calculus Class to
                                  the Grauert--Morrey Theorem  . . . . . . 424--431
                   Erik Talvila   Some Divergent Trigonometric Integrals   432--436
                    Fred Brauer   What Goes Up Must Come Down, Eventually  437--440
         Edsger W. Dijkstra and   
                  Jayadev Misra   Designing a Calculational Proof of
                                  Cantor's Theorem . . . . . . . . . . . . 440--443
              Giuseppe De Marco   For Every $ \epsilon $ There
                                  Continuously Exists a $ \delta $ . . . . 443--444
    Antreas P. Hatzipolakis and   
                       Paul Yiu   The Lucas Circles of a Triangle  . . . . 444--446
              Gerald B. Folland   How to Integrate a Polynomial over a
                                  Sphere . . . . . . . . . . . . . . . . . 446--448
            V. Wiktor Marek and   
                  Jan Mycielski   Foundations of Mathematics in the
                                  Twentieth Century  . . . . . . . . . . . 449--468
               Bogdan Suceav\ua   Problem 10872  . . . . . . . . . . . . . 469--469
             B. J. Venkatachala   Problem 10873  . . . . . . . . . . . . . 469--469
                    Wu Wei Chao   Problem 10874  . . . . . . . . . . . . . 469--469
                Donald E. Knuth   Problem 10875  . . . . . . . . . . . . . 469--469
   Zoltán Sasvári   Problem 10876  . . . . . . . . . . . . . 469--469
                 Emeric Deutsch   Problem 10877  . . . . . . . . . . . . . 470--470
Pál Péter Dályay   Problem 10878  . . . . . . . . . . . . . 470--470
                S. C. Locke and   
                 Phil Tracy and   
                     H.-J. Voss   Highly Cohesive Graphs Have Long
                                  Nonseparating Paths: 10647 . . . . . . . 470--472
              Serge Tabachnikov   Polyhedron Covered Twice by Lines: 10724 472--473
            Peter Lindqvist and   
                Jaak Peetre and   
            Jonathan M. Borwein   Generalized Trigonometric Functions:
                                  10744  . . . . . . . . . . . . . . . . . 473--474
      Marc Deléglise and   
                    Joe Flowers   An Unusual Limit Problem: 10807  . . . . 474--475
           Yehuda Pinchover and   
               Simeon Reich and   
                   Itai Shafrir   The Ptolemy Constant of a Normed Space:
                                  10812  . . . . . . . . . . . . . . . . . 475--476
                Yves Nievergelt   Book Review: \booktitle[untitled]  . . . 477--481
                    David Scott   Book Review: \booktitle[untitled]  . . . 481--485
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 486--487
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 6, June / July, 2001

                 Paul C. Pasles   The Lost Squares of Dr. Franklin: Ben
                                  Franklin's Missing Squares and the
                                  Secret of the Magic Circle . . . . . . . 489--511
               Martin Hanke and   
                 Otmar Scherzer   Inverse Problems Light: Numerical
                                  Differentiation  . . . . . . . . . . . . 512--521
                  Hans Samelson   Differential Forms, the Early Days; or
                                  the Stories of Deahna's Theorem and of
                                  Volterra's Theorem . . . . . . . . . . . 522--530
               C. J. Maxson and   
                    J. H. Meyer   How Many Subspaces Force Linearity?  . . 531--536
                      Wim Pijls   Some Properties Related to Mercator
                                  Projection . . . . . . . . . . . . . . . 537--543
                   Erik Talvila   Necessary and Sufficient Conditions for
                                  Differentiating under the Integral Sign  544--548
            Jean-P. Quadrat and   
           Jean B. Lasserre and   
         Jean-B. Hiriart-Urruty   Pythagoras' Theorem for Areas  . . . . . 549--551
        David A. Sánchez   An Alternative to the Shooting Method
                                  for a Certain Class of Boundary Value
                                  Problems . . . . . . . . . . . . . . . . 552--555
                   Wen-jin Woan   Uniform Partitions of Lattice Paths and
                                  Chung--Feller Generalizations  . . . . . 556--559
                Harley Flanders   From Ford to Fa\`a . . . . . . . . . . . 559--561
                 Mowaffaq Hajja   A Vector Proof of a Theorem of Bang  . . 562--564
                 Walther Janous   Problem 10879  . . . . . . . . . . . . . 565--565
            Razvan A. Satnoianu   Problem 10880  . . . . . . . . . . . . . 565--565
      José Luis Palacios   Problem 10881  . . . . . . . . . . . . . 565--565
                 Erwin Just and   
            Norman Schaumberger   Problem 10882  . . . . . . . . . . . . . 565--565
                 Nick MacKinnon   Problem 10883  . . . . . . . . . . . . . 565--565
                    Zafar Ahmed   Problem 10884  . . . . . . . . . . . . . 566--566
              Kiran Kedlaya and   
                 Sasha Schwartz   Problem 10885  . . . . . . . . . . . . . 566--566
              M. J. Pelling and   
     GCHQ Problem Solving Group   Maximizing Quadratic Forms over Cubes:
                                  10731  . . . . . . . . . . . . . . . . . 566--567
               Alain Grigis and   
                W. Weston Meyer   Reflections of a Billiard Path: 10749    567--567
              Jean Anglesio and   
       Con Amore Problems Group   A Nowhere-Differentiable Function from
                                  Geometry: 10790  . . . . . . . . . . . . 568--568
           Floor van Lamoen and   
                W. Weston Meyer   Euler Lines Concurrent on the Nine-Point
                                  Circle: 10796  . . . . . . . . . . . . . 569--569
        Hassan Ali Shah Ali and   
           Keith A. Kearnes and   
     Ágnes Szenderei and   
                Zafar Ahmed and   
               M. A. Prasad and   
            GCHQ Problems Group   A Difference of Square Roots: 10806  . . 570--570
  Juan-Bosco Romero Marquez and   
             Mohammed Ali Salem   A Parallelogram Inscribed in a
                                  Quadrilateral: 10810 . . . . . . . . . . 571--571
           Razvan Satnoianu and   
                        Li Zhou   Relatives of Erd\Hos--Mordell: 10814 . . 572--572
                Marion D. Cohen   Book Review: \booktitle[untitled]  . . . 573--577
            J. Alan Alewine and   
                 Eric Schechter   Book Review: \booktitle[untitled]  . . . 577--582
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 7, August / September, 2001

               Jeffrey R. Weeks   The Twin Paradox in a Closed Universe    585--590
               Chi-Kwong Li and   
                 Stephen Pierce   Linear Preserver Problems  . . . . . . . 591--605
             David E. Zitarelli   Towering Figures in American
                                  Mathematics, 1890-1950 . . . . . . . . . 606--635
                   Erik Talvila   Rapidly Growing Fourier Integrals  . . . 636--641
                 Soren Boel and   
         Toke Meier Carlsen and   
           Niels Richard Hansen   A Useful Strengthening of the
                                  Stone--Weierstrass Theorem . . . . . . . 642--643
                   Xingzhi Zhan   Linear Preservers That Permute the
                                  Entries of a Matrix  . . . . . . . . . . 643--645
                Darrell Desbrow   A Real Antiderivative by Contour
                                  Integration  . . . . . . . . . . . . . . 645--649
                Vesa Halava and   
                     Tero Harju   Mortality in Matrix Semigroups . . . . . 649--653
                 Michael Atiyah   Mathematics in the 20th Century  . . . . 654--666
Joaquín Gómez Rey   Problem 10886  . . . . . . . . . . . . . 667--667
                  Jean Anglesio   Problem 10887  . . . . . . . . . . . . . 667--667
         William P. Wardlaw and   
             William D. Withers   Problem 10888  . . . . . . . . . . . . . 667--667
                    Klaus Huber   Problem 10889  . . . . . . . . . . . . . 667--667
                Raymond Mortini   Problem 10890  . . . . . . . . . . . . . 668--668
                  Roland Bacher   Problem 10891  . . . . . . . . . . . . . 668--668
               Stephen C. Locke   Problem 10892  . . . . . . . . . . . . . 668--668
              M. J. Pelling and   
                    F. W. Roush   The Sum Divides the Product: 10745 . . . 668--669
              Itshak Borosh and   
         Douglas A. Hensley and   
                  Joel Zinn and   
     GCHQ Problem Solving Group   One Good Congruence Deserves Another:
                                  10748  . . . . . . . . . . . . . . . . . 669--669
             Leonard Smiley and   
               David Callan and   
             David M. Wells and   
                 Said Amghibech   A Rational Generating Function for
                                  Relative Divisors: 10750 . . . . . . . . 670--670
              Jean Anglesio and   
                 Daniele Donini   Special Points of the Triangle of
                                  Excenters: 10763 . . . . . . . . . . . . 671--671
         Barbara S. Bertram and   
                  Otto G. Ruehr   Submultiplicativity of a Function
                                  Defined by a Series: 10815 . . . . . . . 671--672
                    Frank Swetz   Book Review: \booktitle[untitled]  . . . 673--675
                       Eli Maor   Book Review: \booktitle[untitled]  . . . 675--677
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 678--680
                      Anonymous   Lester R. Ford Awards for 2000 . . . . . 681--681
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 8, October, 2001

          David Lindsay Roberts   E. H. Moore's Early Twentieth-Century
                                  Program for Reform in Mathematics
                                  Education  . . . . . . . . . . . . . . . 689--696
                Shaun M. Fallat   Bidiagonal Factorizations of Totally
                                  Nonnegative Matrices . . . . . . . . . . 697--712
                   Don Rawlings   Sequential Searches: Proofreading,
                                  Russian Roulette, and the Incomplete
                                  $q$-Eulerian Polynomials Revisited . . . 713--720
                   Jan E. Holly   Pictures of Ultrametric Spaces, the
                                  $p$-Adic Numbers, and Valued Fields  . . 721--728
               Kenneth R. Meyer   Jacobi Elliptic Functions from a
                                  Dynamical Systems Point of View  . . . . 729--737
              P. J. McKenna and   
         Cillian Ó Tuama   Large Torsional Oscillations in
                                  Suspension Bridges Visited Again:
                                  Vertical Forcing Creates Torsional
                                  Response . . . . . . . . . . . . . . . . 738--745
                    Greg Martin   Absolutely Abnormal Numbers  . . . . . . 746--754
             Christopher Stuart   Limiting Distributions for Derangements  755--755
          Keith McKenzie Rogers   The Finite Field Kakeya Problem  . . . . 756--759
 Airton von Sohsten de Medeiros   The Fundamental Theorem of Algebra
                                  Revisited  . . . . . . . . . . . . . . . 759--760
                 Mowaffaq Hajja   Other Versions of the Steiner--Lehmus
                                  Theorem  . . . . . . . . . . . . . . . . 760--767
  Wladimir de Azevedo Pribitkin   A Simpler Proof of $ s i n \pi z = \pi z
                                  \prod_{k = 1}^\infty (1 - z^2 / k^2) $   767--768
               Jean B. Lasserre   A Quick Proof for the Volume of
                                  $n$-Balls  . . . . . . . . . . . . . . . 768--769
                   Andrei Jorza   Problem 10893  . . . . . . . . . . . . . 770--770
                 Robert Sulanke   Problem 10894  . . . . . . . . . . . . . 770--770
             A\=ug\=ust Wendijk   Problem 10895  . . . . . . . . . . . . . 770--770
      Torben Maack Bisgaard and   
         Zsolt Páles and   
                 Zoltan Sasvari   Problem 10896  . . . . . . . . . . . . . 770--770
                Gregory P. Wene   Problem 10897  . . . . . . . . . . . . . 771--771
                    Wu Wei Chao   Problem 10898  . . . . . . . . . . . . . 771--771
                 R. Martini and   
                     G. F. Post   Problem 10899  . . . . . . . . . . . . . 771--771
               Paul Bracken and   
               Bruce S. Burdick   Euler's Formula for Zeta Function
                                  Convolutions: 10754  . . . . . . . . . . 771--773
              Bruce Reznick and   
                  Bruce Dearden   Completely Multiplicative Functions:
                                  10760  . . . . . . . . . . . . . . . . . 773--773
                Fred Galvin and   
             Radhika Ramamurthi   An Extremal Problem for Independent Sets
                                  in Graphs: 10761 . . . . . . . . . . . . 773--774
              Bruce Dearden and   
               Jerry Metzer and   
                  Robert Gilmer   Invertible Matrices Modulo n: 10767  . . 774--774
          Christian Blatter and   
                    Josh Greene   The Chromatic Number of the Sphere:
                                  10769  . . . . . . . . . . . . . . . . . 774--775
           Enrico Valdinoci and   
                  Robin Chapman   Convergence of a Series: 10808 . . . . . 775--777
             Walther Janous and   
             Anne-Maria Ernvall   A Summation Inequality: 10817  . . . . . 777--777
                   O. A. Laudal   Book Review: \booktitle[untitled]  . . . 778--781
             O. Carruth McGehee   Book Review: \booktitle[untitled]  . . . 782--784
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 9, November, 2001

                William Mueller   Mathematical Wunderkammern . . . . . . . 785--796
           Jimmie D. Lawson and   
                     Yongdo Lim   The Geometric Mean, Matrices, Metrics,
                                  and More . . . . . . . . . . . . . . . . 797--812
                Robert Osserman   Kepler's Laws, Newton's Laws, and the
                                  Search for New Planets . . . . . . . . . 813--820
                 Dan Kalman and   
                 James E. White   Polynomial Equations and Circulant
                                  Matrices . . . . . . . . . . . . . . . . 821--840
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-First William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 841--850
Ákos László   The Sum of Some Convergent Series  . . . 851--855
                     A. G. Ramm   A Simple Proof of the Fredholm
                                  Alternative and a Characterization of
                                  the Fredholm Operators . . . . . . . . . 855--860
            Robert L. Benedetto   An Elementary Product Identity in
                                  Polynomial Dynamics  . . . . . . . . . . 860--864
                    Jeremy Gray   Weierstrass, Luzin, and Intuition  . . . 865--870
                    Gordon Rice   Problem 10900  . . . . . . . . . . . . . 871--871
                   M. J. Knight   Problem 10901  . . . . . . . . . . . . . 871--871
                 Emeric Deutsch   Problem 10902  . . . . . . . . . . . . . 871--871
                  Richard Bagby   Problem 10903  . . . . . . . . . . . . . 871--871
                  Ovidiu Furdui   Problem 10904  . . . . . . . . . . . . . 871--871
             Richard P. Stanley   Problem 10905  . . . . . . . . . . . . . 871--871
                Donald E. Knuth   Problem 10906  . . . . . . . . . . . . . 872--872
             Emeric Deutsch and   
               David Callan and   
               Sabin Cautis and   
Southwest Missouri Problems Group   Another Path to Generalized Catalan
                                  Numbers: 10751 . . . . . . . . . . . . . 872--873
              Louis Shapiro and   
          Richard Ehrenborg and   
               John W. Moon and   
                   Michael Reid   Leaves of Ordered Trees: 10753 . . . . . 873--874
               Mark Kidwell and   
               Donald Knuth and   
                  O. P. Lossers   Leaves of Ordered Trees: 10757 . . . . . 874--875
         Gerard J. Foschini and   
            GCHQ Problems Group   A Sequence of Functions That Doesn't
                                  Span L$_2$ [0,1]: 10821  . . . . . . . . 875--876
           Jeffrey Lagarias and   
                Jade Vinson and   
            GCHQ Problems Group   When Periodic Points Are Real: 10822 . . 876--877
Félix Martínez-Giménez and   
             John H. Lindsey II   A Convergence Property for Infinite
                                  Arrays: 10826  . . . . . . . . . . . . . 877--877
            Donald E. Knuth and   
              Cecil C. Rousseau   A Stirling Series: 10832 . . . . . . . . 877--878
                   Armand Borel   Book Review: \booktitle[untitled]  . . . 879--883
                    Mark A. Kon   Book Review: \booktitle[untitled]  . . . 883--887
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 888--890
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 108, Number 10, December, 2001

              Peter Borwein and   
            Loki Jörgenson   Visible Structures in Number Theory  . . 897--910
              Donald R. Chalice   How to Differentiate and Integrate
                                  Sequences  . . . . . . . . . . . . . . . 911--921
               David Alan Grier   Dr. Veblen Takes a Uniform Mathematics
                                  in the First World War . . . . . . . . . 922--931
              Harriet Pollatsek   Quantum Error Correction: Classic Group
                                  Theory Meets a Quantum Challenge . . . . 932--962
                  Yunhi Cho and   
                 Kyunghwan Park   Inverse Functions of $ y = x^{1 / x} $   963--967
                Hiroshi Maehara   On the Total Edge-Length of a
                                  Tetrahedron  . . . . . . . . . . . . . . 967--969
          Eugenio P. Balanzario   Evaluation of Dirichlet Series . . . . . 969--971
          Timothy G. Feeman and   
                Osvaldo Marrero   Affine Transformations, Polynomials, and
                                  Proportionality  . . . . . . . . . . . . 972--975
   Szilárd András   Problem 10907  . . . . . . . . . . . . . 976--976
                    Wu Wei Chao   Problem 10908  . . . . . . . . . . . . . 976--976
Támás Kalmán   Problem 10909  . . . . . . . . . . . . . 976--976
             Stevo Stevi\'c and   
               Rade Todorovi\'c   Problem 10910  . . . . . . . . . . . . . 976--976
                    Greg Martin   Problem 10911  . . . . . . . . . . . . . 976--976
                  Jean Anglesio   Problem 10912  . . . . . . . . . . . . . 976--976
                Donald E. Knuth   Problem 10913  . . . . . . . . . . . . . 977--977
                 Mark Sapir and   
              O. P. Lossers and   
             Hugh L. Montgomery   The Decimal Expansions of Powers of 9:
                                  10758  . . . . . . . . . . . . . . . . . 977--978
               Peter J. Ferraro   Fibonacci Numbers and Powers: 10765  . . 978--979
            C\ualin Popescu and   
            Jim Vandergriff and   
                     Jim Delany   A Divisibility Result for a Combination
                                  of mth Powers: 10770 . . . . . . . . . . 979--980
             Emeric Deutsch and   
                    Jim Brawner   Three-Dimensional Lattice Walks in the
                                  Upper Half-Space: 10795  . . . . . . . . 980--980
             Jon A. Wellner and   
                  M. L. Glasser   Incognito Hypergeometrics: 10836 . . . . 980--981
               Andrew Vince and   
              Kenneth Schilling   Almost Fixed Sets: 10843 . . . . . . . . 981--982
                    Fred Galvin   A Generalization of Hall's Theorem:
                                  10701  . . . . . . . . . . . . . . . . . 982--982
                   Neal Koblitz   Book Review: \booktitle[untitled]  . . . 983--988
                Anthony Ralston   Book Review: \booktitle[untitled]  . . . 988--992
                  Roger A. Horn   Editor's Endnotes  . . . . . . . . . . . 993--994
                      Anonymous   Volume Information . . . . . . . . . . . 995--1006
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 109, Number 1, January, 2002

                 Robert Almgren   Financial Derivatives and Partial
                                  Differential Equations . . . . . . . . . 1--12
          Richard Evan Schwartz   Lucy and Lily: a Game of Geometry and
                                  Number Theory  . . . . . . . . . . . . . 13--20
              J. A. C. Weideman   Numerical Integration of Periodic
                                  Functions: a Few Examples  . . . . . . . 21--36
              Victor L. Shapiro   Harmonic Functions in the Unit Disk  . . 37--45
       Sérgio B. Volchan   What Is a Random Sequence? . . . . . . . 46--63
              Paolo Roselli and   
                  Michel Willem   A Convexity Inequality . . . . . . . . . 64--70
          William C. Waterhouse   Quadratic Polynomials and Unique
                                  Factorization  . . . . . . . . . . . . . 70--72
              C. Ballantine and   
                     J. Roberts   A Simple Proof of Rolle's Theorem for
                                  Finite Fields  . . . . . . . . . . . . . 72--74
                  Thomas Sellke   Yet Another Proof of the Radon--Nikodým
                                  Theorem  . . . . . . . . . . . . . . . . 74--76
               Giovanni Falcone   Problem 10914  . . . . . . . . . . . . . 77--77
                   C. P. Rupert   Problem 10915  . . . . . . . . . . . . . 77--77
               Gertrude Ehrlich   Problem 10916  . . . . . . . . . . . . . 77--77
     Jürgen Groß and   
             Götz Trenkler   Problem 10917  . . . . . . . . . . . . . 77--77
                  Matthias Beck   Problem 10918  . . . . . . . . . . . . . 77--77
                 Michael Becker   Problem 10919  . . . . . . . . . . . . . 77--78
  André Kündgen and   
             Radhika Ramamurthi   Problem 10920  . . . . . . . . . . . . . 78--78
             Nick MacKinnon and   
         Stephen M. Gagola, Jr.   Fibonacci Twin Primes: 10844 . . . . . . 78--78
            Ciprian Demeter and   
                        Li Zhou   Another Collinearity Result for
                                  Triangles: 10845 . . . . . . . . . . . . 78--79
     Józef Przytycki and   
                  Richard Stong   Shrinking Lattice Curves: 10846  . . . . 79--80
              Robin Chapman and   
            Kimmo Ericksson and   
         Richard P. Stanley and   
                  Reiner Martin   On the Number of Divisors of $n$ in a
                                  Special Interval: 10847  . . . . . . . . 80--80
          Kenneth Stolarsky and   
         NSA Problems Group and   
                  O. P. Lossers   A Characterization of a Quadratic
                                  Polynomial: 10848  . . . . . . . . . . . 80--81
              Richard Bagby and   
                    M. Battaile   The Determinant of a Matrix of Sines:
                                  10849  . . . . . . . . . . . . . . . . . 81--82
            Wolfdieter Lang and   
                 Said Amghibech   On a Matrix Obtained from the Catalan
                                  Generating Function: 10850 . . . . . . . 82--83
         D. S. Mitrinovi\'c and   
                   Slavko Simic   Special Functions from Long Ago: 5626    83--84
                     Stan Wagon   Book Review: \booktitle[untitled]  . . . 85--92
                   Duncan Buell   Book Review: \booktitle[untitled]  . . . 93--98
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 99--101
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 102--102
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 2, February, 2002

                 Eleanor Robson   Words and Pictures: New Light on
                                  Plimpton 322 . . . . . . . . . . . . . . 105--120
                  Audrey Terras   Finite Quantum Chaos . . . . . . . . . . 121--139
               Aaron Abrams and   
                  Robert Ghrist   Finding Topology in a Factory:
                                  Configuration Spaces . . . . . . . . . . 140--150
                 Arthur Baragar   Constructions Using a Compass and
                                  Twice-Notched Straightedge . . . . . . . 151--164
               Frank Morgan and   
                   Roger Bolton   Hexagonal Economic Regions Solve the
                                  Location Problem . . . . . . . . . . . . 165--172
          James Kuzmanovich and   
            Andrey Pavlichenkov   Finite Groups of Matrices Whose Entries
                                  Are Integers . . . . . . . . . . . . . . 173--186
                      Liu Zheng   An Elementary Proof for Two Basic
                                  Alternating Series . . . . . . . . . . . 187--188
                Robert A. Agnew   On the TEAM Approach to Investing  . . . 188--192
                   Craig Huneke   The Friendship Theorem . . . . . . . . . 192--194
             Claude-Alain Faure   A Short Proof of Lebesgue's Density
                                  Theorem  . . . . . . . . . . . . . . . . 194--196
                 Josef Hofbauer   A Simple Proof of $ 1 + (1 / 2)^2 + (1 /
                                  3)^2 + \cdots {} = \pi^2 / 6 $ and
                                  Related Identities . . . . . . . . . . . 196--200
                 David M. Bloom   Problem 10921  . . . . . . . . . . . . . 201--201
                  Mizan R. Khan   Problem 10922  . . . . . . . . . . . . . 201--201
                Stephen B. Gray   Problem 10923  . . . . . . . . . . . . . 201--201
                   A. J. Sasane   Problem 10924  . . . . . . . . . . . . . 201--201
                   David Callan   Problem 10925  . . . . . . . . . . . . . 201--202
                 Harold Diamond   Problem 10926  . . . . . . . . . . . . . 202--202
        Jeffrey C. Lagarias and   
                E. M. Rains and   
                N. J. A. Sloane   Problem 10927  . . . . . . . . . . . . . 202--202
              Jean Anglesio and   
                  Reiner Martin   Continued Fractions for Some Quadratic
                                  Surds: 10773 . . . . . . . . . . . . . . 202--203
               Catalin Zara and   
             Zachary Franco and   
              T. S. Michael and   
                 Todor E. Milev   A High-Powered Fibonacci Identity: 10774 203--204
               Paul Bateman and   
            Dennis Eichhorn and   
                  Robin Chapman   Grouping $k$-Tuples of Integers by the
                                  Sum of Their Squares: 10778  . . . . . . 204--205
              Robin Chapman and   
                   M. A. Prasad   An Expression for Even-Indexed Bernoulli
                                  Numbers: 10789 . . . . . . . . . . . . . 205--206
               Florian Luca and   
                  Nasha Komanda   A Number and Its Totient Are Not
                                  Amicable: 10793  . . . . . . . . . . . . 206--207
             David S. Hough and   
           Rodica E. Simion and   
           Ali Ekber Gürel   Divisors of Generalized Catalan Numbers:
                                  10794  . . . . . . . . . . . . . . . . . 207--208
            C\ualin Popescu and   
                Roy Barbara and   
                    Omran Kouba   A Sum Related to Quadratic Residues:
                                  10852  . . . . . . . . . . . . . . . . . 208--208
                  Gail Ratcliff   Book Review: \booktitle[untitled]  . . . 209--211
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 3, March, 2002

              Warren P. Johnson   The Curious History of Fa\`a di Bruno's
                                  Formula  . . . . . . . . . . . . . . . . 217--234
  Wladimir de Azevedo Pribitkin   Laplace's Integral, the Gamma Function,
                                  and beyond . . . . . . . . . . . . . . . 235--245
                Sam Northshield   Associativity of the Secant Method . . . 246--257
        Aimee S. A. Johnson and   
                Kathleen Madden   Renewal Systems, Sharp-Eyed Snakes, and
                                  Shifts of Finite Type  . . . . . . . . . 258--272
              Warren P. Johnson   Combinatorics of Higher Derivatives of
                                  Inverses . . . . . . . . . . . . . . . . 273--277
               Christian Radoux   The Hankel Determinant of Exponential
                                  Polynomials: a Very Short Proof and a
                                  New Result Concerning Euler Numbers  . . 277--278
               Karl Dilcher and   
                 Kurt Girstmair   Dedekind Sums and Uniform Distributions  279--284
                Robbert Fokkink   R$^3$ Has No Root  . . . . . . . . . . . 285--285
                 John Stillwell   The Continuum Problem  . . . . . . . . . 286--297
          Christopher J. Hillar   Problem 10928  . . . . . . . . . . . . . 298--298
                    Lajos Csete   Problem 10929  . . . . . . . . . . . . . 298--298
                Paul Schweitzer   Problem 10930  . . . . . . . . . . . . . 298--298
                 Robert DiSario   Problem 10931  . . . . . . . . . . . . . 298--298
              Christian Bey and   
              Jerrold R. Griggs   Problem 10932  . . . . . . . . . . . . . 298--299
                   Paul Lescott   Problem 10933  . . . . . . . . . . . . . 299--299
                   Vasile Mihai   Problem 10934  . . . . . . . . . . . . . 299--299
             Hadi Salmasian and   
             NSA Problems Group   Minimizing the Sum of Negative Powers of
                                  Orders of Group Elements: 10775  . . . . 299--299
                Yongge Tian and   
                David W. Carter   Squashing a Matrix by Adding an
                                  Imaginary Part: 10776  . . . . . . . . . 300--300
             Leonard Smiley and   
 GCHQ Problem Solving Group and   
           Helmut Prodinger and   
                  Robin Chapman   A Tree-Counting Identity: 10781  . . . . 300--301
           Douglas Iannucci and   
              O. P. Lossers and   
     GCHQ Problem Solving Group   Divisibility Involving Random Sets of
                                  Integers: 10782  . . . . . . . . . . . . 301--302
             Emeric Deutsch and   
        John Henry Steelman and   
                   David Callan   A Recursively Defined Sequence of
                                  Functions: 10785 . . . . . . . . . . . . 302--304
           Douglas Iannucci and   
                    Kee-Wai Lau   Triperfect Numbers: 10800  . . . . . . . 304--305
                Wu Wei Chao and   
            Geoffrey A. Kandall   The Median Meets the Circle of
                                  Appolonius: 10862  . . . . . . . . . . . 305--305
             Judith V. Grabiner   Book Review: \booktitle[untitled]  . . . 306--309
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 310--312
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 313--314
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 4, April, 2002

                 Alan D. Taylor   The Manipulability of Voting Systems . . 321--337
        Jeffrey C. Lagarias and   
           Colin L. Mallows and   
                 Allan R. Wilks   Beyond the Descartes Circle Theorem  . . 338--361
                    Shay Gueron   Two Applications of the Generalized
                                  Ptolemy Theorem  . . . . . . . . . . . . 362--370
             Rita Aggarwala and   
           Michael P. Lamoureux   Inverting the Pascal Matrix Plus One . . 371--377
                        Liu Wen   A Nowhere Differentiable Continuous
                                  Function Constructed by Infinite
                                  Products . . . . . . . . . . . . . . . . 378--380
               Johannes Huisman   Rino's Flight around the World in
                                  Circles  . . . . . . . . . . . . . . . . 380--383
                     Casey Mann   A Tile with Surround Number 2  . . . . . 383--388
                Reinhard Michel   On Stirling's Formula  . . . . . . . . . 388--390
                  Andrea Vietri   An Inductive Proof of a Known Result
                                  about $ \psi (x) $ . . . . . . . . . . . 390--391
                   Zhibing Chen   Problem 10935  . . . . . . . . . . . . . 392--392
        Andor Lukács and   
          Szilard András   Problem 10936  . . . . . . . . . . . . . 392--392
                David G. Wagner   Problem 10937  . . . . . . . . . . . . . 392--392
            Jean-Pierre Grivaux   Problem 10938  . . . . . . . . . . . . . 392--392
                Aleksandar Ivic   Problem 10939  . . . . . . . . . . . . . 392--392
                Yves Nievergelt   Problem 10940  . . . . . . . . . . . . . 393--393
            Jeffrey C. Lagarias   Problem 10941  . . . . . . . . . . . . . 393--393
               Paul Bateman and   
               Jeffrey Kalb and   
                  Allen Stenger   A Limit Involving Least Common
                                  Multiples: 10797 . . . . . . . . . . . . 393--394
            Paul R. Pudaite and   
                  Owen Byer and   
               Deirdre Smeltzer   A Gambler Urns His Money: 10801  . . . . 394--395
            Stephen Penrice and   
     GCHQ Problem Solving Group   Expected Rank in an NBA Draft Lottery:
                                  10803  . . . . . . . . . . . . . . . . . 395--396
               Floor van Lamoen   Circumcenters on a Circle: 10830 . . . . 396--397
Florian S. Pârvânescu and   
                    Roy Barbara   When ABC Is Equilateral: 10838 . . . . . 397--398
             Jiansheng Yang and   
                Shulin Zhou and   
                  O. P. Lossers   An Elaborate Uniform Convergence: 10840  398--399
                 J. David Logan   Book Review: \booktitle[untitled]  . . . 400--402
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 5, May, 2002

           Jason Cantarella and   
             Dennis DeTurck and   
                   Herman Gluck   Vector Calculus and the Topology of
                                  Domains in $3$-Space . . . . . . . . . . 409--442
                Shay Gueron and   
                    Ran Tessler   The Fermat--Steiner Problem  . . . . . . 443--451
                   M. Ram Murty   Prime Numbers and Irreducible
                                  Polynomials  . . . . . . . . . . . . . . 452--458
        Alf van der Poorten and   
              Gerhard Woeginger   Squares from Products of Consecutive
                                  Integers . . . . . . . . . . . . . . . . 459--462
                Jeff Brooks and   
                     Satha Push   The Cycloidal Pendulum . . . . . . . . . 463--465
                Paulo Viana and   
            Paula Murgel Veloso   Galois Theory of Reciprocal Polynomials  466--471
                  Mira Bhargava   When Is a Group the Union of Proper
                                  Normal Subgroups?  . . . . . . . . . . . 471--473
            Gregory F. Bachelis   A Short Proof of Hall's Theorem on SDRs  473--474
                 Walther Janous   Problem 10942  . . . . . . . . . . . . . 475--475
                C\ualin Popescu   Problem 10943  . . . . . . . . . . . . . 475--475
                   Marcin Mazur   Problem 10944  . . . . . . . . . . . . . 475--475
                   Slavko Simic   Problem 10945  . . . . . . . . . . . . . 475--476
                 Stevo Stevi\'c   Problem 10946  . . . . . . . . . . . . . 476--476
      LSU Problem Solving Group   Problem 10947  . . . . . . . . . . . . . 476--476
                   Peter Walker   Problem 10948  . . . . . . . . . . . . . 476--476
               Antal Fekete and   
                  Johann Cigler   Stirling and Bell and Binomial, Oh My!:
                                  10805  . . . . . . . . . . . . . . . . . 476--477
             David Beckwith and   
                     Karl David   An Identity for Partitions of Integers:
                                  10809  . . . . . . . . . . . . . . . . . 477--478
                 Phil Tracy and   
            NCCU Problems Group   The Distance between the Endpoints of a
                                  Longest Path: 10811  . . . . . . . . . . 478--478
             Emeric Deutsch and   
                   Wen-jin Woan   Special Motzkin Paths: 10816 . . . . . . 478--479
                Cezar Joita and   
                  Robin Chapman   The Functional Equation $ f \circ g = f
                                  $: 10818 . . . . . . . . . . . . . . . . 479--480
                Olaf Krafft and   
       Gabriela St\uanic\ua and   
         Pantelimon St\uanic\ua   A Binomial Coefficient Estimate: 10819   480--481
                 Ho-joo Lee and   
           Marc A. P. Bernstein   Brocard Angle 30 Degrees: 10824  . . . . 481--482
                Ulrich Abel and   
               Douglas B. Tyler   Reminiscent of Gibbs: 10827  . . . . . . 482--482
                Marion D. Cohen   Book Review: \booktitle[untitled]  . . . 483--485
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 486--488
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 6, June / July, 2002

         Elena Anne Marchisotto   The Theorem of Pappus: a Bridge between
                                  Algebra and Geometry . . . . . . . . . . 497--516
            Carrie E. Finch and   
                    Lenny Jones   A Curious Connection between Fermat
                                  Numbers and Finite Groups  . . . . . . . 517--524
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Subtangents -- An Aid to Visual Calculus 525--533
            Jeffrey C. Lagarias   An Elementary Problem Equivalent to the
                                  Riemann Hypothesis . . . . . . . . . . . 534--543
                Leonard Gillman   Two Classical Surprises Concerning the
                                  Axiom of Choice and the Continuum
                                  Hypothesis . . . . . . . . . . . . . . . 544--553
                G. E. Hardy and   
                 M. V. Subbarao   A Modified Problem of Pillai and Some
                                  Related Questions  . . . . . . . . . . . 554--559
                   M. A. Nyblom   Some Curious Sequences Involving Floor
                                  and Ceiling Functions  . . . . . . . . . 559--564
          Timothy G. Feeman and   
                Osvaldo Marrero   The Right-Hand Derivative of an Integral 565--568
               Jeffrey Lagarias   Problem 10949  . . . . . . . . . . . . . 569--569
                  Ovidiu Furdui   Problem 10950  . . . . . . . . . . . . . 569--569
                   Sung Soo Kim   Problem 10951  . . . . . . . . . . . . . 569--569
                   David Callan   Problem 10952  . . . . . . . . . . . . . 569--569
                     Leroy Quet   Problem 10953  . . . . . . . . . . . . . 570--570
                 Erwin Just and   
            Norman Schaumberger   Problem 10954  . . . . . . . . . . . . . 570--570
               Razvan Satnoianu   Problem 10955  . . . . . . . . . . . . . 570--570
               Doru Caragea and   
                Viviana Ene and   
                 Dean Alvis and   
                  Nasha Komanda   A Millennial Polynomial Problem: 10802   570--571
               Fred Richman and   
            NCCU Problems Group   Subspaces of the Vector Space of
                                  $2$-by-$2$ Matrices: 10813 . . . . . . . 571--572
             Stevo Stevi\'c and   
                  Alain Tissier   The Limit of a Sequence: 10853 . . . . . 572--573
             Harold Diamond and   
                  Alain Tissier   Truncated Series Ratios Alternating
                                  about tanh x: 10857  . . . . . . . . . . 573--574
            C\ualin Popescu and   
              Xiaoshen Wang and   
                Thomas McMillan   Compact Subsets Countable: 10864 . . . . 574--574
      Oscar Ciaurri Ramirez and   
                 Daniele Donini   Sum of an Infinite Series: 10867 . . . . 575--576
                  Claude LeBrun   Book Review: \booktitle[untitled]  . . . 577--578
                George H. Swift   Book Review: \booktitle[untitled]  . . . 579--580
                      Anonymous   [untitled] . . . . . . . . . . . . . . . 581--583
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 7, August / September, 2002

                      Bob Witte   The 2001 James R. C. Leitzel Lecture:
                                  What I Have Learned from the Mathematics
                                  Community  . . . . . . . . . . . . . . . 585--594
            Robert F. Brown and   
                 Jack E. Girolo   Isolating Fixed Points . . . . . . . . . 595--611
                 James T. Smith   Thomsen's Equation . . . . . . . . . . . 612--622
                  John McCleary   Trigonometries . . . . . . . . . . . . . 623--638
                 Ezra Brown and   
                 Bruce T. Myers   Elliptic Curves from Mordell to
                                  Diophantus and Back  . . . . . . . . . . 639--649
             Robert L. Lamphere   Solution of the Direct Problem of
                                  Uniform Circular Motion in Non-Euclidean
                                  Geometry . . . . . . . . . . . . . . . . 650--655
                 M. J. Jamieson   Fibonacci Numbers and Cotangent
                                  Sequences  . . . . . . . . . . . . . . . 655--657
                  Iosif Pinelis   An Equidistribution Phenomenon: Is There
                                  a Principle behind It? . . . . . . . . . 657--659
                    P. G. Walsh   On a Question of Kaplansky . . . . . . . 660--661
               Judy A. Holdener   A Theorem of Touchard on the Form of Odd
                                  Perfect Numbers  . . . . . . . . . . . . 661--663
                  John McCarthy   Problem 10956  . . . . . . . . . . . . . 664--664
              Victor Alexandrov   Problem 10957  . . . . . . . . . . . . . 664--664
                  Robin Chapman   Problem 10958  . . . . . . . . . . . . . 664--664
                 George L. Lamb   Problem 10959  . . . . . . . . . . . . . 665--665
                     Oliver Eng   Problem 10960  . . . . . . . . . . . . . 665--665
                   Brian Conrad   Problem 10961  . . . . . . . . . . . . . 665--665
                Mih\`aly Bencze   Problem 10962  . . . . . . . . . . . . . 665--665
           Alberto Facchini and   
          Francesco Barioli and   
              Robin Chapman and   
             Ron Martin Carroll   Nonsingular Sums of Matrices: 10784  . . 665--666
          George E. Andrews and   
              Robin Chapman and   
                 George Andrews   A Sparse Determinant: 10831  . . . . . . 666--667
               Sung Soo Kim and   
       Richard Johnsonbaugh and   
          Ronald E. Prather and   
                   Donald Knuth   Min-Plus Matrix Multiplication: 10834    667--668
        Ernesto Bruno Cossi and   
                  Robin Chapman   Points on a Sphere: 10855  . . . . . . . 668--669
               Jerry Kazdan and   
               Herbert Wilf and   
               Darryl K. Nester   Waiting for the Bus: 10866 . . . . . . . 669--669
                Wu Wei Chao and   
                        Li Zhou   Parallelogram Circumcenters: 10874 . . . 669--670
                 Erwin Just and   
        Norman Schaumberger and   
                    Paul Budney   A Little Convexity: 10882  . . . . . . . 670--670
                Zafar Ahmed and   
                  Knut Dale and   
             George L. Lamb Jr.   Definitely an Integral: 10884  . . . . . 670--671
             Jeffrey Nunemacher   Book Review: \booktitle[untitled]  . . . 672--675
                     Mark Green   Book Review: \booktitle[untitled]  . . . 675--678
                      Anonymous   Telegraphic Reviews  . . . . . . . . . . 679--681
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 8, October, 2002

               Scott Bailey and   
               Theodore Kim and   
           Robert S. Strichartz   Inside the Lévy Dragon  . . . . . . . . . 689--703
            Anthony Philippakis   The Orthic Triangle and the O.K.
                                  Quadrilateral  . . . . . . . . . . . . . 704--728
      F. Rodriguez Villegas and   
                   L. Sadun and   
                   J. F. Voloch   Blet: a Mathematical Puzzle  . . . . . . 729--740
                Mark Levene and   
                  George Loizou   Kemeny's Constant and the Random Surfer  741--745
             Daniel J. Velleman   Partial Fractions, Binomial
                                  Coefficients, and the Integral of an Odd
                                  Power of $ \sec \theta $ . . . . . . . . 746--749
               Per E. Manne and   
                Steven R. Finch   A Solution to the Bent Wire Problem  . . 750--752
                       B. Liseo   A Probabilistic Derivation of Dirichlet
                                  Integrals  . . . . . . . . . . . . . . . 753--754
Roberto Sánchez-Peregrino   A Note on a Closed Formula for
                                  Poly-Bernoulli Numbers . . . . . . . . . 755--756
            Harold R. Parks and   
                  Dean C. Wills   An Elementary Calculation of the
                                  Dihedral Angle of the Regular
                                  $n$-Simplex  . . . . . . . . . . . . . . 756--758
                 Paul Deiermann   Problem 10963  . . . . . . . . . . . . . 759--759
                  H. A. ShahAli   Problem 10964  . . . . . . . . . . . . . 759--759
                  John Melville   Problem 10965  . . . . . . . . . . . . . 759--759
          Jean-Marie de Koninck   Problem 10966  . . . . . . . . . . . . . 759--759
                Douglas B. West   Problem 10967  . . . . . . . . . . . . . 759--759
               Stephen C. Locke   Problem 10968  . . . . . . . . . . . . . 759--760
                Richard Stanley   Problem 10969  . . . . . . . . . . . . . 760--760
                  Ovidiu Furdui   Problem 10950  . . . . . . . . . . . . . 760--760
             M. Mirzavaziri and   
            GCHQ Problems Group   Least Number with Exactly $m$ Divisors:
                                  10820  . . . . . . . . . . . . . . . . . 760--761
          George E. Andrews and   
                 Karl David and   
               S. J. Bernau and   
                    M. Getz and   
                       D. Jones   Periodicity under Shift and Complement:
                                  10823  . . . . . . . . . . . . . . . . . 761--762
                Carl Miller and   
                Donald E. Knuth   A Fibonacci--Lucas Extremum: 10825 . . . 762--763
             Walther Janous and   
              Rolf Richberg and   
                  Raul A. Simon   A Totient Sum: 10829 . . . . . . . . . . 763--763
               Sung Soo Kim and   
       Richard Johnsonbaugh and   
          Ronald E. Prather and   
                   Donald Knuth   Min-Plus Matrix Multiplication: 10834    763--764
        Razvan A. Satnoianu and   
                  O. P. Lossers   The Minimum Median: 10880  . . . . . . . 764--765
                Klaus Huber and   
              O. P. Lossers and   
             Norbert Ortner and   
                      A. Serret   Cassini's Length: 10889  . . . . . . . . 765--766
                Arthur M. Hobbs   Book Review: \booktitle[untitled]  . . . 767--770
               Robert G. Bartle   Book Review: \booktitle[untitled]  . . . 770--773
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 774--776
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 9, November, 2002

               Ulrich Daepp and   
              Pamela Gorkin and   
                Raymond Mortini   Ellipses and Finite Blaschke Products    785--795
              Daniel C. Isaksen   A Cohomological Viewpoint on Elementary
                                  School Arithmetic  . . . . . . . . . . . 796--805
          Bennett Eisenberg and   
              Rosemary Sullivan   The Fundamental Theorem of Calculus in
                                  Two Dimensions . . . . . . . . . . . . . 806--817
                    Iwan Praton   Cutting Polyominos into Equal-Area
                                  Triangles  . . . . . . . . . . . . . . . 818--826
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Second William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 827--839
              Chun-Hung Hsu and   
                   Ming-Chia Li   Transitivity Implies Period Six: a
                                  Simple Proof . . . . . . . . . . . . . . 840--843
               N. J. Wildberger   A New Proof of Cavalieri's Quadrature
                                  Formula  . . . . . . . . . . . . . . . . 843--845
                    Li Yingying   On Euler's Constant-Calculating Sums by
                                  Integrals  . . . . . . . . . . . . . . . 845--850
            Alf van der Poorten   Life on the Edge . . . . . . . . . . . . 850--853
               Razvan Satnoianu   Problem 10970  . . . . . . . . . . . . . 854--854
                   C. P. Rupert   Problem 10971  . . . . . . . . . . . . . 854--854
               Tim Ferguson and   
                    Lenny Jones   Problem 10972  . . . . . . . . . . . . . 854--854
                    L. D. Servi   Problem 10973  . . . . . . . . . . . . . 854--854
                Syrous Marivani   Problem 10974  . . . . . . . . . . . . . 854--855
                 Emeric Deutsch   Problem 10975  . . . . . . . . . . . . . 855--855
                Vitaly Voloshin   Problem 10976  . . . . . . . . . . . . . 855--855
           Howard M. Taylor and   
      Richard A. Groeneveld and   
               John Stufken and   
               J. G. Kemeny and   
                J. L. Snell and   
                    A. W. Knapp   A Careless Walk toward Zero: 10788 . . . 855--856
             David Beckwith and   
            NCCU Problems Group   Additive Atoms: 10828  . . . . . . . . . 856--857
               Anna Dyubina and   
          Stephen M. Gagola Jr.   A Group That Is Not Finitely Generated:
                                  10835  . . . . . . . . . . . . . . . . . 857--858
                 Erwin Just and   
                 Charles Lanski   Consequences of a Relation on a Ring:
                                  10841  . . . . . . . . . . . . . . . . . 858--858
              Bruce Reznick and   
        GCHQ Problems Group and   
                        Li Zhou   Nondivisibility of Binomial
                                  Coefficients: 10842  . . . . . . . . . . 858--859
             David Beckwith and   
                    Li Zhou and   
                   David Callan   A Property of the Binary Sum of a Family
                                  of Sets: 10865 . . . . . . . . . . . . . 859--860
                 R. Martini and   
                 G. F. Post and   
               Gerald Leibowitz   An Inequality of Hardy: 10899  . . . . . 860--860
              Ovidio Furdui and   
               Albert Nijenhuis   A Square Property: 10904 . . . . . . . . 860--861
                   Fred Richman   Book Review: \booktitle[untitled]  . . . 862--865
                      Anonymous   Telegraphic Reviews  . . . . . . . . . . 866--868
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 109, Number 10, December, 2002

             Amy Shell-Gellasch   Mina Rees and the Funding of the
                                  Mathematical Sciences  . . . . . . . . . 873--889
                      Mark Levi   Minimal Perimeter Triangles  . . . . . . 890--899
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Tangents and Subtangents Used to
                                  Calculate Areas  . . . . . . . . . . . . 900--908
         Richard P. Jerrard and   
                 John E. Wetzel   Equilateral Triangles and Triangles  . . 909--915
              Manuel Benito and   
            J. Javier Escribano   An Easy Proof of Hurwitz's Theorem . . . 916--918
               Joshua E. Greene   A New Short Proof of Kneser's Conjecture 918--920
                    Carl Axness   Problem 10977  . . . . . . . . . . . . . 921--921
            Jean-Pierre Grivaux   Problem 10978  . . . . . . . . . . . . . 921--921
            Donald P. Minassian   Problem 10979  . . . . . . . . . . . . . 921--921
                   Ye Zhong Hao   Problem 10980  . . . . . . . . . . . . . 921--921
             Nicholas C. Singer   Problem 10981  . . . . . . . . . . . . . 922--922
                    Yuming Chen   Problem 10982  . . . . . . . . . . . . . 922--922
               Bogdan Suceav\ua   Problem 10983  . . . . . . . . . . . . . 922--922
       Beresford N. Parlett and   
                Olaf Krafft and   
                Martin Schaefer   The Largest Eigenvalue of a Positive
                                  Definite Symmetric Matrix: 10839 . . . . 922--923
               Sung Soo Kim and   
           Charles Diminnie and   
                Roger Zarnowski   Intermediate Value Functions: 10861  . . 923--923
Szilárd András and   
                   Michael Reid   Arithmetic Means and Geometric Means:
                                  10907  . . . . . . . . . . . . . . . . . 924--925
                Wu Wei Chao and   
              Richard Stong and   
                Doyle Henderson   A Functional Equation: 10908 . . . . . . 925--926
Támás Kalmán and   
                  O. P. Lossers   Isodynamic Points of a Triangle: 10909   926--927
             Stevo Stevi\'c and   
           Rade Todorovi\'c and   
                Peter M. Jarvis   $ n x \bmod 1 $: 10910 . . . . . . . . . 927--928
                      Anonymous   Errata: 10948  . . . . . . . . . . . . . 928--928
                      Anonymous   Errata: 10950  . . . . . . . . . . . . . 928--928
                      Anonymous   Errata: 10953  . . . . . . . . . . . . . 928--928
                      Anonymous   Errata: An Expression for Even-Indexed
                                  Bernoulli Numbers: 10789 . . . . . . . . 928--928
                      Anonymous   Errata: Squashing a Matrix by Adding an
                                  Imaginary Part: 10776  . . . . . . . . . 928--928
                      Anonymous   Errata: Triperfect Numbers: 10800  . . . 928--928
                   Marion Cohen   Book Review: \booktitle[untitled]  . . . 929--932
                      Anonymous   Volume Information . . . . . . . . . . . 933--943
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 944--945
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 110, Number 1, January, 2003

             Rüdger Thiele   Hilbert's Twenty-Fourth Problem  . . . . 1--24
                  Glenn Iba and   
                   James Tanton   Candy Sharing  . . . . . . . . . . . . . 25--35
               John E. McCarthy   Pick's Theorem --- What's the Big Deal?  36--45
                   Florian Luca   Fermat Primes and Heron Triangles with
                                  Prime Power Sides  . . . . . . . . . . . 46--49
        Jennifer T. Betcher and   
                 John H. Jaroma   An Extension of the Results of Servais
                                  and Cramer on Odd Perfect and Odd
                                  Multiply Perfect Numbers . . . . . . . . 49--52
                      Alan Nash   A Generalized Parallelogram Law  . . . . 52--57
                      Uri Elias   Rearrangement of a Conditionally
                                  Convergent Series  . . . . . . . . . . . 57--57
                    Yongge Tian   Problem 10984  . . . . . . . . . . . . . 58--58
                   Donald Knuth   Problem 10985  . . . . . . . . . . . . . 58--58
                   Herbert Wilf   Problem 10986  . . . . . . . . . . . . . 58--58
          Kumar N. Prasanna and   
                   B. G. Shenoy   Problem 10987  . . . . . . . . . . . . . 58--58
                    Wu Wei Chao   Problem 10988  . . . . . . . . . . . . . 59--59
                  Roland Bacher   Problem 10989  . . . . . . . . . . . . . 59--59
                     Rick Mabry   Problem 10990  . . . . . . . . . . . . . 59--59
            Donald E. Knuth and   
                 Allan Pedersen   Highly Variable Lists: 10691 . . . . . . 59--60
            Donald E. Knuth and   
                  O. P. Lossers   Exploring All Binary Mazes: 10720  . . . 60--61
             Emeric Deutsch and   
            Doyle Henderson and   
             GCHQ Problem Group   Three Recurrences for a Single Sequence:
                                  10860  . . . . . . . . . . . . . . . . . 61--62
            Raymond Mortini and   
                  Jeff Boersema   Inequivalent Topologies: 10890 . . . . . 62--63
             August Wendijk and   
                 Thomas Hermann   Twin Segments in the Arbelos: 10895  . . 63--64
               M. J. Knight and   
                        Li Zhou   Hidden Arctangents: 10901  . . . . . . . 64--64
             Michael Becker and   
                  Rolf Richberg   A Moment Evaluation: 10919 . . . . . . . 64--65
              Victor Pambuccian   Book Review: \booktitleGeometry: Euclid
                                  and Beyond, by Robin Hartshorne  . . . . 66--70
               Della D. Fenster   Book Review: \booktitle[untitled]  . . . 70--74
                      Anonymous   Telegraphic Reviews  . . . . . . . . . . 75--77
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 78--80
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 2, February, 2003

               R. Michael Range   Complex Analysis: a Brief Tour into
                                  Higher Dimensions  . . . . . . . . . . . 89--108
           Harold L. Schoen and   
            Christian R. Hirsch   Responding to Calls for Change in High
                                  School Mathematics: Implications for
                                  Collegiate Mathematics . . . . . . . . . 109--123
            David J. Hunter and   
             Paul T. von Hippel   How Rare Is Symmetry in Musical $ 12
                                  $-Tone Rows? . . . . . . . . . . . . . . 124--132
                   J. Peter May   Munshi's Proof of the Nullstellensatz    133--140
                J. M. Aldaz and   
                       A. Bravo   Euclid's Argument on the Infinitude of
                                  Primes . . . . . . . . . . . . . . . . . 141--142
              Jack B. Brown and   
               George Kozlowski   Smooth Interpolation, Hölder Continuity,
                                  and the Takagi--van der Waerden Function 142--147
                  Bang-Yen Chen   When Does the Position Vector of a Space
                                  Curve Always Lie in Its Rectifying
                                  Plane? . . . . . . . . . . . . . . . . . 147--152
                   Xingzhi Zhan   The Sharp Rado Theorem for Majorizations 152--153
                Gabriel Navarro   On the Fundamental Theorem of Finite
                                  Abelian Groups . . . . . . . . . . . . . 153--154
                Raymond Mortini   Problem 10991  . . . . . . . . . . . . . 155--155
                   David Lubell   Problem 10992  . . . . . . . . . . . . . 155--155
                Giorgio Goldoni   Problem 10993  . . . . . . . . . . . . . 155--155
                   David Savitt   Problem 10994  . . . . . . . . . . . . . 155--156
               Donato Trigiante   Problem 10995  . . . . . . . . . . . . . 156--156
                    Wu Wei Chao   Problem 10996  . . . . . . . . . . . . . 156--156
                  Ed T. Prothro   Problem 10997  . . . . . . . . . . . . . 156--156
                V. Thebault and   
                  B. J. English   It's a Long Story: 3887  . . . . . . . . 156--158
      Charles Vanden Eynden and   
                  Reiner Martin   A Divisibility Property of Factorials:
                                  10833  . . . . . . . . . . . . . . . . . 158--158
                 Ho-joo Lee and   
                 Gerald Myerson   Consecutive Integers Whose Totients Are
                                  Multiples of n: 10837  . . . . . . . . . 158--159
                 Leroy Quet and   
                  Richard Stong   An Alternating Sum Involving Unsigned
                                  Stirling Numbers: 10863  . . . . . . . . 159--160
                Lenny Jones and   
                   Florian Luca   Euler to the Rescue: 10869 . . . . . . . 160--160
         Hugh L. Montgomery and   
             John H. Lindsey II   Positivity of a Certain Power Series:
                                  10870  . . . . . . . . . . . . . . . . . 160--161
            Donald E. Knuth and   
             Gabriel D. Carroll   Balanced Neighborhood Squares: 10871 . . 161--162
           Bogdan Suceav\va and   
                  Richard Stong   The Fewest $3$-Cycles to Generate an
                                  Even Permutation: 10872  . . . . . . . . 162--162
         M. Victor Wickerhauser   Book Review: \booktitle[untitled]  . . . 163--167
               Steven G. Krantz   Book Review: \booktitle[untitled]  . . . 167--171
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 3, March, 2003

            Robert E. Megginson   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award to Clarence F. Stephens for
                                  Distinguished Service to Mathematics . . 177--180
                    Stan Gudder   Quantum Computation  . . . . . . . . . . 181--201
               John Bamberg and   
               Grant Cairns and   
               Devin Kilminster   The Crystallographic Restriction,
                                  Permutations, and Goldbach's Conjecture  202--209
                Stephen B. Gray   Generalizing the Petr--Douglas--Neumann
                                  Theorem on $N$-Gons  . . . . . . . . . . 210--227
               Lorenz Halbeisen   Can Kirkman's Schoolgirls Walk Abreast
                                  by Forming Arithmetic Progressions?  . . 228--231
      Ján Miná\vc   Newton's Identities Once Again!  . . . . 232--234
                  Michael Hardy   An Illuminating Counterexample . . . . . 234--238
                Ritsuo Nakamoto   A Norm Inequality for Hermitian
                                  Operators  . . . . . . . . . . . . . . . 238--239
                Roberto Tauraso   Problem 10998  . . . . . . . . . . . . . 240--240
                D. P. Minassian   Problem 10999  . . . . . . . . . . . . . 240--240
                    George Lamb   Problem 11000  . . . . . . . . . . . . . 240--240
                     Rick Mabry   Problem 11001  . . . . . . . . . . . . . 240--240
      Y.-F. S. Pétermann   Problem 11002  . . . . . . . . . . . . . 240--241
                Stephen B. Gray   Problem 11003  . . . . . . . . . . . . . 241--241
              Victor Pambuccian   Problem 11004  . . . . . . . . . . . . . 241--241
            M. N. Deshpande and   
          A. V. Kharashikar and   
                 Walther Janous   Recursive Expressions in an Urn Problem:
                                  10868  . . . . . . . . . . . . . . . . . 241--243
         B. J. Venkatachala and   
                Doyle Henderson   An Exponential Diophantine Equation:
                                  10873  . . . . . . . . . . . . . . . . . 243--243
            Donald E. Knuth and   
                  Richard Stong   Animals in a Cage: 10875 . . . . . . . . 243--245
             Emeric Deutsch and   
                 Daniele Donini   Counting Tilings with L-Tiles and
                                  Squares: 10877 . . . . . . . . . . . . . 245--246
                 Walther Janous   Pairs of Squares: 10879  . . . . . . . . 246--247
  José Luis Palacios and   
                  Richard Stong   Going around Randomly in Circles: 10881  247--247
                William Mueller   Book Review: \booktitle[untitled]  . . . 248--254
            Shandelle M. Henson   Book Review: \booktitle[untitled]  . . . 254--258
                      Anonymous   Telegraphic Reviews  . . . . . . . . . . 259--261
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 4, April, 2003

             George W. Cobb and   
                  Yung-Pin Chen   An Application of Markov Chain Monte
                                  Carlo to Community Ecology . . . . . . . 265--288
            Alan F. Beardon and   
                    David Minda   On the Pointwise Limit of Complex
                                  Analytic Functions . . . . . . . . . . . 289--297
             S. C. Coutinho and   
                J. C. McConnell   The Quest for Quotient Rings (Of
                                  Noncommutative Noetherian Rings) . . . . 298--313
                Yuval Peres and   
        Károly Simon and   
                 Boris Solomyak   Fractals with Positive Length and Zero
                                  Buffon Needle Probability  . . . . . . . 314--325
                    L. D. Servi   Nested Square Roots of 2 . . . . . . . . 326--330
                   Nigel Boston   Strategies for the Weakest Link  . . . . 330--334
               Mitsuru Uchiyama   Proofs of Korovkin's Theorems via
                                  Inequalities . . . . . . . . . . . . . . 334--336
                   Peter Walker   The Zeros of the Partial Sums of the
                                  Exponential Series . . . . . . . . . . . 337--339
                 Marty Getz and   
                    Dixon Jones   Problem 11005  . . . . . . . . . . . . . 340--340
               Bogdan Suceav\ua   Problem 11006  . . . . . . . . . . . . . 340--340
Western Maryland College Problems Group   Problem 11007  . . . . . . . . . . . . . 340--340
José Luis Díaz-Barrero and   
       Juan José Egozcue   Problem 11008  . . . . . . . . . . . . . 340--340
              David Borwein and   
        Jonathan M. Borwein and   
                    Jamal Rooin   Problem 11009  . . . . . . . . . . . . . 341--341
                 Erwin Just and   
            Norman Schaumberger   Problem 11010  . . . . . . . . . . . . . 341--341
                    George Lamb   Problem 11011  . . . . . . . . . . . . . 341--341
Zoltán Sasvári and   
                  Richard Stong   Approximating the Binomial Distribution:
                                  10876  . . . . . . . . . . . . . . . . . 341--342
Pál Péter Dályay and   
             Said Amghibech and   
                   David Callan   Another Binomial Coefficient Identity:
                                  10878  . . . . . . . . . . . . . . . . . 342--343
             Nick MacKinnon and   
                   John C. Cock   Tiling Squares with Rectangles: 10883    343--344
Joaquín Gómez Rey and   
           Albert Nijenhuis and   
            Doyle Henderson and   
         Damuele Riccarelli and   
                  Richard Stong   An Unexpected Integer: 10886 . . . . . . 344--345
              Jean Anglesio and   
             Said Amghibech and   
     GCHQ Problem Solving Group   Six Incenters on a Conic: 10887  . . . . 346--347
         William P. Wardlaw and   
         William D. Withers and   
                Ellen Hertz and   
             Horst Brunotte and   
     GCHQ Problem Solving Group   Homomorphisms of Quasigroups: 10888  . . 347--347
             Richard Montgomery   Book Review: \booktitle[untitled]  . . . 348--353
                  Jeffrey Rauch   Book Review: \booktitle[untitled]  . . . 353--357
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 358--359
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 5, May, 2003

             Charles Livingston   Enhanced Linking Numbers . . . . . . . . 361--385
            Mourad Ba\"\iou and   
                Michel Balinski   Admissions and Recruitment . . . . . . . 386--399
          János Pach and   
                   Rom Pinchasi   How Many Unit Equilateral Triangles Can
                                  Be Generated by N Points in Convex
                                  Position?  . . . . . . . . . . . . . . . 400--406
                Byron Schmuland   Random Harmonic Series . . . . . . . . . 407--416
                     Hud Hudson   Four Colors Do Not Suffice . . . . . . . 417--423
                John Duncan and   
              Colin M. McGregor   Carleman's Inequality  . . . . . . . . . 424--431
                   M. A. Nyblom   A Note on the Solvability of a
                                  Diophantine Equation Involving Radicals  431--434
                Jonathan Sondow   Zeros of the Alternating Zeta Function
                                  on the Line R(S) = 1 . . . . . . . . . . 435--437
                C\ualin Popescu   Problem 11012  . . . . . . . . . . . . . 438--438
                   David Callan   Problem 11013  . . . . . . . . . . . . . 438--438
       Achilleas Sinefakopoulos   Problem 11014  . . . . . . . . . . . . . 438--438
                  Ovidiu Furdui   Problem 11015  . . . . . . . . . . . . . 438--438
Juan-Boscoa Romero Márquez   Problem 11016  . . . . . . . . . . . . . 439--439
              C. R. Pranesachar   Problem 11017  . . . . . . . . . . . . . 439--439
                   Slavko Simic   Problem 11018  . . . . . . . . . . . . . 439--439
              Roland Bacher and   
               Albert Nijenhuis   A Surprisingly Simple Determinant: 10891 439--440
           Stephen C. Locke and   
                  Richard Stong   Spanning Cycles in Hypercubes: 10892 . . 440--441
               Andrei Jorza and   
         John H. Lindsey II and   
         Anne-Maria Ernvall and   
                  Reijo Ernvall   Groups of Divisors: 10893  . . . . . . . 441--443
             Robert Sulanke and   
          Jose Luis Arregui and   
           Danijela Vuji\'c and   
    Nelson Castañeda and   
                   David Callan   Another Description of the Central
                                  Delannoy Numbers: 10894  . . . . . . . . 443--444
      Christopher J. Hillar and   
         Patrick J. Fitzsimmons   Convergent Series with Exponents: 10928  444--445
                   Jet Wimp and   
              Kenneth Schilling   Serendipitous Solution: 10428  . . . . . 445--445
                    A. W. Knapp   Book Review: \booktitle[untitled]  . . . 446--455
                   Marion Cohen   Book Review: \booktitle[untitled]  . . . 455--458
                      Anonymous   Telegraphic Reviews  . . . . . . . . . . 459--461
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 6, June / July, 2003

               Steven G. Krantz   A Matter of Gravity  . . . . . . . . . . 465--481
             Godfried Toussaint   Simple Proofs of a Geometric Property of
                                  Four-Bar Linkages  . . . . . . . . . . . 482--494
               Robin Hartshorne   Non-Euclidean III.36 . . . . . . . . . . 495--502
              Franklin Mendivil   Fractals, Graphs, and Fields . . . . . . 503--515
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Sums of Squares of Distances in
                                  $m$-Space  . . . . . . . . . . . . . . . 516--526
                  Martin Klazar   Counting Even and Odd Partitions . . . . 527--532
               Dragan Vukoti\'c   The Isoperimetric Inequality and a
                                  Theorem of Hardy and Littlewood  . . . . 532--536
                 Anton R. Schep   And Still One More Proof of the
                                  Radon--Nikodym Theorem . . . . . . . . . 536--538
              Michael Somos and   
                    Robert Haas   A Linked Pair of Sequences Implies the
                                  Primes Are Infinite  . . . . . . . . . . 539--540
                James D. Harper   Another Simple Proof of $ 1 + 1 / 2^2 +
                                  1 / 3^2 + \cdots = \pi^2 / 6 $ . . . . . 540--541
 Bernardo Recamán Santos   Problem 11019  . . . . . . . . . . . . . 542--542
                  M. L. Glasser   Problem 11020  . . . . . . . . . . . . . 542--542
                Donald E. Knuth   Problem 11021  . . . . . . . . . . . . . 542--542
               Razvan Satnoianu   Problem 11022  . . . . . . . . . . . . . 542--542
                    Wu Wei Chao   Problem 11023  . . . . . . . . . . . . . 542--542
         Vicen\ctiu R\uadulescu   Problem 11024  . . . . . . . . . . . . . 543--543
           Floor van Lamoen and   
                 Darij Grinberg   Problem 11025  . . . . . . . . . . . . . 543--543
                     Rick Mabry   Problem 11001  . . . . . . . . . . . . . 543--543
                Wu Wei Chao and   
                  Gerry Myerson   Divisibility Conditions Holding as Many
                                  Times as You Want: 10898 . . . . . . . . 543--544
              Richard Bagby and   
                  O. P. Lossers   Best Polynomial Approximations: 10903    544--544
               Zhibing Chen and   
                    Shusen Ding   A Higher Mean Value Theorem: 10935 . . . 544--545
        Andor Lucács and   
      Szilard András and   
               Nathan D. Cahill   Convex $n$-Gons: 10936 . . . . . . . . . 545--546
            Yves Nievergelt and   
                 Achava Nakhash   The Complex Geometric Mean: 10940  . . . 546--547
        Jeffrey C. Lagarias and   
             Thomas Hermann and   
                  O. P. Lossers   Decay of a Markov Chain: 10941 . . . . . 547--548
              Ovidiu Furdui and   
                  O. P. Lossers   An Inequality for Triangles: 10950 . . . 548--549
             David G. Schaeffer   Book Review: \booktitle[untitled]  . . . 550--553
          Jeffrey L. Nunemacher   Book Review: \booktitle[untitled]  . . . 554--557
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 7, August / September, 2003

                 Noam D. Elkies   On the Sums $ \sum_{k = - \infty
                                  }^\infty (4 k + 1)^{-n} $  . . . . . . . 561--573
                 Daniel K. Biss   Which Functor Is the Projective Line?    574--592
                   Jerry Lodder   Curvature in the Calculus Curriculum . . 593--605
             Guershon Harel and   
               Jeffrey M. Rabin   Polygons Whose Vertex Triangles Have
                                  Equal Area . . . . . . . . . . . . . . . 606--619
                   Harm Derksen   The Fundamental Theorem of Algebra and
                                  Linear Algebra . . . . . . . . . . . . . 620--623
                   Charles Thas   Projective Generalizations of Two Points
                                  of Concurrence on the Nine-Point Circle  624--627
                    Ulrich Abel   On the Lagrange Remainder of the Taylor
                                  Formula  . . . . . . . . . . . . . . . . 627--633
   Jussi Väisälä   A Proof of the Mazur--Ulam Theorem . . . 633--635
                Jonathan Sondow   Problem 11026  . . . . . . . . . . . . . 636--636
                     H. Reuvers   Problem 11027  . . . . . . . . . . . . . 636--636
             Götz Trenkler   Problem 11028  . . . . . . . . . . . . . 636--636
                     Tim Keller   Problem 11029  . . . . . . . . . . . . . 636--636
                  Steven Butler   Problem 11030  . . . . . . . . . . . . . 637--637
                        Li Zhou   Problem 11031  . . . . . . . . . . . . . 637--637
                    Mark Pinsky   Problem 11032  . . . . . . . . . . . . . 637--637
      Torben Maack Bisgaard and   
         Zsolt Páles and   
Zoltán Sasvári and   
                  Richard Bagby   Determinant of a Matrix in Two
                                  Variables: 10896 . . . . . . . . . . . . 637--638
            Gregory P. Wene and   
                  Robin Chapman   Generators of Ideals of Matrices over
                                  Finite Fields: 10897 . . . . . . . . . . 638--639
                Gordon Rice and   
          Patrick A. Staley and   
             Gerald Myerson and   
                  Robin Chapman   Angles with Rational Cosines: 10900  . . 639--639
             Emeric Deutsch and   
                  Nasha Komanda   Derangements That Don't Rise Too Fast:
                                  10902  . . . . . . . . . . . . . . . . . 639--640
         Richard P. Stanley and   
                  Robin Chapman   An Unexpected Appearance of the Catalan
                                  Numbers: 10905 . . . . . . . . . . . . . 640--642
            Donald E. Knuth and   
               C. P. Rupert and   
                 Alex Smith and   
                  Richard Stong   Recounting the Rationals, Continued:
                                  10906  . . . . . . . . . . . . . . . . . 642--643
                John H. Hubbard   Book Review: \booktitle[untitled]  . . . 644--649
                Marion D. Cohen   Book Review: \booktitle[untitled]  . . . 650--652
                     Ranjan Roy   Book Review: \booktitle[untitled]  . . . 652--657
                      Anonymous   Telegraphic Reviews  . . . . . . . . . . 658--660
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 8, October, 2003

              Charles W. Curtis   Richard Brauer: Sketches from His Life
                                  and Work . . . . . . . . . . . . . . . . 665--678
              Hans Havlicek and   
              Gunter Weiß   Altitudes of a Tetrahedron and Traceless
                                  Quadratic Forms  . . . . . . . . . . . . 679--693
               Daniel J. Acosta   Newton's Rule of Signs for Imaginary
                                  Roots  . . . . . . . . . . . . . . . . . 694--706
              Matthias Beck and   
                Moshe Cohen and   
              Jessica Cuomo and   
                 Paul Gribelyuk   The Number of ``Magic'' Squares, Cubes,
                                  and Hypercubes . . . . . . . . . . . . . 707--717
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Third William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 718--726
            Razvan A. Satnoianu   Erd\Hos--Mordell-Type Inequalities in a
                                  Triangle . . . . . . . . . . . . . . . . 727--729
                   Chris Impens   Stirling's Series Made Easy  . . . . . . 730--735
           Nicolas Lichiardopol   A New Proof of Wedderburn's Theorem  . . 736--737
            Karim Boulabiar and   
                  Gerard Buskes   After the Determinants Are down: a
                                  Criterion for Invertibility  . . . . . . 737--741
            M. N. Deshpande and   
                  R. M. Welukar   Problem 11033  . . . . . . . . . . . . . 742--742
             William P. Wardlaw   Problem 11034  . . . . . . . . . . . . . 742--742
                   Omer Yayenie   Problem 11035  . . . . . . . . . . . . . 742--742
                  M. L. Glasser   Problem 11036  . . . . . . . . . . . . . 743--743
                M. L. J. Hautus   Problem 11037  . . . . . . . . . . . . . 743--743
               Floor van Lamoen   Problem 11038  . . . . . . . . . . . . . 743--743
             Noah Rosenberg and   
                  Richard Stong   Problem 11039  . . . . . . . . . . . . . 743--743
                Greg Martin and   
             Jonathan Bloom and   
                   Dan Saracino   Three Proper Subgroups Covering a Group:
                                  10911  . . . . . . . . . . . . . . . . . 743--744
              Jean Anglesio and   
            Kenneth F. Andersen   A Recursively Defined Series for $ \pi /
                                  4 $: 10912 . . . . . . . . . . . . . . . 744--745
           Giovanni Falcone and   
              Richard Stong and   
                  Nasha Komanda   A Combination of Cyclotomic Polynomials:
                                  10914  . . . . . . . . . . . . . . . . . 745--746
           Gertrude Ehrlich and   
                  Reiner Martin   The Jug Problem with a Source and a
                                  Sink: 10916  . . . . . . . . . . . . . . 746--746
               Mathias Beck and   
                  Nasha Komanda   A Congruence Involving Ceilings: 10918   746--747
  André Kündgen and   
         Radhika Ramamurthi and   
                  Reiner Martin   Maximal Paths in Bipartite Graphs: 10920 747--747
               Marcin Mazur and   
            Roberto Tauraso and   
                Michel Bataille   A Root Inequality: 10944 . . . . . . . . 747--749
                    Alex Kasman   Book Review: \booktitle[untitled]  . . . 750--754
                 Warwick Tucker   Book Review: \booktitle[untitled]  . . . 754--759
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 9, November, 2003

      Iva\"\ilo M. Mladenov and   
                     John Oprea   The Mylar Balloon Revisited  . . . . . . 761--784
           Karanbir S. Sarkaria   Tetrahedron ABCD of Width 1 with Minimum
                                  AB + BC + CD . . . . . . . . . . . . . . 785--799
                 Stephen McAdam   Bell's Theorem and the Demise of Local
                                  Reality  . . . . . . . . . . . . . . . . 800--811
               Chris Groër   The Mathematics of Survival: From
                                  Antiquity to the Playground  . . . . . . 812--825
               Kamal Poorrezaei   Two Proofs of Graves's Theorem . . . . . 826--830
             Jeongseon Baek and   
               Dong-Soo Kim and   
                   Young Ho Kim   A Characterization of the Unit Sphere    830--833
              Michael W. Botsko   An Elementary Proof of Lebesgue's
                                  Differentiation Theorem  . . . . . . . . 834--838
                 Nikita Sidorov   Almost Every Number Has a Continuum of $
                                  \beta $-Expansions . . . . . . . . . . . 838--842
                    Yongge Tian   Problem 11040  . . . . . . . . . . . . . 843--843
                  Oscar Ciaurri   Problem 11041  . . . . . . . . . . . . . 843--843
            M. N. Deshpande and   
                 Kavita Laghate   Problem 11042  . . . . . . . . . . . . . 843--844
                 Michael Golomb   Problem 11043  . . . . . . . . . . . . . 844--844
                Michel Bataille   Problem 11044  . . . . . . . . . . . . . 844--844
            Manoj Prakash Singh   Problem 11045  . . . . . . . . . . . . . 844--844
               Christoph Soland   Problem 11046  . . . . . . . . . . . . . 844--844
            Donald E. Knuth and   
                  Reiner Martin   Products of Transpositions: 10913  . . . 844--845
               C. P. Rupert and   
                  Richard Stong   A Sequence of Integer Polynomials: 10915 845--845
                Lajos Csete and   
                        Li Zhou   Distances to the Sides: 10929  . . . . . 845--846
               Vasile Mihai and   
                        Li Zhou   A Tetrahedron with All Faces Congruent:
                                  10934  . . . . . . . . . . . . . . . . . 846--847
              Aleksandar Ivi\'c   Zetafunctionology: 10939 . . . . . . . . 847--848
               Slavko Simic and   
                 Said Amghibech   An Appell-ing Inequality: 10945  . . . . 848--849
             Stevo Stevi\'c and   
                  Allen Stenger   Asymptotics of a Recurrence: 10946 . . . 849--850
                    Rudy Rucker   Book Review: \booktitle[untitled]  . . . 851--861
            Krishnaswami Alladi   Book Review: \booktitle[untitled]  . . . 861--865
                      Anonymous   Telegraphic Reviews  . . . . . . . . . . 866--868
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 110, Number 10, December, 2003

             Daniel Drucker and   
            Stephen A. Williams   When Does Water Find the Shortest Path
                                  Downhill? The Geometry of Steepest
                                  Descent Curves . . . . . . . . . . . . . 869--885
                 Susanna S. Epp   The Role of Logic in Teaching Proof  . . 886--899
                   Allan Pinkus   Negative Theorems in Approximation
                                  Theory . . . . . . . . . . . . . . . . . 900--911
        Richard E. Chandler and   
              Carl D. Meyer and   
               Nicholas J. Rose   Eudoxus Meets Cayley . . . . . . . . . . 912--927
                    Frank Blume   A Localized Probabilistic Approach to
                                  Circuit Analysis . . . . . . . . . . . . 928--936
               Inta Bertuccioni   A Topological Puzzle . . . . . . . . . . 937--939
               David C. Ullrich   The Ascoli--Arzel\`a Theorem via
                                  Tychonoff's Theorem  . . . . . . . . . . 939--940
                  PL. Kannappan   Klee's Trigonometry Problem  . . . . . . 940--944
                      Paul Loya   Green's Theorem and the Fundamental
                                  Theorem of Algebra . . . . . . . . . . . 944--946
            Dominique Hulin and   
                  Marc Troyanov   Mean Curvature and Asymptotic Volume of
                                  Small Balls  . . . . . . . . . . . . . . 947--950
                 C. W. Groetsch   Timing Is Everything: The French
                                  Connection . . . . . . . . . . . . . . . 950--955
                Syrous Marivani   Problem 11047  . . . . . . . . . . . . . 956--956
              Matthias Beck and   
               Marcin Mazur and   
               Shelemyahu Zacks   Problem 11048  . . . . . . . . . . . . . 956--956
                   Vasile Mihai   Problem 11049  . . . . . . . . . . . . . 956--956
                    Kent Holing   Problem 11050  . . . . . . . . . . . . . 957--957
                 Nick MacKinnon   Problem 11051  . . . . . . . . . . . . . 957--957
               Danrun Huang and   
                  Daniel Scully   Problem 11052  . . . . . . . . . . . . . 957--957
                    Wu Wei Chao   Problem 11053  . . . . . . . . . . . . . 958--958
             David M. Bloom and   
     Christopher N. Swanson and   
              Kenneth Schilling   A Convolution of Middle Binomial
                                  Coefficients: 10921  . . . . . . . . . . 958--959
              Mizan R. Khan and   
              Michael R. Avidon   The Sum of Divisors Won't Die: 10922 . . 959--959
               David Callan and   
                   Harris Kwong   A Permanent Fixture: 10925 . . . . . . . 960--960
          Harold G. Diamond and   
                        Li Zhou   A Continued Fraction for an Arctan
                                  Difference: 10926  . . . . . . . . . . . 960--961
        Jean-Pierre Grivaux and   
              Allen Stenger and   
          J. Ernest Wilkins Jr.   A Rational Definite Integral: 10938  . . 961--962
                 Erwin Just and   
        Norman Schaumberger and   
                 Albert Stadler   Points on a Circle: 10954  . . . . . . . 962--963
                      Anonymous   Erratum: Anagrammatical Attribution:
                                  11021  . . . . . . . . . . . . . . . . . 963--963
                     Ed Waymire   Book Review: \booktitle[untitled]  . . . 964--967
                Marion D. Cohen   Book Review: \booktitle[untitled]  . . . 968--969
               Daniel Gottesman   Book Review: \booktitle[untitled]  . . . 969--972
                      Anonymous   Volume Information . . . . . . . . . . . 973--984
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 111, Number 1, January, 2004

          Ivor Grattan-Guinness   History or Heritage? An Important
                                  Distinction in Mathematics and for
                                  Mathematics Education  . . . . . . . . . 1--12
         Michael A. Bennett and   
                  Bruce Reznick   Positive Rational Solutions to $ x^y =
                                  y^{m x} $: a Number-Theoretic Excursion  13--21
         Richard P. Jerrard and   
                 John E. Wetzel   Prince Rupert's Rectangles . . . . . . . 22--31
           Steven G. Krantz and   
              Jeffery D. McNeal   Creating More Convergent Series  . . . . 32--38
                Burkard Polster   Variations on a Theme in Paper Folding   39--47
                     Sey Y. Kim   An Elementary Proof of the Quadratic
                                  Reciprocity Law  . . . . . . . . . . . . 48--50
             Götz Trenkler   Matrices Which Take a Given Vector into
                                  a Given Vector: Revisited  . . . . . . . 50--52
                Thomas J. Osler   Finding $ \zeta (2 p) $ from a Product
                                  of Sines . . . . . . . . . . . . . . . . 52--54
                 S. H. Kulkarni   A Very Simple and Elementary Proof of a
                                  Theorem of Ingelstam . . . . . . . . . . 54--58
                W. A. Beyer and   
                Andrew Zardecki   The Early History of the Ham Sandwich
                                  Theorem  . . . . . . . . . . . . . . . . 58--61
            Alexander R. Perlis   Roots Appear in Quanta . . . . . . . . . 61--63
                 Shahin Amrahov   Problem 11054  . . . . . . . . . . . . . 64--64
               Razvan Satnoianu   Problem 11055  . . . . . . . . . . . . . 64--64
             John H. Lindsey II   Problem 11056  . . . . . . . . . . . . . 64--64
       Zahlreich Problems Group   Problem 11057  . . . . . . . . . . . . . 64--64
           Óscar Ciaurri   Problem 11058  . . . . . . . . . . . . . 64--64
                    Mark Bowron   Problem 11059  . . . . . . . . . . . . . 64--65
           Matthew Coppenbarger   Problem 11060  . . . . . . . . . . . . . 65--65
               Peter Walker and   
                     Tom Zerger   The Centroid-Circumcenter Distance:
                                  10948  . . . . . . . . . . . . . . . . . 65--66
                 Leroy Quet and   
     GCHQ Problem Solving Group   Functionally Related Convergents: 10953  66--67
           Razvan Satnoianu and   
                   Isaac Sofair   More Triangle Inequalities: 10955  . . . 67--69
             George L. Lamb and   
          Stephen J. Herschkorn   Hypergeometric and Other
                                  Representations: 10959 . . . . . . . . . 69--71
       Mihály Bencze and   
                        Li Zhou   Cosine Inequalities: 10962 . . . . . . . 71--71
                Anthony Ralston   Book Review: \booktitle[untitled]  . . . 72--75
                      Anonymous   [untitled] . . . . . . . . . . . . . . . 75--81
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 82--84
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 85--88
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 2, February, 2004

                   Susan Landau   Polynomials in the Nation's Service:
                                  Using Algebra to Design the Advanced
                                  Encryption Standard  . . . . . . . . . . 89--117
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Isoperimetric and Isoparametric Problems 118--136
                  Charles Radin   Orbits of Orbs: Sphere Packing Meets
                                  Penrose Tilings  . . . . . . . . . . . . 137--149
               Fabrizio Zanello   When Are There Infinitely Many
                                  Irreducible Elements in a Principal
                                  Ideal Domain?  . . . . . . . . . . . . . 150--152
                 David Avis and   
                 Bohdan Kaluzny   Solving Inequalities and Proving
                                  Farkas's Lemma Made Easy . . . . . . . . 152--157
                 Suk-Geun Hwang   Cauchy's Interlace Theorem for
                                  Eigenvalues of Hermitian Matrices  . . . 157--159
                Michael Schmitt   New Designs for the Descartes Rule of
                                  Signs  . . . . . . . . . . . . . . . . . 159--164
                    Wu Wei Chao   Problem 11061  . . . . . . . . . . . . . 165--165
              Kenneth Schilling   Problem 11062  . . . . . . . . . . . . . 165--165
                   Slavko Simic   Problem 11063  . . . . . . . . . . . . . 165--165
                    John Wetzel   Problem 11064  . . . . . . . . . . . . . 165--165
                      Anonymous   Correction: 11034  . . . . . . . . . . . 166--166
               Douglas B. Tyler   Problem 11065  . . . . . . . . . . . . . 166--166
             Sebastian Cioab\ua   Problem 11066  . . . . . . . . . . . . . 166--166
                    George Lamb   Problem 11067  . . . . . . . . . . . . . 166--166
            Donald E. Knuth and   
                  Robin Chapman   Fibonacci in Complex Camouflage: 10858   166--167
        Jeffrey C. Lagarias and   
                E. M. Rains and   
            N. J. A. Sloane and   
                  Nasha Komanda   The EKG Sequence: 10927  . . . . . . . . 167--168
            Paul Schweitzer and   
              Xiaoshen Wang and   
National Security Agency Problems Group   Too Much Commuting: 10930  . . . . . . . 168--169
             Robert DeSario and   
                 LeRoy Wenstrom   Invertible Shuffles: 10931 . . . . . . . 169--170
               Paul Lescott and   
                      Tom Jager   A Group Determined by Relations?: 10933  170--171
            David G. Wagner and   
               Patrick Corn and   
                        Li Zhou   A Cyclotomic Sum: 10937  . . . . . . . . 171--172
          Victor Alexandrov and   
                      Knut Dale   Using Stokes's Theorem on the Sphere:
                                  10957  . . . . . . . . . . . . . . . . . 172--172
                 Steven R. Bell   Book Review: \booktitle[untitled]  . . . 173--176
              Margaret M. Bayer   Book Review: \booktitle[untitled]  . . . 177--180
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 181--184
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 3, March, 2004

            Robert E. Megginson   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award to T. Christine Stevens for
                                  Distinguished Service to Mathematics . . 185--188
               Alan Edelman and   
                 Gilbert Strang   Pascal Matrices  . . . . . . . . . . . . 189--197
          William T. Ingram and   
            William S. Mahavier   Interesting Dynamics and Inverse Limits
                                  in a Family of One-Dimensional Maps  . . 198--215
       Jaume Paradís and   
                  Josep Pla and   
          Pelegrí Viader   Fermat and the Quadrature of the Folium
                                  of Descartes . . . . . . . . . . . . . . 216--229
                  Detlef Gronau   The Spiral of Theodorus  . . . . . . . . 230--237
         Leslie Blackwell Galen   Putting Fractions in Their Place . . . . 238--242
            Tsuneo Ishikawa and   
            Nobuhiko Ishida and   
               Yoshito Yukimoto   On Prime Factors of $ A^n - 1 $  . . . . 243--245
           Lou M. Pretorius and   
            Konrad J. Swanepoel   An Algorithmic Proof of the
                                  Motzkin--Rabin Theorem on Monochrome
                                  Lines  . . . . . . . . . . . . . . . . . 245--251
                  Martin Engman   A Note on Isometric Embeddings of
                                  Surfaces of Revolution . . . . . . . . . 251--255
                      T. Y. Lam   On Subgroups of Prime Index  . . . . . . 256--258
                   Herbert Wilf   Problem 11068  . . . . . . . . . . . . . 259--259
      Péter Ivády   Problem 11069  . . . . . . . . . . . . . 259--259
                Roberto Tauraso   Problem 11070  . . . . . . . . . . . . . 259--259
                 Emeric Deutsch   Problem 11071  . . . . . . . . . . . . . 259--259
                    George Lamb   Problem 11072  . . . . . . . . . . . . . 259--259
         Vicen\ctiu R\uadulescu   Problem 11073  . . . . . . . . . . . . . 260--260
                Dimiter Skordev   Problem 11074  . . . . . . . . . . . . . 260--260
              Roland Bacher and   
              Robin Chapman and   
                  Reiner Martin   A Determinant of Indeterminates: 10859   260--261
     Jürgen Groß and   
         Götz Trenkler and   
                  Xiaoshen Wang   Product and Sum of Projections: 10917    261--262
              Christian Bey and   
                    Garth Isaak   Maximum Antichains of Sets of Distinct
                                  Sizes: 10932 . . . . . . . . . . . . . . 262--263
             Walther Janous and   
                  J. P. V. Abad   Maximum Antichains in the Divisor
                                  Lattice: 10942 . . . . . . . . . . . . . 263--263
            C\ualin Popescu and   
     GCHQ Problem Solving Group   A Divisibility Result: 10943 . . . . . . 264--264
           Jeffrey Lagarias and   
                 Walther Janous   A Generous Bound for Divisor Sums: 10949 264--265
               David Callan and   
                   M. A. Prasad   Counting a Set of Rooted Trees: 10952    265--266
               Brian Conrad and   
             Gheorge Simion and   
                   Patrick Corn   Pi and Rationals: 10961  . . . . . . . . 266--266
                 John B. Little   Book Review: \booktitle[untitled]  . . . 267--271
             Stephen A. Fulling   Book Review: \booktitle[untitled]  . . . 271--275
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 276--278
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 279--280
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 4, April, 2004

                    Roe Goodman   Alice through Looking Glass after
                                  Looking Glass: The Mathematics of
                                  Mirrors and Kaleidoscopes  . . . . . . . 281--298
              Geoffrey Grimmett   Stochastic Apportionment . . . . . . . . 299--307
           Pirooz Mohazzabi and   
            Thomas A. Fournelle   Evaluation of Ill-Behaved Power Series   308--321
          Curtis D. Bennett and   
             A. M. W. Glass and   
 Gábor J. Székely   Fermat's Last Theorem for Rational
                                  Exponents  . . . . . . . . . . . . . . . 322--329
            Bruce C. Berndt and   
                    C. A. Reddi   Two Exams Taken by Ramanujan in India    330--339
               Asuman Aksoy and   
                 Mario Martelli   The Wave Equation, Mixed Partial
                                  Derivatives, and Fubini's Theorem  . . . 340--347
                  Dov Samet and   
                 Iddo Samet and   
               David Schmeidler   One Observation behind Two-Envelope
                                  Puzzles  . . . . . . . . . . . . . . . . 347--351
                    E. Kowalski   On the ``Reducibility'' of Arctangents
                                  of Integers  . . . . . . . . . . . . . . 351--354
                    Paul Monsky   Kepler's First Law: a Remark . . . . . . 355--356
            Hervé Perdry   An Elementary Proof of Krull's
                                  Intersection Theorem . . . . . . . . . . 356--357
                 Jacob Mostovoy   Lattices in $ \mathbb {C} $ and Finite
                                  Subsets of a Circle  . . . . . . . . . . 357--360
             Götz Trenkler   Problem 11075  . . . . . . . . . . . . . 361--361
                      Joel Zinn   Problem 11076  . . . . . . . . . . . . . 361--361
              Gheorge Costovici   Problem 11077  . . . . . . . . . . . . . 361--361
                   Donald Knuth   Problem 11078  . . . . . . . . . . . . . 361--361
                 Brian Cook and   
                James Whitenton   Problem 11079  . . . . . . . . . . . . . 361--362
               Razvan Satnoianu   Problem 11080  . . . . . . . . . . . . . 362--362
                  Stephen Morse   Problem 11081  . . . . . . . . . . . . . 362--362
  LSU Problem Solving Group and   
            Marc A. Chamberland   A Sequence of Composite Numbers: 10947   362--363
               Sung Soo Kim and   
                        Li Zhou   A Sticky Problem: 10951  . . . . . . . . 363--364
              John McCarthy and   
                 Lee Badger and   
                  Marc Williams   The Tower of Stanford: 10956 . . . . . . 364--365
                 Oliver Eng and   
                        Li Zhou   Sliding Dominoes: 10960  . . . . . . . . 365--366
              M. L. Glosser and   
                  J. A. Grzesik   A Nontrivial Zero.: 11020  . . . . . . . 366--367
     Vicen\ctiu R\uadulescu and   
                  Richard Stong   A Limit Problem: 11024 . . . . . . . . . 367--368
               Daniel R. Farkas   Book Review: \booktitle[untitled]  . . . 369--372
                      Paul Zorn   Book Review: \booktitle[untitled]  . . . 373--375
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 376--376
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 5, May, 2004

                Donald G. Saari   Geometry of Chaotic and Stable
                                  Discussions  . . . . . . . . . . . . . . 377--393
              Maya Mohsin Ahmed   How Many Squares Are There, Mr.
                                  Franklin?: Constructing and Enumerating
                                  Franklin Squares . . . . . . . . . . . . 394--410
         Barbara S. Edwards and   
                Michael B. Ward   Surprises from Mathematics Education
                                  Research: Student (Mis)use of
                                  Mathematical Definitions . . . . . . . . 411--424
                 Jeroen Spandaw   Dissecting Cuboids into Cuboids  . . . . 425--429
               Hirofumi Tsumura   An Elementary Proof of Euler's Formula
                                  for $ \zeta (2 m) $  . . . . . . . . . . 430--431
          Grzegorz Rz\kadkowski   A Short Proof of the Explicit Formula
                                  for Bernoulli Numbers  . . . . . . . . . 432--434
               Raymond T. Boute   Moving a Rectangle around a Corner:
                                  Geometrically  . . . . . . . . . . . . . 435--437
          Christoph Leuenberger   An Old Friend Revisited  . . . . . . . . 437--439
                    Wu Wei Chao   Problem 11082  . . . . . . . . . . . . . 440--440
             William P. Wardlaw   Problem 11083  . . . . . . . . . . . . . 440--440
                  H. A. ShahAli   Problem 11084  . . . . . . . . . . . . . 440--440
              Matthias Beck and   
              Jesus DeLoera and   
               Mike Develin and   
                 Julian Pfeifle   Problem 11085  . . . . . . . . . . . . . 440--440
               Stephen C. Locke   Problem 11086  . . . . . . . . . . . . . 440--441
              Robin Chapman and   
             Nicholas C. Singer   Eigenvalues of a Bidiagonal Matrix:
                                  10958  . . . . . . . . . . . . . . . . . 441--441
                 Michael Golomb   Problem 11087  . . . . . . . . . . . . . 441--441
              Richard Holzsager   Problem 11088  . . . . . . . . . . . . . 441--441
             Paul Deiermann and   
             Cape Girardeau and   
            Joseph Chalmers and   
            George L. Lamb, Jr.   An Application of the Mellin Transform:
                                  10963  . . . . . . . . . . . . . . . . . 441--443
            Douglas B. West and   
                  Csaba Megyeri   Adjacency Matrices That Are Incidence
                                  Matrices: 10967  . . . . . . . . . . . . 443--443
           Stephen C. Locke and   
             Philip D. Straffin   The Game of Pathos: 10968  . . . . . . . 443--444
            Vitaly Voloshin and   
    José Heber Nieto and   
      Edward R. Scheinerman and   
                  Robin Chapman   Plucking Stirling Numbers from Trees:
                                  10976  . . . . . . . . . . . . . . . . . 444--445
                Carl Axness and   
                  Bert Kerr and   
  Jean-François Chamayou   Incomplete Gamma and Error Functions:
                                  10977  . . . . . . . . . . . . . . . . . 445--447
               Donald Knuth and   
             BSI Problems Group   Some Bernstein Polynomials: 10985  . . . 447--447
                G. E. Fasshauer   Book Review: \booktitle[untitled]  . . . 448--452
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 453--455
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 456--460
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 461--464
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 6, June / July, 2004

             David E. Zitarelli   The Origin and Early Impact of the Moore
                                  Method . . . . . . . . . . . . . . . . . 465--486
                     Henry Cohn   Projective Geometry over $ \mathbb {F}_1
                                  $ and the Gaussian Binomial Coefficients 487--495
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   A Fresh Look at the Method of Archimedes 496--508
                     Casey Mann   Heesch's Tiling Problem  . . . . . . . . 509--517
               Gilbert Helmberg   A Construction Concerning $ (l^p)^\prime
                                  \subset l^q $  . . . . . . . . . . . . . 518--520
                       Kehe Zhu   Translating Inequalities between Hardy
                                  and Bergman Spaces . . . . . . . . . . . 520--525
                  Xiaoshen Wang   A Simple Proof of Descartes's Rule of
                                  Signs  . . . . . . . . . . . . . . . . . 525--526
             Sam B. Nadler, Jr.   Another Proof That $ R^3 $ Has No Square
                                  Root . . . . . . . . . . . . . . . . . . 527--528
            Steven H. Weintraub   An Interesting Recursion . . . . . . . . 528--530
             Gregory P. Dresden   On the Middle Coefficient of a
                                  Cyclotomic Polynomial  . . . . . . . . . 531--533
                    Sun Soo Kim   Problem 11089  . . . . . . . . . . . . . 534--534
                   Florian Luca   Problem 11090  . . . . . . . . . . . . . 534--534
                   David Callan   Problem 11091  . . . . . . . . . . . . . 534--534
                 Arturo Magidin   Problem 11092  . . . . . . . . . . . . . 534--535
                  Richard Bagby   Problem 11093  . . . . . . . . . . . . . 535--535
                Michel Bataille   Problem 11094  . . . . . . . . . . . . . 535--535
                   Vasile Mihai   Problem 11095  . . . . . . . . . . . . . 535--535
              H. A. ShahAli and   
                    Hamza Ahmad   Graceful Permutations Revisited: 10964   535--536
      Jean-Marie De Koninck and   
                    Stefan Gubo   When the Totient Is the Product of the
                                  Squared Prime Divisors: 10966  . . . . . 536--536
            Richard Stanley and   
                  O. P. Lossers   Comparing Odd Parts in Conjugate
                                  Partitions: 10969  . . . . . . . . . . . 536--539
               C. P. Rupert and   
                  Richard Stong   The First Fibonacci Number Divisible by
                                  a Prime p: 10971 . . . . . . . . . . . . 539--540
               Tim Ferguson and   
            M. D. Frederick and   
                Lenny Jones and   
         Stephen M. Gagola, Jr.   The LCM of the Parts of a Partition:
                                  10972  . . . . . . . . . . . . . . . . . 540--541
             Emeric Deutsch and   
            Julio Kuplinsky and   
                   Tina Garrett   Enumeration of Permutations by Disorder:
                                  10975  . . . . . . . . . . . . . . . . . 541--541
               Douglas R. Shier   Book Review: \booktitle[untitled]  . . . 542--545
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 546--548
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 7, August / September, 2004

                Joan R. Leitzel   The 2003 James R. C. Leitzel Lecture:
                                  Mathematics' Response to Issues in
                                  Higher Education . . . . . . . . . . . . 549--558
               Reinhard Diestel   On Infinite Cycles in Graphs: Or How to
                                  Make Graph Homology Interesting  . . . . 559--571
            Torsten Ekedahl and   
                     Dan Laksov   Two ``Generic'' Proofs of the Spectral
                                  Mapping Theorem  . . . . . . . . . . . . 572--585
                Federico Ardila   The Number of Halving Circles  . . . . . 586--591
                   Darko Veljan   Geometry and Convexity of $ \cos {\sqrt
                                  {x}} $ . . . . . . . . . . . . . . . . . 592--595
                     Bau-Sen Du   A Simple Proof of Sharkovsky's Theorem   595--599
               Tyler Jarvis and   
                   James Tanton   The Hairy Ball Theorem via Sperner's
                                  Lemma  . . . . . . . . . . . . . . . . . 599--603
               Kenzi Satô   Some Subgroups of $ {\rm SO}_3 (\mathbb
                                  {R}) $ Isomorphic to the Free Product $
                                  (\mathbb {Z} / 2 \mathbb {Z}) \ast
                                  (\mathbb {Z} / 3 \mathbb {Z}) $  . . . . 603--607
                  V. I. Arnol'd   From Hilbert's Superposition Problem to
                                  Dynamical Systems  . . . . . . . . . . . 608--624
                 Said Amghibech   Problem 11096  . . . . . . . . . . . . . 625--625
                     Kevin Ford   Problem 11097  . . . . . . . . . . . . . 625--625
         Christopher Hillar and   
                    Darren Rhea   Problem 11098  . . . . . . . . . . . . . 625--625
              Matthias Beck and   
          Richard Ehrenborg and   
               Thomas Zaslavsky   Problem 11099  . . . . . . . . . . . . . 625--626
                C\ualin Popescu   Problem 11100  . . . . . . . . . . . . . 626--626
                Earl F. Skelton   Problem 11101  . . . . . . . . . . . . . 626--626
                     Leroy Quet   Problem 11102  . . . . . . . . . . . . . 626--626
           Razvan Satnoianu and   
                 John G. Heuver   Comparison of Some Squared Distances:
                                  10970  . . . . . . . . . . . . . . . . . 626--627
                L. D. Servi and   
                  Richard Stong   A Disguised Half-Angle Iteration: 10973  627--628
            Syrous Marivani and   
                     Bill Mixon   Digital Roots of Fibonacci Numbers:
                                  10974  . . . . . . . . . . . . . . . . . 628--628
             Emeric Deutsch and   
            Julio Kuplinsky and   
                   Tina Garrett   Enumeration of Permutations by Disorder:
                                  10975  . . . . . . . . . . . . . . . . . 628--629
        Jean-Pierre Grivaux and   
              Tsehaye Andebrhan   Nonnegative Polynomials: 10978 . . . . . 629--630
        Donald P. Minassian and   
                     K. P. Hart   Simple Discontinuities: 10979  . . . . . 630--630
             Nicholas C. Singer   A Divisibility Property of a Recurrence:
                                  10981  . . . . . . . . . . . . . . . . . 631--631
                Yuming Chen and   
                Olaf Krafft and   
                Martin Schaefer   Variation of a Ukrainian Olympiad
                                  Problem: 10982 . . . . . . . . . . . . . 631--632
               Herbert Wilf and   
                  J. A. Grzesik   An Arc Cotangent Series: 10986 . . . . . 632--632
                  David W. Boyd   Book Review: \booktitle[untitled]  . . . 633--636
             Arthur T. Benjamin   Book Review: \booktitle[untitled]  . . . 636--638
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 639--641
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 642--644
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 8, October, 2004

            Steven R. Finch and   
                 John E. Wetzel   Lost in a Forest . . . . . . . . . . . . 645--654
                 Olga Holtz and   
            Volker Mehrmann and   
                 Hans Schneider   Potter, Wielandt, and Drazin on the
                                  Matrix Equation $ A B = \omega B A $:
                                  New Answers to Old Questions . . . . . . 655--667
                  Joel Anderson   Iterated Exponentials  . . . . . . . . . 668--679
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Fourth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 680--690
              Joseph A. Gallian   The First Sixty-Six Years of the Putnam
                                  Competition  . . . . . . . . . . . . . . 691--699
              Kenneth Glass and   
                   Chi-Keung Ng   A Simple Proof of the Hook Length
                                  Formula  . . . . . . . . . . . . . . . . 700--704
              R. L. Devaney and   
                 K. Josi\'c and   
            M. Moreno Rocha and   
                    P. Seal and   
                 Y. Shapiro and   
                  A. T. Frumosu   Playing Catch-up with Iterated
                                  Exponentials . . . . . . . . . . . . . . 704--709
                Daniel A. Klain   An Intuitive Derivation of Heron's
                                  Formula  . . . . . . . . . . . . . . . . 709--712
                     Lars Olsen   A New Proof of Darboux's Theorem . . . . 713--715
                   M. F. Atiyah   Bakerian Lecture, 1975: Global Geometry  716--723
           Gregory Galperin and   
                Hillel Gauchman   Problem 11103  . . . . . . . . . . . . . 724--724
         Vicen\ctiu R\uadulescu   Problem 11104  . . . . . . . . . . . . . 724--724
  Juan-Bosco Romero Marquez and   
              Rick Luttmann and   
           Miguel de Guzman and   
            G. Donald Chakerian   Problem 11105  . . . . . . . . . . . . . 724--725
                   David Callan   Problem 11106  . . . . . . . . . . . . . 725--725
            Michel Émery   Problem 11107  . . . . . . . . . . . . . 725--725
                 Emeric Deutsch   Problem 11108  . . . . . . . . . . . . . 725--725
              Solomon W. Golomb   Problem 11109  . . . . . . . . . . . . . 725--725
              Matthias Beck and   
              Jesus DeLoera and   
               Mike Develin and   
                 Julian Pfeifle   Problem 11085  . . . . . . . . . . . . . 725--725
                Wu Wei Chao and   
                Doyle Henderson   Continuous Additive Functions: 10854 . . 725--726
              John Melville and   
               Jason Heller and   
                    Stony Brook   A Classic Pointed Triangle Inequality:
                                  10965  . . . . . . . . . . . . . . . . . 726--726
           Bogdan Suceav\ua and   
              C. G. Petalas and   
                  T. P. Vidalis   Orthocenter Projection: 10983  . . . . . 726--728
                Yongge Tian and   
                     Carl Meyer   Injective Properties of Complex
                                  Matrices: 10984  . . . . . . . . . . . . 728--728
          Kumar N. Prasanna and   
               B. G. Shenoy and   
                  J. A. Grzesik   Polynomial Nullstellen Avoidance: 10987  729--729
                Wu Wei Chao and   
            Doyle Henderson and   
            John H. Lindsey, II   An Iterative Sequence: 10988 . . . . . . 729--731
               Steven G. Krantz   Book Review: \booktitle[untitled]  . . . 732--735
                Marion D. Cohen   Book Review: \booktitle[untitled]  . . . 735--738
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 739--740
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 9, November, 2004

                Colin Adams and   
             Thomas Fleming and   
             Christopher Koegel   Brunnian Clothes on the Runway: Not for
                                  the Bashful  . . . . . . . . . . . . . . 741--748
                  Ehud Friedgut   Hypergraphs, Entropy, and Inequalities   749--760
                 Skip Garibaldi   The Characteristic Polynomial and
                                  Determinant Are Not Ad Hoc Constructions 761--778
                    Marc Frantz   How Conics Govern Möbius Transformations  779--790
              Warren P. Johnson   How Cauchy Missed Ramanujan's $_1
                                  \psi_1$ Summation  . . . . . . . . . . . 791--800
                   Jan van Mill   A Note on the Effros Theorem . . . . . . 801--806
                 Song Heng Chan   An Elementary Proof of Jacobi's Six
                                  Squares Theorem  . . . . . . . . . . . . 806--811
                  Nils R. Barth   Computing Cavalieri's Quadrature Formula
                                  by a Symmetry of the $n$-Cube  . . . . . 811--813
              Deniz Kazanci and   
                   Andrew Vince   A Property of Normal Tilings . . . . . . 813--816
         Andrzej Nowojewski and   
               Jakub Kallas and   
             Andrzej Dragan and   
              Abe Shenitzer and   
            Stefan Mykytiuk and   
                 John Stillwell   On the Appearance of Moving Bodies . . . 817--821
                  Marius Ghergu   Problem 11110  . . . . . . . . . . . . . 822--822
 Pál Péter Dalyay   Problem 11111  . . . . . . . . . . . . . 822--822
                    Yongge Tian   Problem 11112  . . . . . . . . . . . . . 822--822
                   Isaac Sofair   Problem 11113  . . . . . . . . . . . . . 822--822
                 Benne de Weger   Problem 11114  . . . . . . . . . . . . . 823--823
                     Jack Clark   Problem 11115  . . . . . . . . . . . . . 823--823
                   Darko Veljan   Problem 11116  . . . . . . . . . . . . . 823--823
               Ye Zhong Hao and   
                Wu Wei Chao and   
                      J. Schaer   Gossard Perspector: 10980  . . . . . . . 823--824
              Roland Bacher and   
            Julio Kuplinsky and   
                  Richard Stong   A Family of Polynomials: 10989 . . . . . 824--825
                 Rick Mabry and   
      Bernardo M. Ábrego   The Envelope, Please: 10990  . . . . . . 825--826
            Raymond Mortini and   
                   S. Amghibech   A Nonholomorphic Map of the Disk: 10991  826--827
               David Lubell and   
                 Chris Hill and   
               Albert Nijenhuis   Equal Sums of Reciprocal Products: 10992 827--829
               David Savitt and   
                     Chris Hill   Recognizing $n$-Divergent Sequences:
                                  10994  . . . . . . . . . . . . . . . . . 829--829
              Louis H. Kauffman   Book Review: \booktitle[untitled]  . . . 830--838
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 839--840
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 111, Number 10, December, 2004

             Judith V. Grabiner   Newton, Maclaurin, and the Authority of
                                  Mathematics  . . . . . . . . . . . . . . 841--852
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Figures Circumscribing Circles . . . . . 853--863
           Hartmut Logemann and   
                 Eugene P. Ryan   Asymptotic Behaviour of Nonlinear
                                  Systems  . . . . . . . . . . . . . . . . 864--889
          Stephanie Edwards and   
              Russell A. Gordon   Extreme Curvature of Polynomials . . . . 890--899
    Heinrich v. Weizsäcker   Can One Drop $ L^1 $-Boundedness in
                                  Komlós's Subsequence Theorem? . . . . . . 900--903
            G. D. Chakerian and   
                  M. S. Klamkin   A Three-Point Characterization of
                                  Central Symmetry . . . . . . . . . . . . 903--905
                  Iosif Pinelis   L'Hospital Rules for Monotonicity and
                                  the Wilker--Anglesio Inequality  . . . . 905--909
             Noriaki Kimura and   
            Kenneth S. Williams   Infinitely Many Insolvable Diophantine
                                  Equations  . . . . . . . . . . . . . . . 909--913
Jón R. Stefánsson   Forward Shifts and Backward Shifts in a
                                  Rearrangement of a Conditionally
                                  Convergent Series  . . . . . . . . . . . 913--914
                 Michael Nyblom   Problem 11117  . . . . . . . . . . . . . 915--915
              Vesselin Dimitrov   Problem 11118  . . . . . . . . . . . . . 915--915
                 John Robertson   Problem 11119  . . . . . . . . . . . . . 915--915
                   Bob Berk and   
                    Larry Shepp   Problem 11120  . . . . . . . . . . . . . 915--915
                  H. A. ShahAli   Problem 11121  . . . . . . . . . . . . . 916--916
              Victor Pambuccian   Problem 11122  . . . . . . . . . . . . . 916--916
             Art\=uras Dubickas   Problem 11123  . . . . . . . . . . . . . 916--916
             Giorgi Goldoni and   
                    Alan Berele   An Excenteric Iteration: 10993 . . . . . 916--917
           Donato Trigiante and   
                 Albert Stadler   Where Are the Zeros?: 10995  . . . . . . 917--917
              Ed T. Prothro and   
                     Chris Hill   Prime Divisors of Fermat Numbers: 10997  917--918
            Roberto Tauraso and   
                      Jiri Lebl   Distance to the Boundary: 10998  . . . . 918--918
                George Lamb and   
        Cornelius Stallmann and   
            Gerald Thompson and   
                Zafar Ahmed and   
                  O. P. Lossers   An Integral Three Ways: 11000  . . . . . 918--920
                 Rick Mabry and   
                  Jody Lockhart   Powered Terms in a Series: 11001 . . . . 920--920
  Y.-F. S. Pétermann and   
              C. T. Stretch and   
                  Jamie Simpson   A Problem That Bears Repeating: 11002    920--921
            Stephen B. Gray and   
               Clayton W. Dodge   The Orthocenter and Circumcenter Are
                                  Isogonal Conjugate Points: 11003 . . . . 921--922
                      Anonymous   Errata for 2004: 11089 . . . . . . . . . 922--922
                      Anonymous   Errata for 2004: Fibonacci in Complex
                                  Camouflage: 10858  . . . . . . . . . . . 922--922
                      Anonymous   Errata for 2004: a Group Determined by
                                  Relations?: 10933  . . . . . . . . . . . 922--922
                      Anonymous   Errata for 2004: An Iterative Sequence:
                                  10988  . . . . . . . . . . . . . . . . . 922--922
                      Anonymous   Errata for 2004: Some Bernstein
                                  Polynomials: 10985 . . . . . . . . . . . 922--922
                 Philip Protter   Book Review: \booktitle[untitled]  . . . 923--926
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 927--929
                      Anonymous   Volume Information . . . . . . . . . . . 930--937
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 938--944
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 112, Number 1, January, 2005

                 William Dunham   Touring the Calculus Gallery . . . . . . 1--19
                    Marcel Wild   The Groups of Order Sixteen Made Easy    20--31
               Shif Berhanu and   
                 Ahmed Mohammed   A Harnack Inequality for Ordinary
                                  Differential Equations . . . . . . . . . 32--41
     Janko Hernández and   
                  Leonel Robert   Figures of Constant Width on a
                                  Chessboard . . . . . . . . . . . . . . . 42--50
                 H. S. Bear and   
                     Dale Myers   A Simpler Approach to Integration and
                                  the Fubini Theorem . . . . . . . . . . . 51--60
                Jonathan Sondow   Double Integrals for Euler's Constant
                                  and in $ \ln (4 / \pi) $ and an Analog
                                  of Hadjicostas's Formula . . . . . . . . 61--65
                      Dan Romik   Roots of the Derivative of a Polynomial  66--69
             Joel L. Weiner and   
              George R. Wilkens   Quaternions and Rotations in $ \mathbb
                                  {E}^4 $  . . . . . . . . . . . . . . . . 69--76
José Carlos de Sousa and   
                Oliveira Santos   Another Proof of the Fundamental Theorem
                                  of Algebra . . . . . . . . . . . . . . . 76--78
                    V. F. Kagan   Riemann's Geometric Ideas  . . . . . . . 79--86
                    Bogdan Nica   Problem 11124  . . . . . . . . . . . . . 87--87
                 Shahin Amrahov   Problem 11125  . . . . . . . . . . . . . 87--87
                 James S. Weber   Problem 11126  . . . . . . . . . . . . . 87--87
                        Li Zhou   Problem 11127  . . . . . . . . . . . . . 87--87
                Wu Wei Chao and   
                  O. P. Lossers   Point Causing Equal Angles: 10996  . . . 88--88
                    Tom Apostol   Problem 11128  . . . . . . . . . . . . . 88--88
                    Yongge Tian   Problem 11129  . . . . . . . . . . . . . 88--88
                   Paul Bateman   Problem 11130  . . . . . . . . . . . . . 88--88
          Victor Pambuccian and   
              Michael Wolterman   Saccheri Quadrilateral: 11004  . . . . . 88--89
                 Marty Getz and   
                Dixon Jones and   
                      Ken Dutch   Partitioning by Arithmetic Progressions:
                                  11005  . . . . . . . . . . . . . . . . . 89--90
           Bogdan Suceav\ua and   
                 Daniele Donini   A Circle Centered on the Euler Circle:
                                  11006  . . . . . . . . . . . . . . . . . 90--91
José Luis Díaz-Barrero and   
   Juan José Egozcue and   
             Art\=uras Dubickas   Zero and Coefficient Inequality: 11008   91--92
              David Borwein and   
                 Julien Grivaux   Convex and Concave Functions: 11009  . . 92--93
                 Erwin Just and   
        Norman Schaumberger and   
     GCHQ Problem Solving Group   Regular Polygon Inscription: 11010 . . . 93--94
                  Steve Kennedy   Book Review: \booktitleTuring: A Novel
                                  About Computation, by Christos H.
                                  Papadimitriou  . . . . . . . . . . . . . 95--98
                Marion D. Cohen   Book Review: \booktitleThe Magic of
                                  Numbers, by Benedict Gross; Joe Harris   98--101
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 2, February, 2005

          Gregory S. Warrington   Juggling Probabilities . . . . . . . . . 105--118
               Alex D. D. Craik   Prehistory of Fa\`a di Bruno's Formula   119--130
             Paolo Codec\`a and   
                     Mohan Nair   The Lesser-Known $ \Delta $-Function in
                                  Number Theory  . . . . . . . . . . . . . 131--140
Juan Carlos Álvarez Paiva and   
               Anthony Thompson   On the Perimeter and Area of the Unit
                                  Disc . . . . . . . . . . . . . . . . . . 141--154
                  Ian Doust and   
      Michael D. Hirschhorn and   
                     Jocelyn Ho   Trigonometric Identities, Linear
                                  Algebra, and Computer Algebra  . . . . . 155--164
            Connie Campbell and   
                 William Staton   A Square-Packing Problem of Erd\Hos  . . 165--167
         Laurei\ctiu Panaitopol   On the Representation of Natural Numbers
                                  as Sums of Squares . . . . . . . . . . . 168--171
                   Jiu Ding and   
                  Temple H. Fay   The Perron--Frobenius Theorem and Limits
                                  in Geometry  . . . . . . . . . . . . . . 171--175
             Piotr Haj\lasz and   
              Pawe\l Strzelecki   How to Measure Volume with a Thread  . . 176--179
                N. G. de Bruijn   Problem 11131  . . . . . . . . . . . . . 180--180
                Jonathan Sondow   Problem 11132  . . . . . . . . . . . . . 180--180
                   Paul Bracken   Problem 11133  . . . . . . . . . . . . . 180--180
                 Kent D. Boklan   Problem 11134  . . . . . . . . . . . . . 180--180
                  Ray Redheffer   Problem 11135  . . . . . . . . . . . . . 181--181
                Raymond Mortini   Problem 11136  . . . . . . . . . . . . . 181--181
         Vicen\ctiu R\uadulescu   Problem 11137  . . . . . . . . . . . . . 181--181
                D. P. Minassian   Baire Class One: 10999 . . . . . . . . . 181--182
                George Lamb and   
                    Zafar Ahmed   An Application of the Gaussian Integral:
                                  11011  . . . . . . . . . . . . . . . . . 182--183
            C\ualin Popescu and   
                   Chu Wenchang   Cube Sum Inequalities: 11012 . . . . . . 183--184
               David Callan and   
                   Marc Renault   Dyck Paths Skipping Every Fourth Point:
                                  11013  . . . . . . . . . . . . . . . . . 184--184
   Achilleas Sinefakopoulos and   
                      Knut Dale   A Recursively Defined Series: 11014  . . 184--185
              Ovidiu Furdui and   
                        Li Zhou   Sines in a Triangle: 11015 . . . . . . . 185--186
          C. R. Pranesachar and   
                   S. Amghibech   When the Brocard Points Are Collinear
                                  with a Vertex: 11017 . . . . . . . . . . 186--187
                  Eric S. Weber   Book Review: \booktitleAn Introduction
                                  to Frames and Riesz Bases, by Ole
                                  Christensen  . . . . . . . . . . . . . . 188--191
          Jeffrey L. Nunemacher   Book Review: \booktitleGeometry, by
                                  David A. Brannan; Matthew F. Esplen;
                                  Jeremy J. Gray . . . . . . . . . . . . . 191--194
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 3, March, 2005

            Robert E. Megginson   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award to Gerald L. Alexanderson for
                                  Distinguished Service to Mathematics . . 197--199
               Roger C. Alperin   Trisections and Totally Real Origami . . 200--211
                  John Bryk and   
                 Cesar E. Silva   Measurable Dynamics of Simple $p$-adic
                                  Polynomials  . . . . . . . . . . . . . . 212--232
          Ivor Grattan-Guinness   The ``Ecole Polytechnique'', 1794-1850:
                                  Differences over Educational Purpose and
                                  Teaching Practice  . . . . . . . . . . . 233--250
               William Duke and   
               Kimberly Hopkins   Quadratic Reciprocity in a Finite Group  251--256
                Shay Gueron and   
                   Itai Shafrir   A Weighted Erd\Hos--Mordell Inequality
                                  for Polygons . . . . . . . . . . . . . . 257--263
                  Luo Xuebo and   
                  Zhu-Jun Zheng   An Inequality for Homogeneous
                                  Polynomials on $ \mathbb {R}^n $ . . . . 264--266
          Peter G. Anderson and   
         Arthur T. Benjamin and   
                Jeremy A. Rouse   Combinatorial Proofs of Fermat's,
                                  Lucas's, and Wilson's Theorems . . . . . 266--268
                 Kurt Girstmair   On an Irreducibility Criterion of M. Ram
                                  Murty  . . . . . . . . . . . . . . . . . 269--270
         Robert J. MacG. Dawson   On a ``Singular'' Integration Technique
                                  of Poisson . . . . . . . . . . . . . . . 270--272
                Roberto Tauraso   Problem 11138  . . . . . . . . . . . . . 273--273
                Grahame Bennett   Problem 11139  . . . . . . . . . . . . . 273--273
                 Walther Janous   Problem 11140  . . . . . . . . . . . . . 273--273
                  Richard Bagby   Problem 11141  . . . . . . . . . . . . . 273--273
                   Donald Knuth   Problem 11142  . . . . . . . . . . . . . 273--274
          Alexander Dubinov and   
                 Irina Dubinova   Problem 11143  . . . . . . . . . . . . . 274--274
            Ernst Schulte-Geers   Problem 11144  . . . . . . . . . . . . . 274--274
                      Joel Zinn   Problem 11076  . . . . . . . . . . . . . 274--274
                   Bob Berk and   
                    Larry Shepp   Problem 11120  . . . . . . . . . . . . . 274--274
             Art\=uras Dubickas   Problem 11123  . . . . . . . . . . . . . 274--274
               Slavko Simic and   
                  Richard Stong   Entire Functions of Order Zero: 11018    274--277
Bernardo Recamán Santos and   
               Michail Reid and   
                     Kevin Ford   Cycling via Common Divisors: 11019 . . . 277--278
               Donald Knuth and   
    Silvia Fernández and   
                  Gerry Myerson   A Modular Triple: 11021  . . . . . . . . 279--280
                Wu Wei Chao and   
              Nadjib Bouzar and   
                 Allan K. Swett   A Timely Problem: 11023  . . . . . . . . 280--280
           Razvan Satnoianu and   
                 Walther Janous   A Two-Triangle Inequality: 11022 . . . . 280--280
          Gerald B. Folland and   
              Jeffrey L. Stuart   Book Review: \booktitleLinear Algebra,
                                  by John B. Fraleigh; Raymond A.
                                  Beauregard; Linear Algebra and its
                                  Applications ~by David Lay; Linear
                                  Algebra: A Geometric Approach ~by
                                  Theodore Shifrin; Malcolm R. Adams;
                                  Introduction to Linear Algebra ~by
                                  Gilbert Strang . . . . . . . . . . . . . 281--288
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 4, April, 2005

              Don Shimamoto and   
          Catherine Vanderwaart   Spaces of Polygons in the Plane and
                                  Morse Theory . . . . . . . . . . . . . . 289--310
               Edward B. Burger   A Tail of Two Palindromes  . . . . . . . 311--321
                  Sherman Stein   Remarks on the Gravity Equation  . . . . 322--333
          Christopher S. Simons   An Elementary Approach to the Monster    334--341
             Daniel J. Velleman   The Generalized Simpson's Rule . . . . . 342--350
                   Boris Mirman   Sufficient Conditions for Poncelet
                                  Polygons Not to Close  . . . . . . . . . 351--356
            Jürgen Kindler   A Simple Proof of Sion's Minimax Theorem 356--358
              John Clifford and   
                David James and   
           Michael Lachance and   
                    Joan Remski   A Constructive Approach to Singular
                                  Value Decomposition and Symmetric Schur
                                  Factorization  . . . . . . . . . . . . . 358--363
           Marco Dall'Aglio and   
               Fabio Maccheroni   Fair Division without Additivity . . . . 363--365
                      Joel Zinn   Problem 11145  . . . . . . . . . . . . . 366--366
                    Yongge Tian   Problem 11146  . . . . . . . . . . . . . 366--366
                  Pamela Gorkin   Problem 11147  . . . . . . . . . . . . . 366--366
                  M. L. Glasser   Problem 11148  . . . . . . . . . . . . . 366--366
                Mircea Ivan and   
                      Ioan Rasa   Problem 11149  . . . . . . . . . . . . . 367--367
                 Emeric Deutsch   Problem 11150  . . . . . . . . . . . . . 367--367
                   Donald Knuth   Problem 11151  . . . . . . . . . . . . . 367--367
            Jonathan Sondow and   
              Richard Stong and   
                 Julien Grivaux   An Identity Involving Harmonic Numbers:
                                  11026  . . . . . . . . . . . . . . . . . 367--369
                 H. Reuvers and   
                    Li Zhou and   
                       A. Engle   Triangles Inscribed in a Circle: 11027   369--370
         Götz Trenkler and   
                  G. P. Shannon   Hermitian Products of Hermitian
                                  Matrices: 11028  . . . . . . . . . . . . 370--371
              Steven Butler and   
                   Bruce Ebanks   A Functional Equation: 11030 . . . . . . 371--372
                    Li Zhou and   
                  Robin Chapman   Monster Mean Tamed: 11031  . . . . . . . 372--373
                  David E. Rowe   Book Review: \booktitleMathematicians
                                  under the Nazis, by Sanford L. Segal . . 374--381
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 5, May, 2005

             Arturo Magidin and   
                 David McKinnon   Gauss's Lemma for Number Fields  . . . . 385--416
                 Florian Deloup   The Fundamental Group of the Circle Is
                                  Trivial  . . . . . . . . . . . . . . . . 417--425
               Antonio Behn and   
   Christopher Kribs-Zaleta and   
              Vadim Ponomarenko   The Convergence of Difference Boxes  . . 426--439
                 Paul E. Becker   Do Normal Subgroups Have Straight Tails? 440--449
           Raghib Abu-Saris and   
                    Wajdi Ahmad   Avoiding Eigenvalues in Computing Matrix
                                  Powers . . . . . . . . . . . . . . . . . 450--454
          Francesc Comellas and   
               J. Luis A. Yebra   Exact Solutions for Minimax Optimization
                                  Problems . . . . . . . . . . . . . . . . 454--458
                F. G. Avkhadiev   A Simple Proof of the Gauss-Winckler
                                  Inequality . . . . . . . . . . . . . . . 459--462
                 Mowaffaq Hajja   Copositive Symmetric Cubic Forms . . . . 462--466
                    Mircea Ivan   Problem 11152  . . . . . . . . . . . . . 467--467
                   Paul Bracken   Problem 11153  . . . . . . . . . . . . . 467--467
                    Kent Holing   Problem 11154  . . . . . . . . . . . . . 467--467
              Emmanuel Kowalski   Problem 11155  . . . . . . . . . . . . . 467--467
                Richard Stanley   Problem 11156  . . . . . . . . . . . . . 467--468
                Hillel Gauchman   Problem 11157  . . . . . . . . . . . . . 468--468
                 David Beckwith   Problem 11158  . . . . . . . . . . . . . 468--468
Juan-Bosco Romero Márquez and   
                 Martin Muldoon   Gamma Function Bounds: 11016 . . . . . . 468--468
                 Tim Keller and   
                Doyle Henderson   One Good Factorization Deserves Another:
                                  11029  . . . . . . . . . . . . . . . . . 469--469
                Mark Pinsky and   
                Nicholas Singer   The Stationary Distribution of a
                                  Tridiagonal Row-Stochastic Matrix: 11032 469--470
            M. N. Deshpande and   
              R. M. Welukar and   
              Richard Stong and   
             BSI Problems Group   Expansion by Inclusion-Exclusion: 11033  470--472
               Omer Yayenie and   
                     Joe Geiman   Evaluation of an Integral: 11035 . . . . 472--473
            M. L. J. Hautus and   
                 Julien Grivaux   Shrinking Fréchet Differentiable Maps:
                                  11037  . . . . . . . . . . . . . . . . . 473--474
           Floor van Lamoen and   
                Michel Bataille   Morley's Triangle and Lemma: 11038 . . . 474--474
               Daniel J. Madden   Book Review: \booktitleAbstract Algebra,
                                  by Ronald Solomon; Integers, Polynomials
                                  and Rings ~by Ronald S. Irving . . . . . 475--478
                 John Sylvester   Book Review: \booktitleIntroduction to
                                  the Mathematics of Medical Imaging, by
                                  Charles L. Epstein . . . . . . . . . . . 479--480
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 6, June / July, 2005

         Arthur T. Benjamin and   
              Naiomi T. Cameron   Counting on Determinants . . . . . . . . 481--492
   Jonathan Michael Borwein and   
    Kwok-Kwong Stephen Choi and   
               Wilfried Pigulla   Continued Fractions of Tails of
                                  Hypergeometric Series  . . . . . . . . . 493--501
                Michel Balinski   What Is Just?  . . . . . . . . . . . . . 502--511
             Nathaniel Grossman   A $ C^\infty $ Lagrange Inversion
                                  Theorem  . . . . . . . . . . . . . . . . 512--514
                 Mark A. Pinsky   Mean Values and the Maximum Principle: a
                                  Proof in Search of More Theorems . . . . 515--521
                 H. Maehara and   
                  T. Zamfirescu   On the Perimeter of a Triangle in a
                                  Minkowski Plane  . . . . . . . . . . . . 521--522
                   Daniel Frohn   A (K)-Ring Satisfying the Ascending
                                  Chain Condition on Principal Ideals That
                                  Is Not a Principal Ideal Ring  . . . . . 523--524
                      Lee Lorch   Continuous Ranking of Zeros of Cylinder
                                  Functions  . . . . . . . . . . . . . . . 524--525
       Viktor Blåsjö   The Isoperimetric Problem  . . . . . . . 526--566
                    George Lamb   Problem 11159  . . . . . . . . . . . . . 567--567
               Marc Chamberland   Problem 11160  . . . . . . . . . . . . . 567--567
                 Emeric Deutsch   Problem 11161  . . . . . . . . . . . . . 567--567
                 Paolo Perfetti   Problem 11162  . . . . . . . . . . . . . 567--567
                Michel Bataille   Problem 11163  . . . . . . . . . . . . . 567--567
       Luis Díaz-Barrero   Problem 11164  . . . . . . . . . . . . . 568--568
                    Yogesh More   Problem 11165  . . . . . . . . . . . . . 568--568
         William P. Wardlaw and   
                  Richard Stong   Adjoint over the Smallest Field: 11034   568--569
              M. L. Glasser and   
                    George Lamb   One Easy, One Hard: 11036  . . . . . . . 569--572
             Noah Rosenberg and   
                  Richard Bagby   Integral over a Simplex: 11039 . . . . . 572--573
                Yongge Tian and   
             BSI Problems Group   Range Identities for Hermitian
                                  Idempotent Matrices: 11040 . . . . . . . 573--573
            M. N. Deshpande and   
            John Henry Steelman   An Invariance of Variance over
                                  Expectation: 11042 . . . . . . . . . . . 573--574
               D. J. H. Garling   Book Review: \booktitleThe
                                  Cauchy--Schwarz Master Class: An
                                  Introduction to the Art of Mathematical
                                  Inequalities, by J. Michael Steele . . . 575--579
                Loukas Grafakos   Book Review: \booktitleConstantin
                                  Carathéodory: Mathematics and Politics in
                                  Turbulent Times, by Maria Georgiadou . . 579--581
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 7, August / September, 2005

               Kang-Tae Kim and   
               Steven G. Krantz   The Automorphism Groups of Domains . . . 585--601
               Greg Dresden and   
           Wayne M. Dym\`a\vcek   Finding Factors of Factor Rings over the
                                  Gaussian Integers  . . . . . . . . . . . 602--611
               Dov Aharonov and   
               Alan Beardon and   
                   Kathy Driver   Fibonacci, Chebyshev, and Orthogonal
                                  Polynomials  . . . . . . . . . . . . . . 612--630
              Stephen T. Ahearn   Tolstoy's Integration Metaphor from War
                                  and Peace  . . . . . . . . . . . . . . . 631--638
           Mark Finkelstein and   
                 Robert Whitley   Eigenvalues, Almost Periodic Functions,
                                  and the Derivative of an Integral  . . . 639--641
           J. Araújo and   
                 J. D. Mitchell   An Elementary Proof That Every Singular
                                  Matrix Is a Product of Idempotent
                                  Matrices . . . . . . . . . . . . . . . . 641--645
               Michael J. Grady   A Group Theoretic Approach to a Famous
                                  Partition Formula  . . . . . . . . . . . 645--651
                  David A. Ross   An Elementary Proof of Lyapunov's
                                  Theorem  . . . . . . . . . . . . . . . . 651--653
                      Greg Oman   Problem 11166  . . . . . . . . . . . . . 654--654
         Vicen\ctiu R\uadulescu   Problem 11167  . . . . . . . . . . . . . 654--654
                    Kent Holing   Problem 11168  . . . . . . . . . . . . . 654--654
       Mohammad Hossein Mehrabi   Problem 11169  . . . . . . . . . . . . . 654--654
                 Emeric Deutsch   Problem 11170  . . . . . . . . . . . . . 655--655
                      Chu Cheng   Problem 11171  . . . . . . . . . . . . . 655--655
     Heinz-Jürgen Seiffert   Problem 11172  . . . . . . . . . . . . . 655--655
              Oscar Ciaurri and   
                    Florin Boca   Hyperbolic-Looking Special Functions:
                                  11041  . . . . . . . . . . . . . . . . . 655--657
                 Michael Golomb   Don't the Problem Ebitees Read the
                                  Monthly? 11043 . . . . . . . . . . . . . 657--657
            Michel Bataille and   
                        Li Zhou   A Combinatorial Sum Goes on Tangent:
                                  11044  . . . . . . . . . . . . . . . . . 657--659
              Matthias Beck and   
               Marcin Mazur and   
               Shelemyahu Zacks   ``Ordinary'' Spherical Triangles: 11048  659--660
               Vasile Mihai and   
        Zoltán V\Hor\Hos   One of the Morley Triangles: 11049 . . . 660--661
                Wu Wei Chao and   
The University of Louisiana at Lafayette Math Club   Two Functional Equations: 11053  . . . . 661--662
           Razvan Satnoianu and   
                 Daniele Donini   Medians and Altitudes and the Sum of the
                                  Radii: 11055 . . . . . . . . . . . . . . 662--663
           Kenneth B. Stolarsky   Book Review: \booktitleAnalytic Theory
                                  of Polynomials, by Qazi Ibadur Rahman;
                                  Gerhard Schmeisser; Complex Polynomials
                                  ~by Terry Sheil-Small  . . . . . . . . . 664--671
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 8, October, 2005

               Karl Dilcher and   
           Kenneth B. Stolarsky   A Pascal-Type Triangle Characterizing
                                  Twin Primes  . . . . . . . . . . . . . . 673--681
               David A. Cox and   
                  Jerry Shurman   Geometry and Number Theory on Clovers    682--704
                 George Leibman   A Nonstandard Proof of the Fundamental
                                  Theorem of Algebra . . . . . . . . . . . 705--712
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Fifth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 713--725
                      N. V. Rao   The Stone--Weierstrass Theorem Revisited 726--729
                Jonathan Sondow   A Faster Product for $ \pi $ and a New
                                  Integral for $ \ln \pi / 2 $ . . . . . . 729--734
               I. M. Isaacs and   
                 M. R. Pournaki   Generalizations of Fermat's Little
                                  Theorem via Group Theory . . . . . . . . 734--740
                 Geoffrey Brown   Convexity and Minkowski's Inequality . . 740--742
                B. A. Rosenfeld   The Analytic Principle of Continuity . . 743--748
                M. N. Deshpande   Problem 11173  . . . . . . . . . . . . . 749--749
Pál Péter Dályay   Problem 11174  . . . . . . . . . . . . . 749--749
                William Calbeck   Problem 11175  . . . . . . . . . . . . . 749--749
                Oleg Faynshteyn   Problem 11176  . . . . . . . . . . . . . 749--749
             Dorin M\uarghidanu   Problem 11177  . . . . . . . . . . . . . 750--750
                Jon Bentley and   
                  Colin Mallows   Problem 11178  . . . . . . . . . . . . . 750--750
                 David Beckwith   Problem 11179  . . . . . . . . . . . . . 750--750
        Manoj Prakash Singh and   
                  Richard Stong   A Prime Summandification of n: 11045 . . 750--751
             Shahin Amrabov and   
              Bernard M. Abrego   An Application of Fermat's Little
                                  Theorem: 11054 . . . . . . . . . . . . . 751--751
            Syrous Marivani and   
                  O. P. Lossers   Modular Sequences Defined by
                                  Polynomials: 11047 . . . . . . . . . . . 751--751
         John H. Lindsey II and   
                    Omran Kouba   Maximum Compared to Average: 11056 . . . 752--752
       Óscar Ciaurri and   
                  O. P. Lossers   A Vanishing Infinite Sum: 11058  . . . . 752--753
       Matthew Coppenbarger and   
     GCHQ Problem Solving Group   ``Little Boxes Made of Ticky-Tacky'':
                                  11060  . . . . . . . . . . . . . . . . . 753--754
          Kenneth Schilling and   
             BSI Problems Group   Powered Divergence: 11062  . . . . . . . 754--755
                John Wetzel and   
                        Li Zhou   Lengths of Wrapped Curves: 11064 . . . . 755--755
           Douglas B. Tyler and   
                  Robin Chapman   A More General Presentation: 11065 . . . 755--756
                Judith Grabiner   Book Review: \booktitleFrom Newton to
                                  Hawking: A History of Cambridge
                                  University's Lucasian Professors of
                                  Mathematics, by Kevin C. Knox; Richard
                                  Noakes . . . . . . . . . . . . . . . . . 757--762
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 9, November, 2005

           Ibtesam Bajunaid and   
              Joel M. Cohen and   
             Flavia Colonna and   
                  David Singman   Function Series, Catalan Numbers, and
                                  Random Walks on Trees  . . . . . . . . . 765--785
                     Dan Kalman   Virtual Empirical Investigation: Concept
                                  Formation and Theory Justification . . . 786--798
              Nikolai V. Ivanov   A Differential Forms Perspective on the
                                  Lax Proof of the Change of Variables
                                  Formula  . . . . . . . . . . . . . . . . 799--806
               Roger C. Alperin   The Modular Tree of Pythagoras . . . . . 807--816
                  Ray Redheffer   The Behavior of Solutions near a Stable
                                  or Semistable Stationary Point . . . . . 817--822
                   M. A. Nyblom   More Nested Square Roots of 2  . . . . . 822--825
                A. R. Naghipour   A Simple Proof of Cohen's Theorem  . . . 825--826
            Thierry Coquand and   
                 Henri Lombardi   A Short Proof for the Krull Dimension of
                                  a Polynomial Ring  . . . . . . . . . . . 826--829
                   Robert Myers   An Elementary Proof of Joris's Theorem   829--831
            Michael Monastyrsky   Some Remarks on ``Mathematics at the
                                  Tlirn of the Millennium''  . . . . . . . 832--838
                     Suat Namli   Problem 11180  . . . . . . . . . . . . . 839--839
                M. N. Deshpande   Problem 11181  . . . . . . . . . . . . . 839--839
                 Shahin Amrahov   Problem 11182  . . . . . . . . . . . . . 839--839
                 David Beckwith   Problem 11183  . . . . . . . . . . . . . 839--839
                   Slavko Simic   Problem 11184  . . . . . . . . . . . . . 840--840
              Rainer Brück   Problem 11185  . . . . . . . . . . . . . 840--840
   Angelo J. Christino, Jr. and   
          William C. Waterhouse   Problem 11186  . . . . . . . . . . . . . 840--840
                Kent Holing and   
                  Richard Stong   A Special Set of Integer Points in
                                  Space: 11050 . . . . . . . . . . . . . . 840--841
               Slavko Simic and   
             John H. Lindsey II   Equivalent Asymptotics: 11063  . . . . . 841--843
                George Lamb and   
                  O. P. Lossers   Integral by Mellin Transform: 11067  . . 843--844
            Herbert S. Wilf and   
           Kenneth E. Schilling   Think Rationally: 11068  . . . . . . . . 844--845
                George Lamb and   
                 T. K. Callahan   Evaluate an Integral: 11072  . . . . . . 845--846
                 J. David Logan   Book Review: \booktitleMathematical
                                  Models in Biology, by Elizabeth S.
                                  Allman; John A. Rhodes . . . . . . . . . 847--850
           Virginia M. Warfield   Book Review: \booktitleCount Down: Six
                                  Kids Vie for Glory at the World's
                                  Toughest Math Competition, by Steve
                                  Olson  . . . . . . . . . . . . . . . . . 850--851
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 112, Number 10, December, 2005

          Lisa D. Humphreys and   
              P. Joseph McKenna   When a Mechanical Model Goes Nonlinear:
                                  Unexpected Responses to Low-Periodic
                                  Shaking  . . . . . . . . . . . . . . . . 861--875
                Eric Driver and   
          Philip A. Leonard and   
            Kenneth S. Williams   Irreducible Quartic Polynomials with
                                  Factorizations modulo p  . . . . . . . . 876--890
              Stephen M. Zemyan   On the Zeroes of the Nth Partial Sum of
                                  the Exponential Series . . . . . . . . . 891--909
                Jan J. Dijkstra   On Homeomorphism Groups and the
                                  Compact-Open Topology  . . . . . . . . . 910--912
                 Zhibo Chen and   
                 Gary L. Mullen   Transpositions and Representability  . . 913--919
                  Oleg Pikhurko   Generating Edge-Labeled Trees  . . . . . 919--921
              Adrian Dumitrescu   A Remark on the Erd\Hos--Szekeres
                                  Theorem  . . . . . . . . . . . . . . . . 921--924
                  Seon-Hong Kim   On the Moduli of the Zeros of a
                                  Polynomial . . . . . . . . . . . . . . . 924--925
                   Leif Arkeryd   Nonstandard Analysis . . . . . . . . . . 926--928
                        Li Zhou   Problem 11187  . . . . . . . . . . . . . 929--929
                   David Bailey   Problem 11188  . . . . . . . . . . . . . 929--929
                    Lajos Csete   Problem 11189  . . . . . . . . . . . . . 929--929
José Luis Díaz-Barrero   Problem 11190  . . . . . . . . . . . . . 929--929
             Barthel Wayne Huff   Problem 11191  . . . . . . . . . . . . . 929--930
                  Brett Stevens   Problem 11192  . . . . . . . . . . . . . 930--930
                  Marian Tetiva   Problem 11193  . . . . . . . . . . . . . 930--930
               Floor van Lamoen   Six Surprises from Four Lines: 11025 . . 930--932
         Sebastian Cioab\ua and   
             Tim LeSaulnier and   
                   Dan Saracino   A Sufficient Condition for
                                  Commutativity: 11066 . . . . . . . . . . 932--933
  Péter Ivády and   
                  Richard Stong   Sine Bound: 11069  . . . . . . . . . . . 933--933
         Götz Trenkler and   
              Lawrence J. Baker   An Easy Complex Inequality: 11075  . . . 933--933
          Gheorge Costovici and   
           Uro\vs Milutinovi\'c   An Oscillating Sequence: 11077 . . . . . 934--934
           Razvan Satnoianu and   
                        Li Zhou   A Majorization Consequence: 11080  . . . 934--935
              Stephen Morse and   
                  Robin Chapman   Harmonious Trios Are the Vertices of a
                                  Regular Icosahedron: 11081 . . . . . . . 935--935
                    Wu Wei Chao   Errata: Continuous Additive Functions    936--936
                 Marty Getz and   
                    Dixon Jones   Errata: Partitioning by Arithmetic
                                  Progressions . . . . . . . . . . . . . . 936--936
             Michael Golomb and   
                      Kit Hanes   The Orthocenter of a Simplex: 11087  . . 936--936
              Gerald B. Folland   Book Review: \booktitleFunctional
                                  Analysis, by Peter D. Lax; John Wiley;
                                  Functional Analysis: An Introduction ~by
                                  Yuli Eidelman; Vitaly Milman; Antonis
                                  Tsolomitis . . . . . . . . . . . . . . . 937--940
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 941--946
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                      Anonymous   Volume Information . . . . . . . . . . . ??


American Mathematical Monthly
Volume 113, Number 1, January, 2006

           Andrew Granville and   
                    Greg Martin   Prime Number Races . . . . . . . . . . . 1--33
             John W. Hagood and   
               Brian S. Thomson   Recovering a Function from a Dini
                                  Derivative . . . . . . . . . . . . . . . 34--46
                    Marc Frantz   Some Graphical Solutions of the Kepler
                                  Problem  . . . . . . . . . . . . . . . . 47--56
                     Henry Cohn   A Short Proof of the Simple Continued
                                  Fraction Expansion of $e$  . . . . . . . 57--62
                Thomas J. Osler   A Proof of the Continued Fraction
                                  Expansion of $e$1/M  . . . . . . . . . . 62--66
                  Xiongping Dai   Continuous Differentiablity of Solutions
                                  of ODEs with Respect to Initial
                                  Conditions . . . . . . . . . . . . . . . 66--70
               Stephen Boyd and   
             Persi Diaconis and   
                    Jun Sun and   
                       Lin Xiao   Fastest Mixing Markov Chain on a Path    70--74
          Pawe\l Strzelecki and   
                  Abe Shenitzer   The Poincaré Conjecture?  . . . . . . . . 75--78
              Folkmar Bornemann   Problem 11194  . . . . . . . . . . . . . 79--79
                  Marian Tetiva   Problem 11195  . . . . . . . . . . . . . 79--79
       Mohammad Hossein Mehrabi   Problem 11196  . . . . . . . . . . . . . 79--79
                Oleg Faynshteyn   Problem 11197  . . . . . . . . . . . . . 79--79
            P. R. Parthasarathy   Problem 11198  . . . . . . . . . . . . . 79--79
                   Aliyev Yakub   Problem 11199  . . . . . . . . . . . . . 80--80
                      Joel Zinn   Problem 11200  . . . . . . . . . . . . . 80--80
               A. J. Sasane and   
                  Robin Chapman   Diagonals of a Regular Polygon: 10924    80--81
             Nick MacKinnon and   
              Kenneth Schilling   Optimal Strategy for a Number-Guessing
                                  Game: 11051  . . . . . . . . . . . . . . 81--82
   Zahlreich Problems Group and   
                  C. T. Stretch   A Point with Given Distances: 11057  . . 82--83
                Mark Bowron and   
                  Bruce Burdick   Closure, Complement, and Union: 11059    83--83
            Roberto Tauraso and   
                  Richard Stong   Commuting Analytic Maps: 11070 . . . . . 83--84
              Matthias Beck and   
              Jesus DeLoera and   
               Mike Develin and   
             Julian Pfeifle and   
Northwestern University Math Problem Solving Group   Some Linear Recurrences: 11085 . . . . . 84--85
          Richard Holzsager and   
                 Anton R. Schep   Rearranged Series: 11088 . . . . . . . . 85--85
            Michel Bataille and   
                  O. P. Lossers   Simple Roots for Polynomials: 11094  . . 85--86
                  Charles Radin   Book Review: \booktitleThe Pursuit of
                                  Perfect Packing, by Tomaso Aste; Denis
                                  Weaire; Kelper's Conjecture ~by George
                                  G. Szpiro  . . . . . . . . . . . . . . . 87--90
            Shandelle M. Henson   Book Review: \booktitleComplexities:
                                  Women in Mathematics, by Bettye Anne
                                  Case; Anne M. Leggett  . . . . . . . . . 91--93
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 2, February, 2006

            Jeffrey C. Lagarias   Wild and Wooley Numbers  . . . . . . . . 97--108
                Alejo Blaya and   
Víctor Jiménez López   Is Trivial Dynamics That Trivial?  . . . 109--133
        Vladimir Pozdnyakov and   
               Martin Kulldorff   Waiting Times for Patterns and a Method
                                  of Gambling Teams  . . . . . . . . . . . 134--143
                Louis A. Talman   Simpson's Rule Is Exact for Quintics . . 144--155
              Herbert A. Medina   A Sequence of Polynomials for
                                  Approximating Arctangent . . . . . . . . 156--161
           Reinhard Diestel and   
              Carsten Thomassen   A Cantor--Bernstein Theorem for Paths in
                                  Graphs . . . . . . . . . . . . . . . . . 161--165
             John Konvalina and   
                Jack Heidel and   
                     Jim Rogers   A Mean Paradox . . . . . . . . . . . . . 166--169
                Enrique Arrondo   Another Elementary Proof of the
                                  Nullstellensatz  . . . . . . . . . . . . 169--171
                 P. L. Robinson   The Sphere Is Not Flat . . . . . . . . . 171--173
             Daniel J. Velleman   A Note on $ \lambda $-Permutations . . . 173--178
                 Robert Russell   Problem 11201  . . . . . . . . . . . . . 179--179
                Grahame Bennett   Problem 11202  . . . . . . . . . . . . . 179--179
                     Fuxiang Yu   Problem 11203  . . . . . . . . . . . . . 179--179
          Christopher J. Hillar   Problem 11204  . . . . . . . . . . . . . 179--179
                Wu Wei Chao and   
                     Guang Zhou   Problem 11205  . . . . . . . . . . . . . 179--179
                Mircea Ivan and   
              Alexandru Lupa\cs   Problem 11206  . . . . . . . . . . . . . 180--180
              Michael W. Botsko   Problem 11207  . . . . . . . . . . . . . 180--180
               Andrei Jorza and   
              Edward Ordman and   
                  Richard Stong   No Three Faces with the Same Number of
                                  Edges: 10856 . . . . . . . . . . . . . . 180--183
               Danrun Huang and   
              Daniel Scully and   
             Achava Nakhash and   
                     Karl David   The Limit of a Set-Valued Process: 11052 183--183
     Vicen\ctiu R\vadulescu and   
                  Richard Stong   An Example With Periodic Orbits: 11073   184--186
         Christopher Hillar and   
                Darren Rhea and   
              Godfrey L. Isaacs   An Oldie: 11098  . . . . . . . . . . . . 186--186
             David E. Zitarelli   Book Review: \booktitleR. L. Moore:
                                  Mathematician and Teacher, by John
                                  Parker . . . . . . . . . . . . . . . . . 187--192
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 3, March, 2006

                  Wayne Roberts   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award to Hyman Bass for Distinguished
                                  Service to Mathematics . . . . . . . . . 193--195
            David Pengelley and   
                   Fred Richman   Did Euclid Need the Euclidean Algorithm
                                  to Prove Unique Factorization? . . . . . 196--205
      Lluís Bibiloni and   
      Pelegrí Viader and   
           Jaume Paradís   On a Series of Goldbach and Euler  . . . 206--220
                Rajendra Bhatia   Infinitely Divisible Matrices  . . . . . 221--235
                 Harold P. Boas   Reflections on the Arbelos . . . . . . . 236--249
              Robert E. Hartwig   Note on a Linear Difference Equation . . 250--256
                Lech Maligranda   Simple Norm Inequalities . . . . . . . . 256--260
             Alexander Givental   The Pythagorean Theorem: What Is It
                                  About? . . . . . . . . . . . . . . . . . 261--265
                   YiChuan Yang   A Lattice-Ordered Skew Field Is Totally
                                  Ordered If Squares Are Positive  . . . . 265--266
                        Li Zhou   Problem 11208  . . . . . . . . . . . . . 267--267
          Alexander Dubinov and   
                 Irina Dubinova   Problem 11209  . . . . . . . . . . . . . 267--267
              Michael S. Becker   Problem 11210  . . . . . . . . . . . . . 267--267
           Mihály Bencze   Problem 11211  . . . . . . . . . . . . . 268--268
                 David Beckwith   Problem 11212  . . . . . . . . . . . . . 268--268
             Stanley Rabinowitz   Problem 11213  . . . . . . . . . . . . . 268--268
              Solomon W. Golomb   Problem 11214  . . . . . . . . . . . . . 268--268
              Richard Bagby and   
     GCHQ Problem Solving Group   Differentiable Distance: 11093 . . . . . 268--269
               Vasile Mihai and   
                  O. P. Lossers   Trapezoid Inscribed in Ellipse: 11095    269--269
            C\ualin Popescu and   
                  Richard Stong   A Subset-Sum Inequality: 11100 . . . . . 269--270
            Earl F. Skelton and   
        Zoltán V\Hor\Hos   An Inverse Tangent Integral: 11101 . . . 270--271
   Vincent\ctiu R\vadulescu and   
     GCHQ Problem Solving Group   Periodic Solution of a Differential
                                  Equation: 11104  . . . . . . . . . . . . 271--273
  Juan-Bosco Romero Marquez and   
              Rick Luttmann and   
           Miguel de Guzman and   
        G. Donald Chakerian and   
                        Li Zhou   Cevians and Centroids:11105  . . . . . . 273--274
        Michel Émery and   
Szeged Problem Solving Group Fejéntaláltuka   A Sum Inequality:11107 . . . . . . . . . 274--274
              Marius Ghergu and   
Microsoft Research Problem Group   Set Inclusion and Density:11110  . . . . 274--274
                 Michael Beeson   Book Review: \booktitleA Tour through
                                  Mathematical Logic, by Robert S. Wolf    275--280
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 4, April, 2006

     Óscar Martín   Look-and-Say Biochemistry: Exponential
                                  RNA and Multistranded DNA  . . . . . . . 289--307
               Jasbir S. Chahal   Congruent Numbers and Elliptic Curves    308--317
                 Jeremy Gibbons   Unbounded Spigot Algorithms for the
                                  Digits of Pi . . . . . . . . . . . . . . 318--328
                   Bennet Vance   Counting Ordered Trees by Permuting
                                  Their Parts  . . . . . . . . . . . . . . 329--335
              Nils Abramson and   
                  Jan Boman and   
           Björn Bonnevier   Plane Intersections of Rotational
                                  Ellipsoids . . . . . . . . . . . . . . . 336--339
             Oleg Mushkarov and   
                Nikolai Nikolov   Semiregular Polygons . . . . . . . . . . 339--344
                  R. B. Burckel   Fubinito (Immediately) Implies FTA . . . 344--347
              T. W. Körner   On the Fundamental Theorem of Algebra    347--348
                    Paul Melvin   A Topological Menagerie  . . . . . . . . 348--351
              Eberhard Knobloch   Mathesis Perennis: Mathematics in
                                  Ancient, Renaissance, and Modern Times   352--365
                  Shmuel Rosset   Problem 11215  . . . . . . . . . . . . . 366--366
               Ted Chinburg and   
             Shahriar Shahriari   Problem 11216  . . . . . . . . . . . . . 366--366
                Michel Bataille   Problem 11217  . . . . . . . . . . . . . 366--366
                    Gary Gordon   Problem 11218  . . . . . . . . . . . . . 366--367
                  R. A. Strubel   Problem 11219  . . . . . . . . . . . . . 367--367
                 David Beckwith   Problem 11220  . . . . . . . . . . . . . 367--367
                 Paolo Perfetti   Problem 11221  . . . . . . . . . . . . . 367--367
            Dimiter Skordev and   
                  Gerry Myerson   An Impossible Difference Condition:
                                  11074  . . . . . . . . . . . . . . . . . 367--368
               Donald Knuth and   
                  Robin Chapman   Cube-Free Sums: 11078  . . . . . . . . . 368--369
                 Brian Cook and   
            James Whitenton and   
                  Richard Stong   A Complex Identity: 11079  . . . . . . . 369--370
                Wu Wei Chao and   
National Security Agency Problems Group   A Divisibility Problem: 11082  . . . . . 370--371
         William P. Wardlaw and   
            Jean-Pierre Grivaux   The Null Ideal of a Matrix: 11083  . . . 371--371
              H. A. ShahAli and   
             Timothy LeSaulnier   Finding a Repeated Difference: 11084 . . 371--372
           Stephen C. Locke and   
                  Richard Stong   Coloring Graphs with Few Odd Cycles:
                                  11086  . . . . . . . . . . . . . . . . . 372--372
               Florian Luca and   
                John Ferdinands   Sometimes $n$ Divides $ \sigma k(n) $:
                                  11090  . . . . . . . . . . . . . . . . . 372--373
             Arturo Magidin and   
                      John Cade   The Order of a Product of Group
                                  Elements: 11092  . . . . . . . . . . . . 373--373
                 Paul G. Goerss   Book Review: \booktitleTopology: A
                                  Geometric Approach, by Terry Lawson  . . 374--377
                     Carol Wood   Book Review: \booktitleAlfred Tarski:
                                  Life and Logic, by Anita Burdman
                                  Feferman; Solomon Feferman . . . . . . . 377--379
                      L. Elsner   Book Review: \booktitleGer\vsgorin and
                                  His Circles, by Richard S. Varga . . . . 379--381
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 5, May, 2006

         Michael J. Mossinghoff   A \$1 Problem  . . . . . . . . . . . . . 385--402
           Le Baron O. Ferguson   What Can Be Approximated by Polynomials
                                  with Integer Coefficients  . . . . . . . 403--414
           Marcelo Sobottka and   
         Luiz P. L. de Oliveira   Periodicity and Predictability in
                                  Chaotic Systems  . . . . . . . . . . . . 415--424
  José Antonio Adell and   
                Alberto Lekuona   The Simplest Example of a Normal
                                  Asymptotic Expansion . . . . . . . . . . 425--442
                 Mowaffaq Hajja   The Arbitrariness of the Cevian Triangle 443--447
               Gilbert Helmberg   Curiosities concerning Weak Topology in
                                  Hilbert Space  . . . . . . . . . . . . . 447--452
                   Hei-Chi Chan   More Formulas for $ \pi $  . . . . . . . 452--455
             Detlef Gröger   On Gauss's Entry from January 6, 1809    455--458
                Jonathan Sondow   Problem 11222  . . . . . . . . . . . . . 459--459
         Christopher Hillar and   
                  Lionel Levine   Problem 11123  . . . . . . . . . . . . . 459--459
          Dietrich Trenkler and   
             Götz Trenkler   Problem 11224  . . . . . . . . . . . . . 459--459
José Luis Díaz-Barrero   Problem 11225  . . . . . . . . . . . . . 459--459
            Franck Beaucoup and   
    Tamás Erdélyi   Problem 11226  . . . . . . . . . . . . . 460--460
                Syrous Marivani   Problem 11227  . . . . . . . . . . . . . 460--460
                  Marian Tetiva   Problem 11228  . . . . . . . . . . . . . 460--460
             Emeric Deutsch and   
                   Marc Renault   A Variation on $t$-Catalan Paths: 11071  460--461
               David Callan and   
     GCHQ Problem Solving Group   The Maximum Associativeness of Division:
                                  11091  . . . . . . . . . . . . . . . . . 462--463
             Said Amghibech and   
        José Heber Nieto   An Application of Newton's Identities:
                                  11096  . . . . . . . . . . . . . . . . . 463--464
                 Kevin Ford and   
                  Robin Chapman   Ratio of Consecutive Divisors: 11097 . . 464--464
              Matthias Beck and   
          Richard Ehrenborg and   
           Thomas Zaslavsky and   
          Michael R. Avidon and   
            John H. Lindsey, II   Magic Squares and Nontransitive Dice:
                                  11099  . . . . . . . . . . . . . . . . . 464--465
           Gregory Galperin and   
            Hillel Gauchman and   
                   Jany C. Binz   Another Summation Identity Involving
                                  Binomial Coefficients: 11103 . . . . . . 465--466
             Emeric Deutsch and   
        José Heber Nieto   Counting Elevated Schröder Paths: 11108   466--467
Pál Péter Dalyay and   
     GCHQ Problem Solving Group   Periodic Solution to a Functional
                                  Equation: 11111  . . . . . . . . . . . . 467--467
                    Yongge Tian   On the Inverse of a Product of
                                  Orthogonal Projectors: 11112 . . . . . . 467--468
             Jeffrey Nunemacher   Book Review: \booktitlePrime Obsession,
                                  by John Derbyshire; Stalking the Riemann
                                  Hypothesis ~by Dan Rockmore  . . . . . . 469--473
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 6, June / July, 2006

            David H. Bailey and   
        Jonathan M. Borwein and   
             Vishaal Kapoor and   
              Eric W. Weisstein   Ten Problems in Experimental Mathematics 481--509
                    Aaron Levin   A Geometric Interpretation of an
                                  Infinite Product for the Lemniscate
                                  Constant . . . . . . . . . . . . . . . . 510--520
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Solids Circumscribing Spheres  . . . . . 521--540
                   Filip Saidak   On Goldbach's Conjecture for Integer
                                  Polynomials  . . . . . . . . . . . . . . 541--545
                        P. Shiu   Moment Sums Associated with Binary
                                  Linear Forms . . . . . . . . . . . . . . 545--550
                   J. J. Koliha   A Fundamental Theorem of Calculus for
                                  Lebesgue Integration . . . . . . . . . . 551--555
            Carlos D'Andrea and   
          Emiliano Gómez   The Broken Spaghetti Noodle  . . . . . . 555--557
                  A. F. Beardon   Contractions of the Real Line  . . . . . 557--558
               Boris A. Kushner   The Constructive Mathematics of A. A.
                                  Markov . . . . . . . . . . . . . . . . . 559--566
                  Ovidiu Furdui   Problem 11229  . . . . . . . . . . . . . 567--567
               Gregory Keselman   Problem 11230  . . . . . . . . . . . . . 567--567
             Christopher Hillar   Problem 11231  . . . . . . . . . . . . . 567--567
              Michael W. Botsko   Problem 11232  . . . . . . . . . . . . . 567--567
                  Robert Downes   Problem 11233  . . . . . . . . . . . . . 568--568
                Jim Brennan and   
              Richard Ehrenborg   Problem 11234  . . . . . . . . . . . . . 568--568
                Lenny Jones and   
                  Rachel Keller   Problem 11235  . . . . . . . . . . . . . 568--568
         Stanley Rabinowitz and   
                Roberto Tauraso   One from 1995: 10483 . . . . . . . . . . 568--569
                  Joel Zinn and   
              Gagik Amirkhanyan   Related Divergent Series: 11076  . . . . 569--571
               Sung Soo Kim and   
             C. Ray Rosentrater   Another Stick-Breaking Game: 11089 . . . 571--572
                 Leroy Quet and   
              Peter Òrno   A Continued Fraction Related to $ \pi $:
                                  11102  . . . . . . . . . . . . . . . . . 572--573
          Solomon W. Golomb and   
                   Pat Costello   A Consequence of Dirichlet's Theorem:
                                  11109  . . . . . . . . . . . . . . . . . 573--573
               Isaac Sofair and   
                     Otto Ruehr   Integrated by Fourier Transform: 11113   573--574
                 Jack Clark and   
                  Jaime Vinuesa   A Sequence Given in Terms of Harmonic
                                  Numbers: 11115 . . . . . . . . . . . . . 574--574
                  Steve Kennedy   Book Review: \booktitleMusings of the
                                  Masters, by Raymond G. Ayoub . . . . . . 575--580
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 7, August / September, 2006

               David Alan Grier   Irene Stegun, the ``Handbook of
                                  Mathematical Functions'', and the
                                  Lingering Influence of the New Deal  . . 585--597
                  Jon McCammond   Noncrossing Partitions in Surprising
                                  Locations  . . . . . . . . . . . . . . . 598--610
            Ole Christensen and   
         Khadija L. Christensen   Linear Independence and Series
                                  Expansions in Function Spaces  . . . . . 611--627
      Bernd S. W. Schröder   Rearranging the Calculus Sequence to
                                  Better Serve Its Partner Disciplines . . 628--636
                Jonathan Sondow   A Geometric Proof that $e$ Is Irrational
                                  and a New Measure of Its Irrationality   637--641
             Valerio De Angelis   Pairings and Signed Permutations . . . . 642--644
            Anupan Netyanun and   
               Donald C. Solmon   Iterated Products of Projections in
                                  Hilbert Space  . . . . . . . . . . . . . 644--648
         Danielle Silverman and   
                    Jim Wiseman   Noting the Difference: Musical Scales
                                  and Permutations . . . . . . . . . . . . 648--651
                        Hao Pan   On a Congruence modulo a Prime . . . . . 652--654
                     Jim Owings   Problem 11236  . . . . . . . . . . . . . 655--655
                 Emeric Deutsch   Problem 11237  . . . . . . . . . . . . . 655--655
            Aviezri S. Fraenkel   Problem 11238  . . . . . . . . . . . . . 655--655
                Michel Bataille   Problem 11239  . . . . . . . . . . . . . 655--655
Pál Péter Dályay   Problem 11240  . . . . . . . . . . . . . 655--655
                Roberto Tauraso   Problem 11241  . . . . . . . . . . . . . 656--656
                Gerd Herzog and   
                 Roland Lemmert   Problem 11242  . . . . . . . . . . . . . 656--656
               David Callan and   
              Kenneth Bernstein   A Lattice Path Equality: 11106 . . . . . 656--657
               Darko Veljan and   
                  Philipp Lampe   Incenter Distances in a Triangulation:
                                  11116  . . . . . . . . . . . . . . . . . 657--657
          Vesselin Dimitrov and   
                  Robin Chapman   A Modular Binomial Coefficient Identity:
                                  11118  . . . . . . . . . . . . . . . . . 657--658
             John Robertson and   
Microsoft Research Problems Group   A Property of the Generalized Pell
                                  Equation: 11119  . . . . . . . . . . . . 658--659
              H. A. ShahAli and   
                   Michael Reid   Powers of Consecutive Integers: 11121    659--660
                    Li Zhou and   
                 Michael Avidon   An Inequality of Cosines and Sines:
                                  11127  . . . . . . . . . . . . . . . . . 660--661
            N. G. de Bruijn and   
                  Rolf Richberg   Sum of a Series: 11131 . . . . . . . . . 661--662
             David E. Zitarelli   Book Review: \booktitleWhen Computers
                                  Were Human, by David Alan Grier  . . . . 663--668
                 Bruce P. Palka   Editor's Endnotes  . . . . . . . . . . . 669--672
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 8, October, 2006

             Kevin O'Bryant and   
              Bruce Reznick and   
             Monika Serbinowska   Almost Alternating Sums  . . . . . . . . 673--688
             Daniel J. Velleman   Exponential vs. Factorial  . . . . . . . 689--704
                    Jeff Suzuki   Lagrange's Proof of the Fundamental
                                  Theorem of Algebra . . . . . . . . . . . 705--714
               Alois Kufner and   
            Lech Maligranda and   
              Lars-Erik Persson   The Prehistory of the Hardy Inequality   715--732
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Sixth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 733--743
Héctor E. Lomelí and   
  César L. García   Variations on a Theorem of Korovkin  . . 744--750
               Ian Abramson and   
                Larry Goldstein   A Statistical Characterization of
                                  Regular Simplices  . . . . . . . . . . . 750--752
               Lyle N. Long and   
                   Howard Weiss   How Terminal Is Terminal Velocity? . . . 752--755
                   Dinesh Singh   The Spectrum in a Banach Algebra . . . . 756--758
                   Donald Knuth   Problem 11243  . . . . . . . . . . . . . 759--759
              Jolene Harris and   
               Bogdan Suceav\va   Problem 11244  . . . . . . . . . . . . . 759--760
                 Cezar Lupu and   
                   Tudorel Lupu   Problem 11245  . . . . . . . . . . . . . 760--760
                  Lee Goldstein   Problem 11246  . . . . . . . . . . . . . 760--760
            Jürgen Eckhoff   Problem 11247  . . . . . . . . . . . . . 760--760
Pál Péter Dályay   Problem 11248  . . . . . . . . . . . . . 760--760
                 David Beckwith   Problem 11249  . . . . . . . . . . . . . 760--760
             Benne de Weger and   
Microsoft Research Problems Group   How Many Powers of 2 Must Survive? 11114 760--761
             Michael Nyblom and   
             Giulio Francot and   
                Roberto Tauraso   Counting Powers by Inclusion and
                                  Exclusion: 11117 . . . . . . . . . . . . 762--762
                   Bob Berk and   
                    Larry Shepp   Gaussian Convex Hull: 11120  . . . . . . 762--763
             Shahin Amrahov and   
             Andrew D. Loveless   Now, What Year Is It? 11125  . . . . . . 763--763
            Raymond Mortini and   
         Patrick J. Fitzsimmons   Countably Linearly Independent: 11136    763--764
            Grahame Bennett and   
                  O. P. Lossers   An Odd Inequality: 11139 . . . . . . . . 764--764
             Walther Janous and   
                  Rolf Richberg   A Completely Monotonic Function: 11140   764--765
              Richard Bagby and   
                  O. P. Lossers   Implicit Derivative Continuous: 11141    765--766
                  Joel Zinn and   
                Grahame Bennett   A Sum Inequality: 11145  . . . . . . . . 766--766
                Ramesh Gangolli   Book Review: \booktitleDark Hero of the
                                  Information Age: In Search of Norbert
                                  Wiener, the Father of Cybernetics, by
                                  Flo Conway; Jim Siegelman  . . . . . . . 767--774
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 9, November, 2006

                   Gabriel Katz   Curves in Cages: An Algebro-Geometric
                                  Zoo  . . . . . . . . . . . . . . . . . . 777--791
                  Ion Barbu and   
                 Sarah Glaz and   
                 JoAnne Growney   Ut Algebra Poesis (As Algebra, So
                                  Poetry)  . . . . . . . . . . . . . . . . 792--793
               Aaron Melman and   
                     Bill Gragg   An Optimization Framework for Polynomial
                                  Zerofinders  . . . . . . . . . . . . . . 794--804
              Glen Anderson and   
        Mavina Vamanamurthy and   
                 Matti Vuorinen   Monotonicity Rules in Calculus . . . . . 805--816
               Ingram Olkin and   
                    Larry Shepp   Several Colorful Inequalities  . . . . . 817--822
                David F. Snyder   Combinatorics of Barycentric Subdivision
                                  and Characters of Simplicial
                                  Two-Complexes  . . . . . . . . . . . . . 822--826
               Thomas Brady and   
                     Colum Watt   On Products of Euclidean Reflections . . 826--829
                Vilmos Komornik   Another Short Proof of Descartes's Rule
                                  of Signs . . . . . . . . . . . . . . . . 829--830
              Piotr Pragacz and   
              Abe Shenitzer and   
             John Stillwell and   
                     Roman Duda   The Life and Work of Alexander
                                  Grothendieck . . . . . . . . . . . . . . 831--846
                    Sun Wen Cai   Problem 11250  . . . . . . . . . . . . . 847--847
                  Marian Tetiva   Problem 11251  . . . . . . . . . . . . . 847--847
                Ovidiu Bagdasar   Problem 11252  . . . . . . . . . . . . . 847--847
                 David Beckwith   Problem 11253  . . . . . . . . . . . . . 847--847
                    Lenny Jones   Problem 11254  . . . . . . . . . . . . . 847--848
                   Slavko Simic   Problem 11255  . . . . . . . . . . . . . 848--848
                Finbarr Holland   Problem 11256  . . . . . . . . . . . . . 848--848
                Gerd Herzog and   
                 Roland Lemmert   Problem 11242  . . . . . . . . . . . . . 848--848
          Victor Pambuccian and   
                  Robin Chapman   Pythagorean Triangles Are Not Quite
                                  Perfect: 11122 . . . . . . . . . . . . . 848--850
                 James S. Weber   How Many Histograms Can a Data Set Have?
                                  11126  . . . . . . . . . . . . . . . . . 850--851
                Yongge Tian and   
                  Robin Chapman   Inequalities Involving Rank and
                                  Kronecker Product: 11129 . . . . . . . . 851--851
               Paul Bateman and   
              Michael R. Avidon   Approximating the Reciprocal of Zeta:
                                  11130  . . . . . . . . . . . . . . . . . 852--854
              Pamela Gorkin and   
            Raymond Mortini and   
the Microsoft Research Problems Group   A Meromorphic Function: 11147  . . . . . 854--854
             Charles R. Hampton   Book Review: \booktitlePhilosophy of
                                  Mathematics: An Introduction to the
                                  World of Proofs Pictures, by James
                                  Robert Brown; Philosophies of
                                  Mathematics ~by Alexander George; Daniel
                                  J. Velleman; Thinking about Mathematics:
                                  The Philosophy of Mathematics ~by
                                  Stewart Shapiro  . . . . . . . . . . . . 855--860
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 113, Number 10, December, 2006

              Emmanuel Kowalski   Bernstein Polynomials and Brownian
                                  Motion . . . . . . . . . . . . . . . . . 865--886
             Rachel W. Hall and   
                Paul Klingsberg   Asymmetric Rhythms and Tiling Canons . . 887--896
           Pamela B. Pierce and   
             Daniel J. Velleman   Some Generalizations of the Notion of
                                  Bounded Variation  . . . . . . . . . . . 897--904
            Richard O. Hill and   
               Thomas H. Parker   A Study of Core-Plus Students Attending
                                  Michigan State University  . . . . . . . 905--921
              Andrew J. Simoson   Sliding along a Chord through a Rotating
                                  Earth  . . . . . . . . . . . . . . . . . 922--928
                     A. G. Ramm   Dynamical Systems Method and a
                                  Homeomorphism Theorem  . . . . . . . . . 928--933
              Benjamin Baumslag   A Simple Way of Proving the
                                  Jordan--Hölder--Schreier Theorem  . . . . 933--935
                 Andrew Browder   Complex Numbers and the Ham Sandwich
                                  Theorem  . . . . . . . . . . . . . . . . 935--937
                   Filip Saidak   A New Proof of Euclid's Theorem  . . . . 937--938
                Raimond Struble   Problem 11257  . . . . . . . . . . . . . 939--939
                  Manuel Kauers   Problem 11258  . . . . . . . . . . . . . 939--939
                   Nobuhisa Abe   Problem 11259  . . . . . . . . . . . . . 939--939
                 Paolo Perfetti   Problem 11260  . . . . . . . . . . . . . 939--939
                   Isaac Sofair   Problem 11261  . . . . . . . . . . . . . 940--940
                Ashay Burungale   Problem 11262  . . . . . . . . . . . . . 940--940
               Gregory Keselman   Problem 11263  . . . . . . . . . . . . . 940--940
               Christoph Soland   Secondary Inradii: 11046 . . . . . . . . 940--941
           Arturas Dubickas and   
                Chris Smyth and   
                  Richard Stong   Polynomials with Three Distinct Zeros
                                  Summing to Zero: 11123 . . . . . . . . . 941--942
              Ray Redheffer and   
                  Richard Stong   A Cousin of Gronwall's Inequality: 11135 942--943
            Roberto Tauraso and   
                  O. P. Lossers   Perfect Squares From Punctured Squares:
                                  11138  . . . . . . . . . . . . . . . . . 943--944
                Mircea Ivan and   
Microsoft Research Problems Group   Patrial Fractions, Product Log: 11152    945--945
          Emmanuel Kowalski and   
                 Tanguy Rivoall   A Positive Polynomial: 11155 . . . . . . 945--946
                      Anonymous   Errata and End Notes for 2006  . . . . . 946--946
               Della D. Fenster   Book Review: \booktitleSaunders Mac
                                  Lane: A Mathematical Autobiography, by
                                  Saunders Mac Lane  . . . . . . . . . . . 947--951
                Steven Galovich   Book Review: \booktitleAnts, Bikes, and
                                  Clocks: Problem Solving for
                                  Undergraduates, by William Briggs  . . . 951--954
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                      Anonymous   Volume Information . . . . . . . . . . . ??


American Mathematical Monthly
Volume 114, Number 1, January, 2007

                Peter Maier and   
                  Werner Nickel   Attainable Patterns in Alien Tiles . . . 1--13
                Tanya Leise and   
                   Andrew Cohen   Nonlinear Oscillators at Our Fingertips  14--28
                    Dave Auckly   Solving the Quartic with a Pencil  . . . 29--39
          Donatella Merlini and   
            Renzo Sprugnoli and   
            Maria Cecilia Verri   The Method of Coefficients . . . . . . . 40--57
            William F. Ford and   
              James A. Pennline   When Does Convergence in the Mean Imply
                                  Uniform Convergence? . . . . . . . . . . 58--60
                   \vSime Ungar   The Koch Curve: a Geometric Proof  . . . 61--66
               Dong-Soo Kim and   
                   Young Ho Kim   A Characterization of Ellipses . . . . . 66--70
            Jonathan M. Borwein   A Class of Dirichlet Series Integrals    70--76
                   Donald Knuth   Problem 11264  . . . . . . . . . . . . . 77--77
               Steve Butler and   
                        Jia Mao   Problem 11265  . . . . . . . . . . . . . 77--77
                  Marian Tetiva   Problem 11266  . . . . . . . . . . . . . 77--77
               Eugene A. Herman   Problem 11267  . . . . . . . . . . . . . 77--77
                  M. L. Glasser   Problem 11268  . . . . . . . . . . . . . 78--78
            Hervé Moulin   Problem 11269  . . . . . . . . . . . . . 78--78
                   Sergey Sadov   Problem 11270  . . . . . . . . . . . . . 78--78
                 David Beckwith   An Accidental Repetition of the All-Ones
                                  Problem: 10851 . . . . . . . . . . . . . 78--79
                Tom Apostol and   
Microsoft Research Problems Group   Summing the Initial Inverted Powers:
                                  11128  . . . . . . . . . . . . . . . . . 79--80
              M. L. Glasser and   
                  Richard Stong   An Elementary Integral: 11148  . . . . . 80--81
                Mircea Ivan and   
                  loan Rasa and   
                   M. A. Prasad   Limit with Nested Logs: 11149  . . . . . 81--81
               Paul Bracken and   
         Michael Goldenberg and   
                    Mark Kaplan   A Nonlinear Recurrence: 11153  . . . . . 81--82
            Hillel Gauchman and   
Northwestern University Math Problem Solving Group   Square Root Inequality: 11157  . . . . . 82--83
                  Greg Oman and   
              Michael W. Botsko   Isomorphic Rings of Functions: 11166 . . 83--83
   Mohammad Hossein Mehrabi and   
                  O. P. Lossers   A Gamma Function Inequality: 11169 . . . 83--84
               Slavko Simic and   
     GCHQ Problem Solving Group   Maximum Real Part of a Zero of a
                                  Polynomial: 11184  . . . . . . . . . . . 84--84
       Fernando Q. Gouvêa   Book Review: \booktitleA First Course in
                                  Modular Forms, by Fred Diamond; Jerry
                                  Shurman  . . . . . . . . . . . . . . . . 85--90
             Daniel J. Velleman   Editor's Endnotes  . . . . . . . . . . . 91--91
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 2, February, 2007

                 Richard K. Guy   The Lighthouse Theorem, Morley &
                                  Malfatti: a Budget of Paradoxes  . . . . 97--141
                      Po-Ru Loh   Stepping to Infinity Along Gaussian
                                  Primes . . . . . . . . . . . . . . . . . 142--151
                     Bau-Sen Du   A Simple Proof of Sharkovsky's Theorem
                                  Revisited  . . . . . . . . . . . . . . . 152--155
               Gwen Spencer and   
              Francis Edward Su   The LSB Theorem Implies the KKM Lemma    156--159
         Sam B. Nadler, Jr. and   
                Donna M. Zitney   Pointwise Products of Uniformly
                                  Continuous Functions on Sets in the Real
                                  Line . . . . . . . . . . . . . . . . . . 160--163
                  Iliya Bluskov   Problem 11271  . . . . . . . . . . . . . 164--164
                   Vasile Mihai   Problem 11272  . . . . . . . . . . . . . 164--164
                  Marian Tetiva   Problem 11273  . . . . . . . . . . . . . 164--165
                   Donald Knuth   Problem 11274  . . . . . . . . . . . . . 165--165
              Michael S. Becker   Problem 11275  . . . . . . . . . . . . . 165--165
                  Eugene Herman   Problem 11276  . . . . . . . . . . . . . 165--165
     Vicen\ctiu R\uadulescu and   
                  Richard Stong   Exponential Growth of a Solution: 11137  165--166
                George Lamb and   
                  J. A. Grzesik   A Quadrature on a Sphere: 11159  . . . . 167--167
             Paolo Perfetti and   
Microsoft Research Problems Group   Series with Sines: 11162 . . . . . . . . 167--168
     Vicen\ctiu R\uadulescu and   
Microsoft Research Problems Group   Ginzburg--Landau Energy: 11167 . . . . . 168--170
                 Suat Namli and   
                  O. P. Lossers   A Functional Equation with Exponential
                                  Solutions: 11180 . . . . . . . . . . . . 170--171
            Grahame Bennett and   
               Eugene A. Herman   Apply Hölder: 11202 . . . . . . . . . . . 171--171
              Gerald B. Folland   Book Review: \booktitleAnalysis I:
                                  Convergence, Elementary Functions, by
                                  Roger Godement; Analysis II:
                                  Differential and Integral Calculus,
                                  Fourier Series, Holomorphic Functions
                                  ~by Roger Godement . . . . . . . . . . . 172--176
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 3, March, 2007

               Amy Cohen-Corwin   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award to Lee Lorch for Distinguished
                                  Service to Mathematics . . . . . . . . . 181--182
               Robyn Curtis and   
                 Marcel Steiner   Configuration Spaces of Planar Pentagons 183--201
                Katherine Socha   Circles in Circles: Creating a
                                  Mathematical Model of Surface Water
                                  Waves  . . . . . . . . . . . . . . . . . 202--216
            Anders Claesson and   
               T. Kyle Petersen   Conway's Napkin Problem  . . . . . . . . 217--231
                Dante Manna and   
                 Victor H. Moll   A Simple Example of a New Class of
                                  Landen Transformation  . . . . . . . . . 232--241
              Michael W. Botsko   Exactly Which Bounded Darboux Functions
                                  Are Derivatives? . . . . . . . . . . . . 242--246
                      Mark Levi   Riemann Mapping Theorem by Steepest
                                  Descent  . . . . . . . . . . . . . . . . 246--251
              David H. Armitage   Entire Functions That Tend to Zero on
                                  Every Line . . . . . . . . . . . . . . . 251--256
                 Mark A. Pinsky   Stirling's Formula via the Poisson
                                  Distribution . . . . . . . . . . . . . . 256--258
                  Prithwijit De   Problem 11277  . . . . . . . . . . . . . 259--259
                   Slavko Simic   Problem 11278  . . . . . . . . . . . . . 259--259
              Vitaly Stakhovsky   Problem 11279  . . . . . . . . . . . . . 259--259
                   Harris Kwong   Problem 11280  . . . . . . . . . . . . . 259--259
              Max Alekseyev and   
                 Emeric Deutsch   Problem 11281  . . . . . . . . . . . . . 259--259
 Dragomir \vZ. \Dbarkovi\'c and   
                   Kaiming Zhao   Problem 11282  . . . . . . . . . . . . . 260--260
                 John Abbot and   
                Umberto Zannier   Problem 11283  . . . . . . . . . . . . . 260--260
            Stephen B. Gray and   
            Thomas McMillan and   
                  Xiaoshen Wang   Stepping to Regularity: 10923  . . . . . 260--261
             Kent D. Boklan and   
              Michael R. Avidon   Heronian Triangles: 11134  . . . . . . . 261--262
        Ernst Schulte-Geers and   
                     Karl David   An Identity Involving Rooted Forest:
                                  11144  . . . . . . . . . . . . . . . . . 262--264
                Yongge Tian and   
               Eugene A. Herman   Matrix Systems with the Same Sets: 11146 264--264
             Emeric Deutsch and   
                  O. P. Lossers   Peaks in Dyck Paths: 11150 . . . . . . . 264--265
            Donald E. Knuth and   
                  O. P. Lossers   Partitions of a Circular Set: 11151  . . 265--266
                Kent Holing and   
              Michael R. Avidon   Indivisibility of the Sum of Squares:
                                  11154  . . . . . . . . . . . . . . . . . 266--266
                 John Stillwell   Book Review: \booktitleGod Created the
                                  Integers, by Stephen Hawking . . . . . . 267--271
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 4, April, 2007

     Alberto A. Martínez   Euler's ``Mistake''? The Radical Product
                                  Rule in Historical Perspective . . . . . 273--285
       Christopher Francese and   
                 David Richeson   The Flaw in Euler's Proof of His
                                  Polyhedral Formula . . . . . . . . . . . 286--296
      Gopala Krishna Srinivasan   The Gamma Function: An Eclectic Tour . . 297--315
               Bennett Chow and   
             David Glickenstein   Semidiscrete Geometric Flows of Polygons 316--328
                Colin Adams and   
               Frank Morgan and   
               John M. Sullivan   When Soap Bubbles Collide  . . . . . . . 329--337
         Arthur T. Benjamin and   
             Gregory P. Dresden   A Combinatorial Proof of Vandermonde's
                                  Determinant  . . . . . . . . . . . . . . 338--341
               Michael A. Allen   Evaluation of Some Improper Integrals
                                  Involving Hyperbolic Functions . . . . . 341--343
             Robin Pemantle and   
              Carsten Schneider   When Is 0.999... Equal to 1? . . . . . . 344--350
                Brendan Foreman   Ghys's Theorem and Semi-Osculating
                                  Conics of Planar Curves  . . . . . . . . 351--356
               Gilbert Helmberg   An Absolutely Continuous Function in L1
                                  (R) W1,1 (R) . . . . . . . . . . . . . . 356--357
                      Greg Oman   Problem 11284  . . . . . . . . . . . . . 358--358
                   Yakub Aliyev   Problem 11285  . . . . . . . . . . . . . 358--358
                Marc LeBrun and   
            David Applegate and   
                N. J. A. Sloane   Problem 11286  . . . . . . . . . . . . . 358--358
          Stephen J. Herschkorn   Problem 11287  . . . . . . . . . . . . . 359--359
         Christopher Hillar and   
               Troels Windfeldt   Problem 11288  . . . . . . . . . . . . . 359--359
                Oleh Faynshteyn   Problem 11289  . . . . . . . . . . . . . 359--359
                 Cezar Lupu and   
                   Tudorel Lupu   Problem 11290  . . . . . . . . . . . . . 359--359
            Jonathan Sondow and   
                  Richard Stong   Choice Bounds: 11132 . . . . . . . . . . 359--360
               Paul Bracken and   
     Heinz-Jürgen Seiffert   An Integral Inequality: 11133  . . . . . 360--361
               Donald Knuth and   
                Roberto Tauraso   A Combinatorial Maximum: 11142 . . . . . 361--362
            Richard Stanley and   
     GCHQ Problem Solving Group   Inverting a Matrix of Striling Numbers:
                                  11156  . . . . . . . . . . . . . . . . . 362--362
             Emeric Deutsch and   
Lafayette College Problem Group   Compositions without Common Factors:
                                  11161  . . . . . . . . . . . . . . . . . 363--363
            Michel Bataille and   
                  Richard Stong   Counting Lattice Quadrilaterals Tangent
                                  to an Ellipse: 11163 . . . . . . . . . . 363--364
José Luis Díaz-Barrero and   
                Ulrich Abel and   
                    Mircea Ivan   A Recurrent Identify: 11164  . . . . . . 364--365
               John P. D'Angelo   Book Review: \booktitleGeometric
                                  Function Theory: Explorations in Complex
                                  Analysis, by Steven G. Krantz  . . . . . 366--370
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 5, May, 2007

                Yuval Peres and   
               Oded Schramm and   
            Scott Sheffield and   
                David B. Wilson   Random-Turn Hex and Other Selection
                                  Games  . . . . . . . . . . . . . . . . . 373--387
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Unwrapping Curves from Cylinders and
                                  Cones  . . . . . . . . . . . . . . . . . 388--416
             Graham Everest and   
              Shaun Stevens and   
             Duncan Tamsett and   
                       Tom Ward   Primes Generated by Recurrence Sequences 417--431
                J. W. Neuberger   The Continuous Newton's Method, Inverse
                                  Functions, and Nash--Moser . . . . . . . 432--437
                 Anthony Mendes   A Note on Alternating Permutations . . . 437--440
          Michael Kerckhove and   
                    Gary Lawlor   The Circle and the Cycloid: a Surprising
                                  Link . . . . . . . . . . . . . . . . . . 441--443
                       Jack Ohm   A Matrix Approach to Zero-Divisors in
                                  R[x] . . . . . . . . . . . . . . . . . . 444--450
            Richard Jerrard and   
                    John Wetzel   Problem 11291  . . . . . . . . . . . . . 451--451
                   David Callan   Problem 11292  . . . . . . . . . . . . . 451--451
                   Sergey Sadov   Problem 11293  . . . . . . . . . . . . . 451--451
                John Zucker and   
                 Ross McPhedran   Problem 11294  . . . . . . . . . . . . . 452--452
                 Stefano Siboni   Problem 11295  . . . . . . . . . . . . . 452--452
                 Said Amghibech   Problem 11296  . . . . . . . . . . . . . 452--452
                  Marian Tetiva   Problem 11297  . . . . . . . . . . . . . 452--452
                Bogdan Nica and   
                   S. Amghibech   Similarities of Euclidean Space: 11124   452--453
          Alexander Dubinov and   
                 Irina Dubinova   Closed Form Closure: 11143 . . . . . . . 453--453
             David Beckwith and   
                   Harris Kwong   Prime Powers Dividing a Factorial: 11158 453--454
           Marc Chamberland and   
              C. R. Pranesachar   Fermat to the Rescue: 11160  . . . . . . 454--454
                Yogesh More and   
                  Robin Chapman   The Sum of Catalan Numbers, Modulo 3:
                                  11165  . . . . . . . . . . . . . . . . . 454--455
                Kent Holing and   
Microsoft Research Problems Group   Properties of Pythagorean Triples: 11168 455--456
             Emeric Deutsch and   
                    S. C. Locke   Dissecting a Polygon: 11170  . . . . . . 456--457
     Heinz-Jürgen Seiffert   Familiar Identities in Disguise: 11172   457--458
              David M. Bressoud   Book Review: \booktitleMaking
                                  Transcendence Transparent, by B. Burger;
                                  Robert Tubbs . . . . . . . . . . . . . . 459--461
                  Mark Schwartz   Book Review: \booktitleConics, by Keith
                                  Kendig . . . . . . . . . . . . . . . . . 461--464
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 6, June / July, 2007

               Brian S. Thomson   Rethinking the Elementary Real Analysis
                                  Course . . . . . . . . . . . . . . . . . 469--490
           Andrew J. Hetzel and   
                Jay S. Liew and   
               Kent E. Morrison   The Probability That a Matrix of
                                  Integers Is Diagonalizable . . . . . . . 491--499
            Brody Dylan Johnson   The Nonholonomy of the Rolling Sphere    500--508
               Dierk Schleicher   Hausdorff Dimension, Its Properties, and
                                  Its Surprises  . . . . . . . . . . . . . 509--528
              Ling-Ling Shi and   
                        Hao Pan   A $q$-Analogue of Wolstenholme's
                                  Harmonic Series Congruence . . . . . . . 529--531
      Jürgen Bliedtner and   
                  Peter A. Loeb   A Local Maximal Function Simplifying
                                  Measure Differentiation  . . . . . . . . 532--536
          Boris Adamczewski and   
                   Yann Bugeaud   A Short Proof of the Transcendence of
                                  Thue--Morse Continued Fractions  . . . . 536--540
                 Joseph Bak and   
               Pisheng Ding and   
                  Donald Newman   Extremal Points, Critical Points, and
                                  Saddle Points of Analytic Functions  . . 540--546
                  Jakob Jonsson   Problem 11298  . . . . . . . . . . . . . 547--547
      Pablo Fern\`andez Refolio   Problem 11299  . . . . . . . . . . . . . 547--547
                    Ulrich Abel   Problem 11300  . . . . . . . . . . . . . 547--547
                Finbarr Holland   Problem 11301  . . . . . . . . . . . . . 547--547
                    Horst Alzer   Problem 11302  . . . . . . . . . . . . . 547--547
                    M. Farrokhi   Problem 11303  . . . . . . . . . . . . . 548--548
    Teodora-Liliana R\uadulescu   Problem 11304  . . . . . . . . . . . . . 548--548
            M. N. Deshpande and   
            J. P. Shiwalkar and   
     GCHQ Problem Solving Group   Two Heads Are Better than One: 11173 . . 548--549
                Jon Bentley and   
              Colin Mallows and   
                  Richard Stong   Learning from Experience: 11178  . . . . 549--550
             David Beckwith and   
                        Li Zhou   A Determinant by Möbius Inversion: 11179  550--550
             Shahin Amrahov and   
             Nicholas C. Singer   Perfect Powers in an Arithmetic
                                  Progression: 11182 . . . . . . . . . . . 550--551
             David Beckwith and   
          Vadim Ponomarenko and   
                      Rob Pratt   Building Two Piles of Equal Height:
                                  11183  . . . . . . . . . . . . . . . . . 551--552
          Rainer Brück and   
                  Robin Chapman   When Does It Converge: 11185 . . . . . . 552--554
                    Li Zhou and   
Northwestern University Math Problem Solving Group and   
   Christopher Carl Heckman and   
                   Jerry Minkus   Tiling $4$-Rowed Rectangles with
                                  Dominoes: 11187  . . . . . . . . . . . . 554--556
              Susan Jane Colley   Book Review: \booktitleIntroduction to
                                  Plane Algebraic Curves, by Ernst Kunz;
                                  Richard G. Belshoff  . . . . . . . . . . 557--561
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 7, August / September, 2007

Enrique A. González- Velasco   James Gregory's Calculus in the
                                  ``Geometriæ Pars Universalis''  . . . . . 565--576
            Roman Dwilewicz and   
  Ján Miná\vc and   
             Andrew Schultz and   
                   John Swallow   Hilbert 90 for Biquadratic Extensions    577--587
                Arno Berger and   
               Theodore P. Hill   Newton's Method Obeys Benford's Law  . . 588--601
                    Jin Akiyama   Tile-Makers and Semi-Tile-Makers . . . . 602--609
            Byron L. Walden and   
                 Lesley A. Ward   A Harmonic Measure Interpretation of the
                                  Arithmetic-Geometric Mean  . . . . . . . 610--622
         Carlos A. Escudero and   
  Agustí Reventós   An Interesting Property of the Evolute   623--628
                  Jack Cook and   
            Jonathan Lovett and   
                   Frank Morgan   Rotation in a Normed Plane . . . . . . . 628--632
             Arjeh M. Cohen and   
                   D. E. Taylor   On a Certain Lie Algebra Defined by a
                                  Finite Group . . . . . . . . . . . . . . 633--639
                Vahan Mkrtchyan   Problem 11305  . . . . . . . . . . . . . 640--640
               Alexandru Rosoiu   Problem 11306  . . . . . . . . . . . . . 640--640
                   David Callan   Problem 11307  . . . . . . . . . . . . . 640--640
                  Ovidiu Furdui   Problem 11308  . . . . . . . . . . . . . 640--640
              Roman Witu\la and   
                  Damian S\lota   Problem 11309  . . . . . . . . . . . . . 640--640
                     Erwin Just   Problem 11310  . . . . . . . . . . . . . 641--641
          Stephen J. Herschkorn   Problem 11311  . . . . . . . . . . . . . 641--641
            William Calbeck and   
                  Richard Stong   Another Diophantine Equation: 11175  . . 641--642
            M. N. Deshpande and   
     GCHQ Problem Solving Group   An Urn Problem with Labeled and
                                  Unlabeled Balls: 11181 . . . . . . . . . 642--642
   Angelo J. Christino, Jr. and   
      William C. Waterhouse and   
         the NSA Problems Group   A Group of Invertible Matrices: 11186    642--643
               David Bailey and   
              M. L. Glasser and   
                  Richard Stong   A Hypergeometric Identity: 11188 . . . . 643--645
                Lajos Csete and   
                  O. P. Lossers   A Quick Inequality: 11189  . . . . . . . 645--645
José Luis Díaz-Barrero and   
                 Julien Grivaux   A Polynomial and Its Zeros: 11190  . . . 645--647
                  Marian Tetiva   A Cyclic AM-GM Inequality: 11193 . . . . 647--647
              Marian Tetiva and   
Pál Péter Dályay   Ratio Circum-to-In-Radius: 11195 . . . . 648--649
              R. A. Strubel and   
              Donald R. Bridges   A Zeta Function Quickie: 11219 . . . . . 649--649
               Aliyev Yakub and   
                  David B. Leep   Symmetric Inequality: 11199  . . . . . . 649--649
             Stephen A. Fulling   Book Review: \booktitleLinearity,
                                  Symmetry, and Prediction in the Hydrogen
                                  Atom, by Stephanie Frank Singer  . . . . 650--653
                  James Fey and   
                  Eric Hart and   
           Christian Hirsch and   
              Harold Schoen and   
                Ann Watkins and   
             Daniel J. Velleman   Editor's Endnotes  . . . . . . . . . . . 654--661
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 8, October, 2007

                    David Benko   A New Approach to Hilbert's Third
                                  Problem  . . . . . . . . . . . . . . . . 665--676
             John H. Jaroma and   
              Kamaliya N. Reddy   Classical and Alternative Approaches to
                                  the Mersenne and Fermat Numbers  . . . . 677--687
Gábor J. Székely and   
                 Maria L. Rizzo   The Uncertainty Principle of Game Theory 688--702
               Harm Derksen and   
        Christian Eggermont and   
             Arno van den Essen   Multimagic Squares . . . . . . . . . . . 703--713
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Seventh William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 714--724
                   Peter D. Lax   The Cauchy Integral Theorem  . . . . . . 725--727
          Folkmar Bornemann and   
               Thomas Schmelzer   Taming a Hydra of Singularities  . . . . 727--732
               M. Ram Murty and   
                   Nithum Thain   Pick's Theorem via Minkowski's Theorem   732--736
                  F. Albiac and   
                   N. J. Kalton   A Characterization of Real $ C(K)
                                  $-Spaces . . . . . . . . . . . . . . . . 737--743
                   David Callan   Problem 11312  . . . . . . . . . . . . . 744--744
                 Cezar Lupu and   
                   Tudorel Lupu   Problem 11313  . . . . . . . . . . . . . 744--744
                   Yakub Aliyev   Problem 11314  . . . . . . . . . . . . . 744--744
                    M. Farrokhi   Problem 11315  . . . . . . . . . . . . . 744--744
                  Ovidiu Furdui   Problem 11316  . . . . . . . . . . . . . 745--745
                Michel Bataille   Problem 11317  . . . . . . . . . . . . . 745--745
              Roman Witu\la and   
                  Damian S\lota   Problem 11318  . . . . . . . . . . . . . 745--745
                R. V. Heath and   
                Christian Boyer   Better Late than Never: E 496  . . . . . 745--746
          Folkmar Bornemann and   
               Robert B. Israel   A Disguised Radius of Convergence: 11194 746--747
            Oleg Faynshteyn and   
                     Arkady Alt   A Crux Inequality: 11197 . . . . . . . . 747--748
                  Joel Zinn and   
                  O. P. Lossers   Kronecker-Like Convergence: 11200  . . . 748--749
          Michael S. Becker and   
                  Zuofeng Shang   Cosine Infinite Product: 11210 . . . . . 749--749
       Mihály Bencze and   
     Heinz-Jürgen Seiffert   More A-G Inequalities: 11211 . . . . . . 749--750
José Luis Díaz-Barrero and   
                  Eugene Herman   Limit of an Integral: 11225  . . . . . . 750--750
              Ovidiu Furdui and   
              Michael R. Avidon   A Gamma Limit: 11229 . . . . . . . . . . 751--751
              Warren P. Johnson   Book Review: \booktitleMathematics and
                                  Social Utopias in France: Olinde
                                  Rodrigues and His times, by Simon
                                  Altmann; Eduardo L. Ortiz  . . . . . . . 752--758
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 9, November, 2007

           Thomas Callaghan and   
             Peter J. Mucha and   
                Mason A. Porter   Random Walker Ranking for NCAA Division
                                  I-A Football . . . . . . . . . . . . . . 761--777
                  John Starrett   Solving Differential Equations by
                                  Symmetry Groups  . . . . . . . . . . . . 778--792
           Tomasz Bartnicki and   
          Jaroslaw Grytczuk and   
            H. A. Kierstead and   
                     Xuding Zhu   The Map-Coloring Game  . . . . . . . . . 793--803
         Hugh L. Montgomery and   
          Ulrike M. A. Vorhauer   Biased Trigonometric Polynomials . . . . 804--809
                   Omer Adelman   $ \sum \frac {1}{n} = \infty $: a
                                  Micro-Lesson on Probability and Symmetry 809--810
              Benjamin A. Lotto   Stacked Groups . . . . . . . . . . . . . 811--812
              Brett A. Harrison   On the Reducibility of Cyclotomic
                                  Polynomials over Finite Fields . . . . . 813--818
                  Marston Morse   Topology and Equilibria  . . . . . . . . 819--834
                 David Beckwith   Problem 11319  . . . . . . . . . . . . . 835--835
                   Donald Knuth   Problem 11320  . . . . . . . . . . . . . 835--835
             Christopher Hillar   Problem 11321  . . . . . . . . . . . . . 835--835
                Jonathan Sondow   Problem 11322  . . . . . . . . . . . . . 835--835
           Jody M. Lockhart and   
             William P. Wardlaw   Problem 11323  . . . . . . . . . . . . . 835--835
               Martin Kochanski   Problem 11324  . . . . . . . . . . . . . 836--836
            Finbarr Holland and   
                      Jim Leahy   Problem 11325  . . . . . . . . . . . . . 836--836
José Luis Díaz-Barrero and   
      Pantelimon George Popescu   Problem 11326  . . . . . . . . . . . . . 836--836
Pál Péter Dályay and   
National Security Agency Problems Group   Periodic Composition: 11174  . . . . . . 836--837
            Oleg Faynshteyn and   
                   Yan-loi Wong   Another Triangle Inequality: 11176 . . . 837--838
         Dorin M\varghidanu and   
                  Henry Ricardo   $ {\rm GM} \leq {\rm AMF} $: 11177 . . . 838--838
         Barthel Wayne Huff and   
               Gregory Keselman   Another Urn and Balls Problem: 11191 . . 838--839
              Brett Stevens and   
                  Richard Stong   A Sudoku Solution from Orthogonal Latin
                                  Squares: 11192 . . . . . . . . . . . . . 839--840
                     Fuxiang Yu   An Old Fermatian Problem: 11203  . . . . 840--840
      Christopher J. Hillar and   
         John H. Lindsey II and   
                  Robin Chapman   The Trace of the Sum of All Products of
                                  Two Matrices: 11204  . . . . . . . . . . 840--841
                    Li Zhou and   
           Chris Mackeprang and   
                   Kellen Myers   Coloring Graphs on Sponges: 11208  . . . 842--842
                  Edward Nelson   Book Review: \booktitle18 Unconventional
                                  Essays on the Nature of Mathematics, by
                                  Reuben Hersh . . . . . . . . . . . . . . 843--848
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 114, Number 10, December, 2007

             Charles R. Hadlock   Practicing Mathematics in the Public
                                  Arena: Challenges and Outcomes in Some
                                  Prominent Case Studies . . . . . . . . . 849--870
           Markku Halmetoja and   
           Pentti Haukkanen and   
           Teuvo Laurinolli and   
         Jorma K. Merikoski and   
           Timo Tossavainen and   
                   Ari Virtanen   On Direct and Inverse Proportionality    871--881
                Thomas C. Hales   The Jordan Curve Theorem, Formally and
                                  Informally . . . . . . . . . . . . . . . 882--894
                  Mark Levi and   
              Serge Tabachnikov   The Poncelet Grid and Billiards in
                                  Ellipses . . . . . . . . . . . . . . . . 895--908
               Alain Connes and   
                     Don Zagier   A Property of Parallelograms Inscribed
                                  in Ellipses  . . . . . . . . . . . . . . 909--914
            Johan Wästlund   An Elementary Proof of the Wallis
                                  Product Formula for $ \pi $  . . . . . . 914--917
      Christopher J. Hillar and   
                 Darren L. Rhea   Automorphisms of Finite Abelian Groups   917--923
António Guedes de Oliveira   On the Adjugate of a Matrix  . . . . . . 923--924
                 Rick Mabry and   
                Debbie Shepherd   Problem 11327  . . . . . . . . . . . . . 925--925
             Dmitris Vartziotis   Problem 11328  . . . . . . . . . . . . . 925--925
              T. Amdeberhan and   
                 Victor H. Moll   Problem 11329  . . . . . . . . . . . . . 925--925
                  Marian Tetiva   Problem 11330  . . . . . . . . . . . . . 925--925
                  Richard Bagby   Problem 11331  . . . . . . . . . . . . . 926--926
                Roberto Tauraso   Problem 11332  . . . . . . . . . . . . . 926--926
 Pablo Fernández Refolio   Problem 11333  . . . . . . . . . . . . . 926--926
                  Chu Cheng and   
                  Marius Stefan   A Quadrilateral and Its Circles: 11171   926--927
                Wu Wei Chao and   
Pál Péter Dályay   A Triangle Inequality: 11205 . . . . . . 928--928
                Mircea Ivan and   
          Alexandru Lupa\cs and   
               Richard A. Stong   A Limit Involving Euler's Constant:
                                  11206  . . . . . . . . . . . . . . . . . 928--929
          Michael W. Botsko and   
               Robert B. Israel   Disguised Cauchy Sequence: 11207 . . . . 929--930
          Alexander Dubinov and   
             Irina Dubinova and   
                      Knut Dale   Can ``Closed Form'' Involve Lambert?
                                  11209  . . . . . . . . . . . . . . . . . 930--931
            Michel Bataille and   
                  Richard Stong   Finding the Greatest Lower Bound: 11217  931--931
                      Anonymous   Errata: 11307  . . . . . . . . . . . . . 932--932
                    Kent Holing   Unsolved No Longer: 11154  . . . . . . . 932--932
                    Bogdan Nica   Reverse Engineering: 11124 . . . . . . . 932--932
                  Michael Henle   Book Review: \booktitleDivine
                                  Proportions: Rational Trigonometry to
                                  Universal Geometry, by N. J. Wildberger  933--937
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                      Anonymous   Volume Information . . . . . . . . . . . ??


American Mathematical Monthly
Volume 115, Number 1, January, 2008

         Frederick V. Henle and   
                 James M. Henle   Squaring the Plane . . . . . . . . . . . 3--12
           Michelle Previte and   
                      Sean Yang   A Novel Way to Generate Fractals . . . . 13--32
Péter Komjáth and   
                   Vilmos Totik   Ultrafilters . . . . . . . . . . . . . . 33--44
             Ray Cavalcante and   
               Todor D. Todorov   A Lost Theorem: Definite Integrals in an
                                  Asymptotic Setting . . . . . . . . . . . 45--56
                    Greg Martin   A Simple Polynomial for a Simple
                                  Transposition  . . . . . . . . . . . . . 57--60
            Banyat Sroysang and   
             John E. Wetzel and   
           Wacharin Wichiramala   Covers for Angleworms  . . . . . . . . . 61--65
                Stefanie Ucsnay   A Note on Tarski's Note  . . . . . . . . 66--68
                 Simon Marshall   Another Simple Proof of the High Girth,
                                  High Chromatic Number Theorem  . . . . . 68--70
             Jonathan Bober and   
               Jeffrey Lagarias   Problem 11334  . . . . . . . . . . . . . 71--71
Juan López González   Problem 11335  . . . . . . . . . . . . . 71--71
                   Donald Knuth   Problem 11336  . . . . . . . . . . . . . 71--71
                  Marian Tetiva   Problem 11337  . . . . . . . . . . . . . 71--71
                  Ovidiu Furdui   Problem 11338  . . . . . . . . . . . . . 71--71
José Luis Díaz-Barrero   Problem 11339  . . . . . . . . . . . . . 72--72
       Óscar Ciaurri and   
                     Luz Roncal   Problem 11340  . . . . . . . . . . . . . 72--72
   Mohammad Hossein Mehrabi and   
Pál Péter Dályay   A Condition on the Commutator: 11196 . . 72--72
             Robert Russell and   
           Christoph Soland and   
          William Dickinson and   
              William Dickenson   Can One Recover a (Spherical) Triangle
                                  from Its Medial Triangle? 11201  . . . . 73--74
             Paolo Perfetti and   
                  Richard Bagby   Differentiable and Discontinuous
                                  Densely: 11221 . . . . . . . . . . . . . 74--75
         Christopher Hillar and   
              Lionel Levine and   
                    S. C. Locke   Snapshots for Velocities: 11223  . . . . 75--76
            Franck Beaucoup and   
Tamás Erdélyi and   
Microsoft Research Problems Group   A Unique Solution: 11226 . . . . . . . . 76--76
          Michael W. Botsko and   
                 Albert Stadler   A Function Inequality: 11232 . . . . . . 77--77
              Marian Tetiva and   
                       Minh Can   A Triangle Inequality: 11228 . . . . . . 77--77
              Robert Downes and   
            Jean-Pierre Grivaux   A Derivative Formula: 11233  . . . . . . 78--78
             Jeffrey Nunemacher   Book Review: \booktitleFearless
                                  Symmetry: Exposing the Hidden Patterns
                                  of Numbers, by Avner Ash; Robert Gross   79--82
                    Ron Solomon   Book Review: \booktitleSymmetry and the
                                  Monster, by Mark Ronan . . . . . . . . . 82--85
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 2, February, 2008

      Christopher S. Hardin and   
                 Alan D. Taylor   A Peculiar Connection between the Axiom
                                  of Choice and Predicting the Future  . . 91--96
                Michel Balinski   Fair Majority Voting (or How to
                                  Eliminate Gerrymandering)  . . . . . . . 97--113
            Hugh Nelson Howards   Brunnian Spheres . . . . . . . . . . . . 114--124
            Jonathan M. Borwein   Hilbert's Inequality and Witten's
                                  Zeta-Function  . . . . . . . . . . . . . 125--137
               Abraham A. Ungar   From Möbius to Gyrogroups . . . . . . . . 138--144
                   Aaron Melman   Bounds on the Zeros of the Derivative of
                                  a Polynomial with All Real Zeros . . . . 145--147
                      Uri Elias   Qualitative Analysis of a Differential
                                  Equation of Abel . . . . . . . . . . . . 147--149
           W. Holszty\'nski and   
               J. Mycielski and   
              G. C. O'Brien and   
             S. \'Swierczkowski   Closed Curves on Spheres . . . . . . . . 149--153
       E. F. Cornelius, Jr. and   
                  Phill Schultz   Sequences Generated by Polynomials . . . 154--158
       Krzysztof Ciesielski and   
               Zdzis\law Pogoda   On Ordering the Natural Numbers, or, The
                                  Sharkovski Theorem . . . . . . . . . . . 159--165
                     Cezar Lupu   Problem 11341  . . . . . . . . . . . . . 166--166
               Luis H. Gallardo   Problem 11342  . . . . . . . . . . . . . 166--166
                 David Beckwith   Problem 11343  . . . . . . . . . . . . . 166--166
                 Albert Stadler   Problem 11344  . . . . . . . . . . . . . 166--166
              Roger Cuculi\`ere   Problem 11345  . . . . . . . . . . . . . 166--166
             Christopher Hillar   Problem 11346  . . . . . . . . . . . . . 166--167
           Mihály Bencze   Problem 11347  . . . . . . . . . . . . . 167--167
          Solomon W. Golomb and   
                Kyle Calderhead   Orthogonal Sudoku Squares: 11214 . . . . 167--168
              Shmuel Rosset and   
        José Heber Nieto   Maximum Velocity on a Car Trip: 11215    168--169
                Jim Brennan and   
          Richard Ehrenborg and   
               Eugene A. Herman   Goes Back to Boole: 11234  . . . . . . . 169--170
                 Jim Owings and   
              Marian Tetiva and   
             Matthew Huddleston   Coloring the Plane: 11236  . . . . . . . 170--172
Pál Péter Dályay and   
                   A. K. Shafie   Ex-To-In-Radius Ratio: 11240 . . . . . . 172--172
              Jolene Harris and   
           Bogdan Suceav\va and   
                      Knut Dale   Iterational Rate of Covergence: 11244    173--173
                   Marion Cohen   Book Review: \booktitleLetters to a
                                  Young Mathematician, by Ian Stewart  . . 174--177
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 3, March, 2008

               Amy Cohen-Corwin   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for 2008 to Lida K. Barrett for
                                  Distinguished Service to Mathematics . . 183--184
                  Fan Chung and   
                     Ron Graham   Primitive Juggling Sequences . . . . . . 185--194
                Jin Akiyama and   
             Hiroshi Fukuda and   
                  Chie Nara and   
            Toshinori Sakai and   
                  Jorge Urrutia   Universal Measuring Boxes with
                                  Triangular Bases . . . . . . . . . . . . 195--201
         Diego M. Benardete and   
             V. W. Noonburg and   
                     B. Pollina   Qualitative Tools for Studying Periodic
                                  Solutions and Bifurcations as Applied to
                                  the Periodically Harvested Logistic
                                  Equation . . . . . . . . . . . . . . . . 202--219
              Lee W. Jacobi and   
               Daniel J. Madden   On $ a^4 + b^4 + c^4 + d^4 = (a + b + c
                                  + d)^4 $ . . . . . . . . . . . . . . . . 220--236
               Takashi Agoh and   
                   Karl Dilcher   Reciprocity Relations for Bernoulli
                                  Numbers  . . . . . . . . . . . . . . . . 237--244
                Krassimir Penev   The Fubini Principle . . . . . . . . . . 245--248
   Franciszek Prus-Wi\'sniowski   A Refinement of Raabe's Test . . . . . . 249--252
               Ay\cse Alaca and   
              \cSaban Alaca and   
            Kenneth S. Williams   Arithmetic Progressions and Binary
                                  Quadratic Forms  . . . . . . . . . . . . 252--254
          Peter W. Saltzman and   
                   Pingzhi Yuan   On Sums of Consecutive Integral Roots    254--261
             Richard P. Stanley   Problem 11348  . . . . . . . . . . . . . 262--262
                     Cezar Lupu   Problem 11349  . . . . . . . . . . . . . 262--262
          Bhavana Deshpande and   
                M. N. Deshpande   Problem 11350  . . . . . . . . . . . . . 262--262
                  Marian Tetiva   Problem 11351  . . . . . . . . . . . . . 262--262
                    Daniel Reem   Problem 11352  . . . . . . . . . . . . . 263--263
            Ernst Schulte-Geers   Problem 11353  . . . . . . . . . . . . . 263--263
              Matthias Beck and   
            Alexander Berkovich   Problem 11354  . . . . . . . . . . . . . 263--263
             Hans V. Gerber and   
          Daniel Neuenschwander   Unsolved in 1990: 6576 . . . . . . . . . 263--264
                Gerd Herzog and   
                 Roland Lemmert   A Determinant Indentity: 11242 . . . . . 264--265
                  Lee Goldstein   A Bessel Function Identity: 11246  . . . 265--266
        Jürgen Eckhoff and   
                        Li Zhou   A Strip Problem: 11247 . . . . . . . . . 266--266
                Sun Wen Cai and   
              Vitaly Stakhovsky   Double Sum Inequality: 11250 . . . . . . 266--267
              Marian Tetiva and   
              Vitaly Stakhovsky   An Inequality Proved Without Computer
                                  Assistance: 11251  . . . . . . . . . . . 267--268
            Ovidiu Bagdasar and   
                  Marian Tetiva   A Productive Inequality: 11252 . . . . . 268--269
            Raimond Struble and   
            Jean-Pierre Grivaux   A Myth About Infinite Products: 11257    269--269
                   Martin Davis   Book Review: \booktitleInexhaustibility:
                                  A Non-Exhaustive Treatment, by Torkel
                                  Franzén; Gödel's Theorem: An Incomplete
                                  Guide to Its Use and Misuse ~by Torkel
                                  Franzén . . . . . . . . . . . . . . . . . 270--275
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 276--276
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 4, April, 2008

               Andrew Granville   Prime Number Patterns  . . . . . . . . . 279--296
                Robert A. Agnew   Optimal Congressional Apportionment  . . 297--303
               Steven G. Krantz   The Carathéodory and Kobayashi Metrics
                                  and Applications in Complex Analysis . . 304--329
                     Dan Kalman   An Elementary Proof of Marden's Theorem  330--338
        Mihály Bessenyei   The Hermite--Hadamard Inequality on
                                  Simplices  . . . . . . . . . . . . . . . 339--345
          John P. Robertson and   
              Keith R. Matthews   A Continued Fractions Approach to a
                                  Result of Feit . . . . . . . . . . . . . 346--349
            Gerhard Larcher and   
       Friedrich Pillichshammer   The Sum of Distances between Vertices of
                                  a Convex Polygon with Unit Perimeter . . 350--355
          Cayanne McFarlane and   
            Wm. Douglas Withers   Dynamical Systems and Irrational Angle
                                  Construction by Paper-Folding  . . . . . 355--358
                   Marc Renault   Lost (and Found) in Translation: André's
                                  Actual Method and Its Application to the
                                  Generalized Ballot Problem . . . . . . . 358--363
              Amitabha Tripathi   On Sums of Positive Integers That Are
                                  Not of the Form $ a x + b y $  . . . . . 363--364
            Jeffrey C. Lagarias   Problem 11355  . . . . . . . . . . . . . 365--365
              Michael Poghosyan   Problem 11356  . . . . . . . . . . . . . 365--365
                 Mehmet \cSahin   Problem 11357  . . . . . . . . . . . . . 365--365
                  Marian Tetiva   Problem 11358  . . . . . . . . . . . . . 365--365
                    J. Monterde   Problem 11359  . . . . . . . . . . . . . 365--365
                     Cezar Lupu   Problem 11360  . . . . . . . . . . . . . 365--366
             David Beckwith and   
               Harris Kwong and   
                  Rob Pratt and   
                Nicholas Singer   A Vanishing Alternating Sum: 11212/11220 366--366
                Finbarr Holland   Problem 11361  . . . . . . . . . . . . . 366--366
         Stanley Rabinowitz and   
             NSA Problems Group   Sometimes an Integer: 11213  . . . . . . 366--367
                Gary Gordon and   
               Bruce S. Burdick   The Number between $1$ and $n$ That Is
                                  Least Prime: 11218 . . . . . . . . . . . 367--368
Pál Péter Dályay and   
                  Jaime Vinuesa   A Romanian Olympiad Problem Generalized:
                                  11248  . . . . . . . . . . . . . . . . . 368--369
               Slavko Simic and   
                  O. P. Lossers   A Symmetric Inequality: 11255  . . . . . 369--370
            Finbarr Holland and   
                Michel Bataille   Perimeter by Integral: 11256 . . . . . . 370--371
           Gregory Keselman and   
                     E. Leonard   A Choice Sum: 11263  . . . . . . . . . . 371--372
              Leslie Hogben and   
              Wolfgang Kliemann   Book Review: \booktitleApplied Linear
                                  Algebra, by Peter J. Olver; Chehrzad
                                  Shakiban . . . . . . . . . . . . . . . . 373--378
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 5, May, 2008

               R. A. Bailey and   
           Peter J. Cameron and   
                Robert Connelly   Sudoku, Gerechte Designs, Resolutions,
                                  Affine Space, Spreads, Reguli, and
                                  Hamming Codes  . . . . . . . . . . . . . 383--404
                  J. Arroyo and   
                O. J. Garay and   
            J. J. Mencía   When Is a Periodic Function the
                                  Curvature of a Closed Plane Curve? . . . 405--414
                 Hieu D. Nguyen   Rearing Its Ugly Head: The Cosmological
                                  Constant and Newton's Greatest Blunder   415--430
           Jasbir S. Chahal and   
                 Brian Osserman   The Riemann Hypothesis for Elliptic
                                  Curves . . . . . . . . . . . . . . . . . 431--442
                       Igor Pak   Inflating the Cube Without Stretching    443--445
          Robert Kantrowitz and   
             Michael M. Neumann   Yet Another Proof of Minkowski's
                                  Inequality . . . . . . . . . . . . . . . 445--447
                Kathy Q. Ji and   
                Herbert S. Wilf   Extreme Palindromes  . . . . . . . . . . 447--451
                F. Mendivil and   
                   T. D. Taylor   Thin Sets with Fat Shadows: Projections
                                  of Cantor Sets . . . . . . . . . . . . . 451--456
               Larry Eifler and   
                   Noah H. Rhee   The $n$-Dimensional Pythagorean Theorem
                                  via the Divergence Theorem . . . . . . . 456--457
          Grzegorz Rz\kadkowski   Derivatives and Eulerian Numbers . . . . 458--460
                   David Callan   Problem 11362  . . . . . . . . . . . . . 461--461
                Oleh Faynshteyn   Problem 11363  . . . . . . . . . . . . . 461--461
Pál Péter Dályay   Problem 11364  . . . . . . . . . . . . . 461--462
            Aviezri S. Fraenkel   Problem 11365  . . . . . . . . . . . . . 462--462
                 Nicolae Anghel   Problem 11366  . . . . . . . . . . . . . 462--462
                Andrew Cusumano   Problem 11367  . . . . . . . . . . . . . 462--462
                 Wei-Dong Jiang   Problem 11368  . . . . . . . . . . . . . 462--462
            P. R. Parthasarathy   Generating Functions and Hypergeometric
                                  Series and Continued Fractions! 11198    462--464
               Ted Chinburg and   
         Shahriar Shahriari and   
                Reid Huntsinger   Groups, Rings, Fields, and Power Series:
                                  11216  . . . . . . . . . . . . . . . . . 464--465
            Jonathan Sondow and   
GCHQ Problem Solving Group Cheltenham   An Infinite Product Based on a Base:
                                  11222  . . . . . . . . . . . . . . . . . 465--466
          Dietrich Trenkler and   
         Götz Trenkler and   
                   Patrick Corn   The Square Root of a Certain Matrix:
                                  11224  . . . . . . . . . . . . . . . . . 466--467
                 Cezar Lupu and   
               Tudorel Lupu and   
                Ronald A. Kopas   A New Bound for r/R: 11245 . . . . . . . 467--468
             Paolo Perfetti and   
                  Richard Stong   Evaluate the Series: 11260 . . . . . . . 468--468
                     Ranjan Roy   Book Review: \booktitleEuler Through
                                  Time: A New Look at Old Themes, by V. S.
                                  Varadarajan  . . . . . . . . . . . . . . 469--473
                Mark E. Kidwell   Book Review: \booktitleKing of Infinite
                                  Space: Donald Coxeter, the Man Who Saved
                                  Geometry, by Siobhan Roberts . . . . . . 474--476
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 6, June / July, 2008

           Andrew M. Baxter and   
                   Ronald Umble   Periodic Orbits for Billiards on an
                                  Equilateral Triangle . . . . . . . . . . 479--491
                 Niklas Eriksen   The Freshman's Approach to Conway's
                                  Napkin Problem . . . . . . . . . . . . . 492--498
               Shlomo Engelberg   Edge Detection Using Fourier
                                  Coefficients . . . . . . . . . . . . . . 499--513
                   Sayel A. Ali   The mth Ratio Test: New Convergence
                                  Tests for Series . . . . . . . . . . . . 514--524
           Thomas Schmelzer and   
                 Robert Baillie   Summing a Curious, Slowly Convergent
                                  Series . . . . . . . . . . . . . . . . . 525--540
            Daniel Birmajer and   
                    Juan B. Gil   Arithmetic in the Ring of Formal Power
                                  Series with Integer Coefficients . . . . 541--549
                Wouter Castryck   A Shortened Classical Proof of the
                                  Quadratic Reciprocity Law  . . . . . . . 550--551
            Rajendra Bhatia and   
            J. A. Dias da Silva   Infinite Divisibility of GCD Matrices    551--553
           Alexey Yu. Volovikov   Borsuk--Ulam Implies Brouwer: a Direct
                                  Construction Revisited . . . . . . . . . 553--556
              George Koumoullis   On the Radon--Nikodym Theorem  . . . . . 556--558
              William M. Kantor   Cycles in Graphs and Groups  . . . . . . 559--562
          Michael D. Hirschhorn   A Letter from Fitzroy House  . . . . . . 563--566
                   Donald Knuth   Problem 11369  . . . . . . . . . . . . . 567--567
         Michael Goldenberg and   
                    Mark Kaplan   Problem 11370  . . . . . . . . . . . . . 567--567
                  Ovidiu Furdui   Problem 11371  . . . . . . . . . . . . . 567--568
     Jennifer Vandenbussche and   
                Douglas B. West   Problem 11372  . . . . . . . . . . . . . 568--568
                 Emeric Deutsch   Problem 11373  . . . . . . . . . . . . . 568--568
            Harley Flanders and   
             Hugh L. Montgomery   Problem 11374  . . . . . . . . . . . . . 568--568
                     Cezar Lupu   Problem 11375  . . . . . . . . . . . . . 568--568
            Syrous Marivani and   
Missouri State University Problem Solving Group   Consecutive Squares with a Square
                                  Average: 11227 . . . . . . . . . . . . . 568--569
               Isaac Sofair and   
              C. R. Pranesachar   Inscribed Triangle Area: 11261 . . . . . 569--571
            Hervé Moulin   A Combinatorial Inequality: 11269  . . . 571--573
               Vasile Mihai and   
                 Sin Hitotumatu   The Euler Line after All: 11272  . . . . 573--574
              Jeffrey D. Vaaler   Book Review: \booktitleAn Invitation to
                                  Modern Number Theory, by Steven J.
                                  Miller; Bamin Takloo-Bighash . . . . . . 575--578
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 7, August / September, 2008

                Wolfhard Hansen   A Strong Version of Liouville's Theorem  583--595
       Patrick D. McSwiggen and   
               Kenneth R. Meyer   Conjugate Phase Portraits of Linear
                                  Systems  . . . . . . . . . . . . . . . . 596--614
              Kenneth Hicks and   
             Gary L. Mullen and   
            Joseph L. Yucas and   
                  Ryan Zavislak   A Polynomial Analogue of the 3n + 1
                                  Problem  . . . . . . . . . . . . . . . . 615--622
           Mehrdad Khosravi and   
              Michael D. Taylor   The Wedge Product and Analytic Geometry  623--644
                 Stan Wagon and   
                     Peter Webb   Venn Symmetry and Prime Numbers: a
                                  Seductive Proof Revisited  . . . . . . . 645--648
            Harald Hanche-Olsen   On Goursat's Proof of Cauchy's Integral
                                  Theorem  . . . . . . . . . . . . . . . . 648--652
                   Arnaud Bodin   Number of Irreducible Polynomials in
                                  Several Variables over Finite Fields . . 653--660
            Stefan Schröer   Baer's Result: The Infinite Product of
                                  the Integers Has No Basis  . . . . . . . 660--663
           Bogdan M. Baishanski   Problem 11376  . . . . . . . . . . . . . 664--664
         Christopher Hillar and   
                  Lionel Levine   Problem 11377  . . . . . . . . . . . . . 664--664
                    Daniel Troy   Problem 11378  . . . . . . . . . . . . . 664--664
      Oskar Maria Baksalary and   
             Götz Trenkler   Problem 11379  . . . . . . . . . . . . . 664--664
            Hugh Montgomery and   
              Harold S. Shapiro   Problem 11380  . . . . . . . . . . . . . 665--665
      Jesús Guillera and   
                Jonathan Sondow   Problem 11381  . . . . . . . . . . . . . 665--665
                Roberto Tauraso   Problem 11382  . . . . . . . . . . . . . 665--665
      Christopher J. Hillar and   
                  O. P. Lossers   A Group In Which Equations Are Solvable:
                                  11231  . . . . . . . . . . . . . . . . . 665--666
                Lenny Jones and   
              Rachel Keller and   
               Toni Ernvall and   
Anne-Maria Ernvall-Hytönen   A Special Prime: 11235 . . . . . . . . . 666--666
             Emeric Deutsch and   
              John H. Smith and   
                 Albert Stadler   An Equality for Parts in Partitions of
                                  n: 11237 . . . . . . . . . . . . . . . . 666--667
            Aviezri S. Fraenkel   Sequences Built from the Golden Ratio:
                                  11238  . . . . . . . . . . . . . . . . . 667--668
               Donald Knuth and   
              Robin Chapman and   
                  Reiner Martin   Perfect Parity Patterns: 11243 . . . . . 668--670
          Michael S. Becker and   
             David Beckwith and   
                   Hongwei Chen   Double Integral with Log and Sinh: 11275 670--671
             Said Amghibech and   
          Joanna Chachulska and   
              Wojciech Matysiak   A Matrix Inequality: 11296 . . . . . . . 671--671
                Donald G. Saari   Book Review: \booktitleThe Three Body
                                  Problem, by Mauri Valtonen; Hannu
                                  Karrunen . . . . . . . . . . . . . . . . 672--676
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 8, October, 2008

                   D. Minda and   
                      S. Phelps   Triangles, Ellipses, and Cubic
                                  Polynomials  . . . . . . . . . . . . . . 679--689
       Rémi Langevin and   
               Pewel G. Walczak   Holomorphic Maps and Pencils of Circles  690--700
            Andrew Bashelor and   
                   Amy Ksir and   
                    Will Traves   Enumerative Algebraic Geometry of Conics 701--728
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Eighth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 729--739
               Steven J. Miller   A Probabilistic Proof of Wallis's
                                  Formula for $ \pi $  . . . . . . . . . . 740--745
                 Mikael Passare   How to Compute $ \sum 1 / n^2 $ by
                                  Solving Triangles  . . . . . . . . . . . 745--752
      Remco van der Hofstad and   
                  Michael Keane   An Elementary Proof of the Hitting Time
                                  Theorem  . . . . . . . . . . . . . . . . 753--756
                 Michael Nyblom   Problem 11383  . . . . . . . . . . . . . 757--757
              Moubinool Omarjee   Problem 11384  . . . . . . . . . . . . . 757--757
José Luis Díaz-Barrero   Problem 11385  . . . . . . . . . . . . . 757--757
                 Greg Markowsky   Problem 11386  . . . . . . . . . . . . . 757--757
          Oskar Maria Baksalary   Problem 11387  . . . . . . . . . . . . . 758--758
                    M. Farrokhi   Problem 11388  . . . . . . . . . . . . . 758--758
          Elizabeth R. Chen and   
            Jeffrey C. Lagarias   Problem 11389  . . . . . . . . . . . . . 758--758
              Prithwijit De and   
                        E. Omey   Recalling 11159 and Sixty-Sixth Putnam
                                  A5: 11277  . . . . . . . . . . . . . . . 758--759
               Slavko Simic and   
             John H. Lindsey II   Entire Limit: 11278  . . . . . . . . . . 759--759
              Vitaly Stakhovsky   Sliding Beads: 11279 . . . . . . . . . . 759--760
               Harris Kwong and   
     GCHQ Problem Solving Group   What We Mean, Not What We Say: 11280 . . 760--761
               Yakub Aliyev and   
            Apostolis Demis and   
            Apostolis Denis and   
 The GCHQ Problem Solving Group   A Triangular Result: 11285 . . . . . . . 761--762
      Stephen J. Herschkorn and   
             BSI Problems Group   Continuous Blackjack: 11287  . . . . . . 762--764
            Oleh Faynshteyn and   
                 Marian Tetival   Formulas Involving the Angles of a
                                  Triangle: 11289  . . . . . . . . . . . . 764--764
               Daniel T. Kaplan   Book Review: \booktitleGoogle's PageRank
                                  and Beyond: The Science of Search Engine
                                  Rankings, by Amy N. Langville; Carl D.
                                  Meyer  . . . . . . . . . . . . . . . . . 765--768
           Jeffrey Lagarias and   
              Colin Mallows and   
                Allan Wilks and   
             Daniel J. Velleman   Editor's Endnotes  . . . . . . . . . . . 769--770
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 9, November, 2008

               Steven G. Krantz   Complex Analysis as Catalyst . . . . . . 775--794
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   New Descriptions of Conics via Twisted
                                  Cylinders, Focal Disks, and Directors    795--812
            William W. Hackborn   Projectile Motion: Resistance Is Fertile 813--819
           Eugen J. Ionascu and   
               Dan Pritikin and   
              Stephen E. Wright   $k$-Dependence and Domination in Kings
                                  Graphs . . . . . . . . . . . . . . . . . 820--836
             Ed Scheinerman and   
              Christian Blatter   Four Shots for a Convex Quadrilateral    837--843
                Reinhard Michel   The (n + 1)th Proof of Stirling's
                                  Formula  . . . . . . . . . . . . . . . . 844--845
                   Bent Fuglede   A Sharpening of Wielandt's
                                  Characterization of the Gamma Function   845--850
          Jesús Guillera   Easy Proofs of Some Borwein Algorithms
                                  for $ \pi $  . . . . . . . . . . . . . . 850--854
            Jeffrey C. Lagarias   Problem 11390  . . . . . . . . . . . . . 855--855
                  Marian Tetiva   Problem 11391  . . . . . . . . . . . . . 855--855
                    Omran Kouba   Problem 11392  . . . . . . . . . . . . . 855--855
                 Cosmin Pohoata   Problem 11393  . . . . . . . . . . . . . 856--856
                    K. S. Bhanu   Problem 11394  . . . . . . . . . . . . . 856--856
                    M. Farrokhi   Problem 11395  . . . . . . . . . . . . . 856--856
            Gérard Letac   Problem 11396  . . . . . . . . . . . . . 856--856
           Gregory Keselman and   
          Aleksandar Ili\'c and   
                  O. P. Lossers   Generalizing $ (1 - 1)^n = 0 $: 11230    856--857
            Michel Bataille and   
                 John W. Hagood   If AB Preserves A, then BA Preserves B:
                                  11239  . . . . . . . . . . . . . . . . . 857--858
            Roberto Tauraso and   
                  O. P. Lossers   Fibonacci Numbers and Tilling a Board
                                  with Cuts: 11241 . . . . . . . . . . . . 858--859
             David Beckwith and   
          Michael R. Avidon and   
                        Li Zhou   ``The Ballot Problem in Disguise'', in
                                  Disguise: 11249  . . . . . . . . . . . . 859--860
             David Beckwith and   
                Michel Bataille   A Permanent Lower Bound: 11253 . . . . . 860--861
                Lenny Jones and   
                   Toni Ernvall   Primes with Special Primitive Roots:
                                  11254  . . . . . . . . . . . . . . . . . 861--861
               Nobuhisa Abe and   
                  Marian Tetiva   Never a Square: 11259  . . . . . . . . . 862--862
            Ashay Burungale and   
          Kenneth Schilling and   
       Christopher Carl Heckman   Getting to Know You, Directly and
                                  Indirectly: 11262  . . . . . . . . . . . 862--862
                    Peter Duren   Book Review: \booktitlePrinceton
                                  Lectures in Analysis, by Elias M. Stein;
                                  Rami Shakarchi . . . . . . . . . . . . . 863--866
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 115, Number 10, December, 2008

             Stephan C. Carlson   The Quest for a Fuzzy Tychonoff Theorem  871--887
             Robert Baillie and   
              David Borwein and   
            Jonathan M. Borwein   Surprising Sinc Sums and Integrals . . . 888--901
                Wolfgang Stadje   The Maximum Average Gain in a Sequence
                                  of Bernoulli Games . . . . . . . . . . . 902--910
               Jack Bookman and   
            Susan L. Ganter and   
                    Rick Morgan   Developing Assessment Methodologies for
                                  Quantitative Literacy: a Formative Study 911--929
             Ed Scheinerman and   
          Thomas J. Pickett and   
                    Ann Coleman   Another Continued Fraction for $ \pi $   930--933
                    Bakir Farhi   A Curious Result Related to Kempner's
                                  Series . . . . . . . . . . . . . . . . . 933--938
                Andrei Vernescu   The Summation of a Family of Series  . . 939--943
              Washek F. Pfeffer   A Devil's Platform . . . . . . . . . . . 943--947
                Grahame Bennett   Problem 11397  . . . . . . . . . . . . . 948--948
                  Stanley Huang   Problem 11398  . . . . . . . . . . . . . 948--948
                 Biaggi Ricceri   Problem 11399  . . . . . . . . . . . . . 948--948
                   Paul Bracken   Problem 11400  . . . . . . . . . . . . . 948--948
                 Marius Cavachi   Problem 11401  . . . . . . . . . . . . . 949--949
              Catalin Barboianu   Problem 11402  . . . . . . . . . . . . . 949--949
                      Yaming Yu   Problem 11403  . . . . . . . . . . . . . 949--949
              Manuel Kauers and   
                  Richard Stong   A Telescoping Fibonacci Sum: 11258 . . . 949--950
              Eugene Herman and   
               Mark D. Meyerson   3-D Rotations and Translations: 11276    950--950
              M. L. Glasser and   
                  O. P. Lossers   A Sinh a Series: 11286 . . . . . . . . . 950--951
                 Cezar Lupu and   
            Kenneth F. Andersen   A Variant Intermediate Value: 11290  . . 951--952
             Stefano Siboni and   
                  O. P. Lossers   Double Integral: 11295 . . . . . . . . . 952--953
              Marian Tetiva and   
             John H. Lindsey II   A Tricky Minimum: 11297  . . . . . . . . 953--954
                      Anonymous   Errata and End Notes for 2008  . . . . . 954--955
           Ioannis Kontoyiannis   Book Review: \booktitleInformation and
                                  Complexity in Statistical Modeling, by
                                  Jorma Rissanen . . . . . . . . . . . . . 956--960
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                      Anonymous   Volume Information . . . . . . . . . . . ??


American Mathematical Monthly
Volume 116, Number 1, January, 2009

             Judith V. Grabiner   Why Did Lagrange ``Prove'' the Parallel
                                  Postulate? . . . . . . . . . . . . . . . 3--18
              Mike Paterson and   
                      Uri Zwick   Overhang . . . . . . . . . . . . . . . . 19--44
                Larry Goldstein   A Probabilistic Proof of the
                                  Lindeberg--Feller Central Limit Theorem  45--60
José Ángel Cid and   
     Rodrigo López Pouso   Does Lipschitz with Respect to $x$ Imply
                                  Uniqueness for the Differential Equation
                                  $ y^\prime = f(x, y) $ ? . . . . . . . . 61--66
             Ed Scheinerman and   
                 Anton R. Schep   A Simple Complex Analysis and an
                                  Advanced Calculus Proof of the
                                  Fundamental Theorem of Algebra . . . . . 67--68
Natalia Casás Ferreño   Yet Another Proof of the Irrationality
                                  of $ \sqrt 2 $ . . . . . . . . . . . . . 68--69
                 Giovanni Panti   A General Lagrange Theorem . . . . . . . 70--74
            Romeo Me\vstrovi\'c   A Note on the Congruence $ \left
                                  ({\array {cc} n & d \\ . . . . . . . . . 75--77
                Sheldon M. Ross   A Simple Solution to a Multiple Player
                                  Gambler's Ruin Problem . . . . . . . . . 77--81
                Raimond Struble   Problem 11404  . . . . . . . . . . . . . 82--82
                  Ovidiu Furdui   Problem 11405  . . . . . . . . . . . . . 82--82
         A. A. Dzhumadi\'ldaeva   Problem 11406  . . . . . . . . . . . . . 82--82
                     Erwin Just   Problem 11407  . . . . . . . . . . . . . 82--82
                 Marius Cavachi   Problem 11408  . . . . . . . . . . . . . 83--83
                 Paolo Perfetti   Problem 11409  . . . . . . . . . . . . . 83--83
                    Omran Kouba   Problem 11410  . . . . . . . . . . . . . 83--83
            Richard Jerrard and   
                John Wetzel and   
               Mark D. Meyerson   A Solid with the Rupert Property: 11291  83--84
  Pablo Fern\`andez Refolio and   
              Timothy Achenbach   An Infinite Product: 11299 . . . . . . . 84--84
                    Ulrich Abel   A Bernstein Polynomial Integral: 11300   84--85
            Finbarr Holland and   
                 Byoung Tae Bae   A Quartic Inequality:- 11301 . . . . . . 85--86
                    Horst Alzer   A Series with Harmonic Numbers: 11302    86--87
    Teodora-Liliana R\vadulescu   Signed Series Terms: 11304 . . . . . . . 87--88
           Alexandru Rosoiu and   
              Victor Pambuccian   An Inequality for Triangles: 11306 . . . 88--89
                   Erik Talvila   Book Review: \booktitleA Garden of
                                  Integrals, by Frank E. Burk  . . . . . . 90--94
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 2, February, 2009

          Thomas L. Bartlow and   
             David E. Zitarelli   Who Was Miss Mullikin? . . . . . . . . . 99--114
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   A New Look at the So-Called Trammel of
                                  Archimedes . . . . . . . . . . . . . . . 115--133
                   Frank Morgan   Manifolds with Density and Perelman's
                                  Proof of the Poincaré Conjecture  . . . . 134--142
                 Joseph Bak and   
                   Pisheng Ding   Shape Distortion by Analytic Functions   143--150
            Christian Haase and   
                  Josef Schicho   Lattice Polygons and the Number 2i + 7   151--165
               Stephen K. Lucas   Approximations to $ \pi $ Derived from
                                  Integrals with Nonnegative Integrands    166--172
             Juan Pablo Pinasco   New Proofs of Euclid's and Euler's
                                  Theorems . . . . . . . . . . . . . . . . 172--174
             Janusz Januszewski   A Note on Covering a Square of Side
                                  Length $ 2 + \varepsilon $ with Unit
                                  Squares  . . . . . . . . . . . . . . . . 174--178
                 Alun Wyn-jones   Problem 11411  . . . . . . . . . . . . . 179--179
                    Omran Kouba   Problem 11412  . . . . . . . . . . . . . 179--179
           Mihály Bencze   Problem 11413  . . . . . . . . . . . . . 179--179
                  Marian Tetiva   Problem 11414  . . . . . . . . . . . . . 179--180
                 Finbar Holland   Problem 11415  . . . . . . . . . . . . . 180--180
                      Yaming Yu   Problem 11416  . . . . . . . . . . . . . 180--180
                     Cezar Lupu   Problem 11417  . . . . . . . . . . . . . 180--180
               Steve Butler and   
                        Jia Mao   Graphs with Few Edges, All in Short
                                  Cycles: 11265  . . . . . . . . . . . . . 180--181
              Marian Tetiva and   
                  Robin Chapman   Partitioning Values of a Polynomial into
                                  Sets of Equal Sum: 11266 . . . . . . . . 181--183
           Eugene A. Herman and   
                  Richard Stong   Commuting Transformations: 11267 . . . . 183--183
              Ovidiu Furdui and   
              Vitaly Stakhovsky   An Inequality with Trig: 11308 . . . . . 183--184
              Roman Witu\la and   
               Damian S\lta and   
            Arman Darbinyan and   
                  David Borwein   A Trig-Of-Trig Inequality: 11309 . . . . 184--185
          Stephen J. Herschkorn   A Game with Coins and Balls: 11311 . . . 185--186
              V. S. Varadarajan   Book Review: \booktitleIntroduction to
                                  Calculus and Classical Analysis, by Omar
                                  Hijab  . . . . . . . . . . . . . . . . . 187--190
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 3, March, 2009

                 Barbara Faires   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for 2009 to Robert E. Megginson
                                  for Distinguished Service to Mathematics 195--196
             Alan H. Schoenfeld   Working with Schools: The Story of a
                                  Mathematics Education Collaboration  . . 197--217
              Russell A. Gordon   Some Integrals Involving the Cantor
                                  Function . . . . . . . . . . . . . . . . 218--227
                Jerzy Kocik and   
                Andrzej Solecki   Disentangling a Triangle . . . . . . . . 228--237
                   Aaron Melman   Overshooting Properties of Newton-Like
                                  and Ostrowski-Like Methods . . . . . . . 238--250
              Serge Troubetzkoy   Dual Billiards, Fagnano Orbits, and
                                  Regular Polygons . . . . . . . . . . . . 251--260
            Shirley Llamado Yap   The Poincaré Lemma and an Elementary
                                  Construction of Vector Potentials  . . . 261--267
        Emmanuel Preissmann and   
               Maurice Mischler   Seating Couples around the King's Table
                                  and a New Characterization of Prime
                                  Numbers  . . . . . . . . . . . . . . . . 268--272
                Amir Akbary and   
              Zachary Friggstad   Superabundant Numbers and the Riemann
                                  Hypothesis . . . . . . . . . . . . . . . 273--275
                    George Lamb   Problem 11418  . . . . . . . . . . . . . 276--276
                   Vasile Mihai   Problem 11419  . . . . . . . . . . . . . 276--276
                    Kent Holing   Problem 11420  . . . . . . . . . . . . . 277--277
       Sergio Falcón and   
             Ángel Plaza   Problem 11421  . . . . . . . . . . . . . 277--277
             Christopher Hillar   Problem 11422  . . . . . . . . . . . . . 277--277
                 Gregory Minton   Problem 11423  . . . . . . . . . . . . . 277--277
                 Emeric Deutsch   Problem 11424  . . . . . . . . . . . . . 277--277
               Donald Knuth and   
                  Richard Stong   Reversal by Swaps: 11264 [2007, 77]  . . 277--278
                 Cezar Lupu and   
                        Li Zhou   From Integral to Derivative: 11313
                                  [2007, 744]  . . . . . . . . . . . . . . 279--279
               Yakub Aliyev and   
                  Marian Tetiva   A Floor Equation: 11314 [2007, 744]  . . 279--281
              Ovidiu Furdui and   
National Security Agency Problems Group   Convergence of an Improper Integral with
                                  Three Parameters: 11316 [2007, 745]  . . 281--283
             David Beckwith and   
     GCHQ Problem Solving Group   Sum of Digits: 11319 [2008, 835] . . . . 283--283
             Philip D. Straffin   Book Review: \booktitleMr. Hopkins' Men:
                                  Cambridge Reform and British Mathematics
                                  in the 19th Century, by Alex D. D. Craik 284--288
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 4, April, 2009

            Michael F. Barnsley   Transformations between Self-Referential
                                  Sets . . . . . . . . . . . . . . . . . . 291--304
            B. Ross Barmish and   
                   Nigel Boston   Risk and Return Considerations in ``The
                                  Weakest Link'' . . . . . . . . . . . . . 305--315
                H. Fejzi\'c and   
                C. Freiling and   
                       D. Rinne   Descartes' Rule of Signs, Alternations
                                  of Data Sets, and Balanced Differences   316--327
                  D. Drinen and   
              K. G. Kennedy and   
                W. M. Priestley   An Optimization Problem with a
                                  Surprisingly Simple Solution . . . . . . 328--341
                 Ethan D. Bloch   A Simple Proof of a Generalized No
                                  Retraction Theorem . . . . . . . . . . . 342--350
                  Bruce Solomon   Central Cross-Sections Make Surfaces of
                                  Revolution Quadric . . . . . . . . . . . 351--355
                Idris D. Mercer   On Furstenberg's Proof of the Infinitude
                                  of Primes  . . . . . . . . . . . . . . . 355--356
                   J. J. Koliha   Mean, Meaner, and the Meanest Mean Value
                                  Theorem  . . . . . . . . . . . . . . . . 356--361
             Giedrius Alkauskas   A Curious Proof of Fermat's Little
                                  Theorem  . . . . . . . . . . . . . . . . 362--364
                     Erwin Just   Problem 11425  . . . . . . . . . . . . . 365--365
                  M. L. Glasser   Problem 11426  . . . . . . . . . . . . . 365--365
             Viorel B\vandil\va   Problem 11427  . . . . . . . . . . . . . 365--365
                Walter Blumberg   Problem 11428  . . . . . . . . . . . . . 365--365
                     Cezar Lupu   Problem 11429  . . . . . . . . . . . . . 365--366
                          He Yi   Problem 11430  . . . . . . . . . . . . . 366--366
            Finbarr Holland and   
                  Stephen Wills   Problem 11431  . . . . . . . . . . . . . 366--366
              Marian Tetiva and   
                  Robin Chapman   Partitioning Values of a Polynomial into
                                  Sets of Equal Sum: 11266 [2007, 77]  . . 366--368
               Sergey Sadov and   
                   Harris Kwong   The Determinant of a Spiral Matrix:
                                  11270 [2007, 78] . . . . . . . . . . . . 368--369
                  Iliya Bluskov   Covering the Chessboard with Sets of
                                  Non-Attacking Queens: 11271 [2007, 164]  369--370
               Sergey Sadov and   
              Kim McInturff and   
                  Santa Barbara   Determinant of Another Spiral Matrix:
                                  11293 [2007, 451]  . . . . . . . . . . . 370--371
              Jakob Jonsson and   
               Annie Carter and   
                   David Callan   Oddly Triangulated Polygons: 11298
                                  [2007, 547]  . . . . . . . . . . . . . . 371--372
                M. Farrokhi and   
                  T. S. Michael   A Characterization of Permutation
                                  Matrices: 11303 [2007, 548]  . . . . . . 372--372
                  James W. Vick   Book Review: \booktitleTopology Now!, by
                                  Robert Messer; Philip Straffin;
                                  Introduction to Topology: Pure and
                                  Applied ~by Colin Adams; Robert Franzosa 373--375
                Kristopher Tapp   Book Review: \booktitleDifferential
                                  Geometry and Its Applications, by John
                                  Oprea  . . . . . . . . . . . . . . . . . 375--377
             Daniel J. Velleman   Editor's Endnotes  . . . . . . . . . . . 378--382
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 5, May, 2009

        Jonathan M. Borwein and   
             Neil J. Calkin and   
                    Dante Manna   Euler--Boole Summation Revisited . . . . 387--412
                  Mira Bhargava   Groups as Unions of Proper Subgroups . . 413--422
                 Rick Mabry and   
                 Paul Deiermann   Of Cheese and Crust: a Proof of the
                                  Pizza Conjecture and Other Tasty Results 423--438
               Nieves Alamo and   
                  Carlos Criado   Parallel Transport and Thomas--Wigner
                                  Rotation . . . . . . . . . . . . . . . . 439--446
               Daniel Heath and   
               I. M. Isaacs and   
              John Kiltinen and   
                  Jessica Sklar   Symmetric and Alternating Groups
                                  Generated by a Full Cycle and Another
                                  Element  . . . . . . . . . . . . . . . . 447--451
           Michael J. Evans and   
                  Paul D. Humke   Revisiting a Century-Old
                                  Characterization of Baire Class One,
                                  Darboux Functions  . . . . . . . . . . . 451--455
                Chris Bernhardt   A Proof of the Cayley--Hamilton Theorem  456--457
                   Peter Wagner   A New Constructive Proof of the
                                  Malgrange--Ehrenpreis Theorem  . . . . . 457--462
                  Marian Tetiva   Problem 11432  . . . . . . . . . . . . . 463--463
                 Marius Cavachi   Problem 11433  . . . . . . . . . . . . . 463--463
                   Slavko Simic   Problem 11434  . . . . . . . . . . . . . 463--463
             Panagiote Ligouras   Problem 11435  . . . . . . . . . . . . . 463--463
                   Y. N. Aliyev   Problem 11436  . . . . . . . . . . . . . 463--464
    Tomás Erdélyi   Problem 11437  . . . . . . . . . . . . . 464--464
                David H. Bailey   Problem 11438  . . . . . . . . . . . . . 464--464
              Marian Tetiva and   
                Byron Schmuland   A Sequence of Partitions into Sets with
                                  Equal Sum: 11273 [2007, 164] . . . . . . 464--465
              Max Alekseyev and   
            John Henry Steelman   Counting Permutations with Two
                                  Displacement Values: 11281 [2007, 259]   465--465
                 John Abbot and   
                 John Wilkinson   Irreducible Polynomials from a Theorem
                                  of Fermat: 11283 [2007, 260] . . . . . . 465--466
                  Greg Oman and   
                   Manuel Reyes   Rings That are Fields: 11284 [2007, 358] 466--466
                    Marc LeBrun   Descending Dungeons: 11286 [2007, 358]   466--467
         Christopher Hillar and   
                 Said Amghibech   A Polynomial Identity: 11288 [2007, 359] 468--468
               David Callan and   
                  Robin Chapman   Divisibility of a Central Binomial Sum:
                                  11292 & 11307 [2007, 451 & 640]  . . . . . 468--470
                M. Farrokhi and   
            Tuomas Hytönen   The Prime Exponentiation of an Integer:
                                  11315 [2007, 744]  . . . . . . . . . . . 470--470
                   Allen Holder   Book Review: \booktitleUnderstanding and
                                  Using Linear Programming, by Ji\vrí
                                  Matou\vsek; Bernd Gärtner; Introduction
                                  to Optimization ~by Pablo Pedregal . . . 471--476
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 6, June / July, 2009

            Alissa S. Crans and   
            Thomas M. Fiore and   
                Ramon Satyendra   Musical Actions of Dihedral Groups . . . 479--495
         Julius B. Barbanel and   
            Steven J. Brams and   
              Walter Stromquist   Cutting a Pie Is Not a Piece of Cake . . 496--514
                 Jack S. Calcut   Gaussian Integers and Arctangent
                                  Identities for $ \pi $ . . . . . . . . . 515--530
             Kevin Beanland and   
           James W. Roberts and   
                Craig Stevenson   Modifications of Thomae's Function and
                                  Differentiability  . . . . . . . . . . . 531--535
                Ulrich Abel and   
                    Mircea Ivan   Over-Iterates of Bernstein's Operators:
                                  a Short and Elementary Proof . . . . . . 535--538
                Paul Levrie and   
                   Walter Daems   Evaluating the Probability Integral
                                  Using Wallis's Product Formula for $ \pi
                                  $  . . . . . . . . . . . . . . . . . . . 538--541
                    Gerald Kuba   Counting Fields of Complex Numbers . . . 541--546
             Stephen Herschkorn   Problem 11439  . . . . . . . . . . . . . 547--547
                 Stefano Siboni   Problem 11440  . . . . . . . . . . . . . 547--547
                   Y. N. Aliyev   Problem 11441  . . . . . . . . . . . . . 547--547
José Luis Díaz-Barrero and   
José Gibergans-Báguena   Problem 11442  . . . . . . . . . . . . . 547--548
                  Eugen Ionascu   Problem 11443  . . . . . . . . . . . . . 548--548
                  Marian Tetiva   Problem 11444  . . . . . . . . . . . . . 548--548
                  H. A. ShahAli   Problem 11445  . . . . . . . . . . . . . 548--548
               Donald Knuth and   
                    Julian Hook   Sums and Powers, Set Counting, and
                                  Coefficient Tracking: 11274 [2007, 165]  548--549
Dragomir \vZ. \Dbarokovi\'c and   
                  Richard Stong   A Unipotent Matrix: 11282 [2007, 260]    549--550
            Vahan Mkrtchyan and   
                   Codrut Grosu   Disjoint Maximum-Sized Matchings: 11305
                                  [2007, 640]  . . . . . . . . . . . . . . 550--551
                 Erwin Just and   
                     Tom Kezlan   An Exponential Condition for
                                  Commutativity: 11310 [2007, 641] . . . . 551--552
               David Callan and   
                   Marc Renault   Uniformly Distributed Valleys: 11312
                                  [2007, 744]  . . . . . . . . . . . . . . 552--553
            Michel Bataille and   
                      John Cade   From Quadrilateral to Trapezoid: 11317
                                  [2007, 745]  . . . . . . . . . . . . . . 553--554
           Branko Grünbaum   Book Review: \booktitleThe Symmetries of
                                  Things, by John H. Conway; Heidi
                                  Burgiel; Chaim Goodman-Strauss . . . . . 555--562
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 7, August / September, 2009

      Nayandeep Deka Baruah and   
            Bruce C. Berndt and   
                 Heng Huat Chan   Ramanujan's Series for $ 1 / \pi $: a
                                  Survey . . . . . . . . . . . . . . . . . 567--587
                Greg Martin and   
                  Erick B. Wong   Almost All Integer Matrices Have No
                                  Integer Eigenvalues  . . . . . . . . . . 588--597
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   New Insight into Cycloidal Areas . . . . 598--611
             Richard Kenyon and   
                  Peter Winkler   Branched Polymers  . . . . . . . . . . . 612--628
                  Shui-Hung Hou   On a Theorem of Abel . . . . . . . . . . 629--630
                Jonathan Sondow   Ramanujan Primes and Bertrand's
                                  Postulate  . . . . . . . . . . . . . . . 630--635
               Shawn Hedman and   
                     David Rose   Light Subsets of N with Dense Quotient
                                  Sets . . . . . . . . . . . . . . . . . . 635--641
                 Juan Sabia and   
                 Susana Tesauri   The Least Prime in Certain Arithmetic
                                  Progressions . . . . . . . . . . . . . . 641--643
                  Oliver Deiser   A Simple Continuous Bijection from
                                  Natural Sequences to Dyadic Sequences    643--646
             Christopher Hillar   Problem 11446  . . . . . . . . . . . . . 647--647
              Ovidiu Furdui and   
                  Campia Turzii   Problem 11447  . . . . . . . . . . . . . 647--647
                 Wei-Dong Jiang   Problem 11448  . . . . . . . . . . . . . 647--647
                Michel Bataille   Problem 11449  . . . . . . . . . . . . . 647--647
                 Cosmin Pohoata   Problem 11450  . . . . . . . . . . . . . 647--647
                      Greg Oman   Problem 11451  . . . . . . . . . . . . . 648--648
                   Donald Knuth   Problem 11452  . . . . . . . . . . . . . 648--648
               Roman Witula and   
               Damian Stota and   
Szeged Problem Group `Fejéntaláltuka'   An Iteration Convergence: 11318 [2007,
                                  745] . . . . . . . . . . . . . . . . . . 648--649
               Donald Knuth and   
                  O. P. Lossers   Solving a Recurrence by Binary
                                  Expansion: 11320 [2007, 835] . . . . . . 649--649
         Christopher Hillar and   
           Bruce S. Burdick and   
                 Roger Williams   Polynomials Not Associated with
                                  Symmetric Matrices: 11321 [2007, 835]    649--650
            Jonathan Sondow and   
             George Lamb Tucson   A Double Integral: 11322 [2007, 835] . . 650--650
           Jody M. Lockhart and   
         William P. Wardlaw and   
                  O. P. Lossers   On the Sum of Integer Powers of a
                                  Matrix: 11323 [2007, 835]  . . . . . . . 650--651
           Martin Kochanski and   
                  Richard Stong   Measuring the Growth Rate of a Bernoulli
                                  Polynomial: 11324 [2007, 836]  . . . . . 651--653
            Finbarr Holland and   
                   Michael Vowe   A Triangle Inequality from 1953: 11325
                                  [2007, 836]  . . . . . . . . . . . . . . 653--654
José Luis Díaz-Barrero and   
Pál Péter Dályay   A Problem Rescued from Incorrectness:
                                  11326 [2007, 836]  . . . . . . . . . . . 654--655
                 Rick Mabry and   
            Debbie Shepherd and   
              Kenneth Schilling   A Chancy Function: 11327 [2007, 925] . . 655--656
         Dmitris Vartziotis and   
                Michel Bataille   Van Aubel's Theorem: 11328 [2007, 925]   656--656
                   Neil Falkner   Book Review: \booktitleBasic Real
                                  Analysis, by Anthony W. Knapp; Advanced
                                  Real Analysis ~by Anthony W. Knapp . . . 657--664
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 8, October, 2009

             Zajj Daugherty and   
        Alexander K. Eustis and   
             Gregory Minton and   
             Michael E. Orrison   Voting, the Symmetric Group, and
                                  Representation Theory  . . . . . . . . . 667--687
                  Steven V. Sam   A Bijective Proof for a Theorem of
                                  Ehrhart  . . . . . . . . . . . . . . . . 688--701
                J. Scott Provan   Sudoku: Strategy versus Structure  . . . 702--707
            Michael Bukatin and   
            Ralph Kopperman and   
             Steve Matthews and   
              Homeira Pajoohesh   Partial Metric Spaces  . . . . . . . . . 708--718
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Sixty-Ninth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 719--726
                 Ezra Brown and   
                 Nicholas Loehr   Why Is $ {\rm PSL}(2, 7) \cong {\rm
                                  GL}(3, 2) $? . . . . . . . . . . . . . . 727--732
           David V. Feldman and   
                Daniel A. Klain   Angles as Probabilities  . . . . . . . . 732--735
      Villö Csiszár   Jump Home and Shift: An Acyclic
                                  Operation on Permutations  . . . . . . . 735--738
                      Hojoo Lee   Ptolemy Meets Erd\Hos and Mordell Again  738--742
          Anca I. Bonciocat and   
           Nicolae C. Bonciocat   On the Irreducibility of Polynomials
                                  with Leading Coefficient Divisible by a
                                  Large Prime Power  . . . . . . . . . . . 743--745
                Michel Bataille   Problem 11449  . . . . . . . . . . . . . 746--746
                Richard Stanley   Problem 11453  . . . . . . . . . . . . . 746--746
                   Azer Kerimov   Problem 11454  . . . . . . . . . . . . . 746--746
              Christian Blatter   Problem 11455  . . . . . . . . . . . . . 746--746
                Raymond Mortini   Problem 11456  . . . . . . . . . . . . . 747--747
                  M. L. Glasser   Problem 11457  . . . . . . . . . . . . . 747--747
                     Cezar Lupu   Problem 11458  . . . . . . . . . . . . . 747--747
Pál Péter Dályay   Problem 11459  . . . . . . . . . . . . . 747--747
              T. Amdeberhan and   
             Victor H. Moll and   
                   Hongwei Chen   Two Log Gamma Integrals: 11329 [2007,
                                  925] . . . . . . . . . . . . . . . . . . 747--748
              Marian Tetiva and   
          João Guerreiro   A New Lower Bound for the Sum of the
                                  Altitudes: 11330 [2007, 925] . . . . . . 748--749
              Marian Tetiva and   
              Peter Nüesch   A Bisector Inequality: 11337 [2008, 71]  749--750
              Ovidiu Furdui and   
                  O. P. Lossers   A Gamma Limit: 11338 [2008, 71]  . . . . 750--750
       Óscar Ciaurri and   
                 Luz Roncal and   
                  Nora Thornber   Raindrops Flying from a Spinning
                                  Umbrella: 11340 [2008, 72] . . . . . . . 750--752
                 Cezar Lupu and   
                  Marian Tetiva   An Application of Popovidu's Inequality:
                                  11341 [2008, 166]  . . . . . . . . . . . 752--753
          Roger Cuculi\`ere and   
                  Richard Stong   A Functional Equation: 11345 [2008, 166] 753--753
                  Judy Holdener   Book Review: \booktitleRoots to
                                  Research: A Vertical Development of
                                  Mathematical Problems, by Judith D.
                                  Sally; Paul J. Sally, Jr.  . . . . . . . 754--758
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 9, November, 2009

              Mike Paterson and   
                Yuval Peres and   
              Mikkel Thorup and   
              Peter Winkler and   
                      Uri Zwick   Maximum Overhang . . . . . . . . . . . . 763--787
             Persi Diaconis and   
                   Jason Fulman   Carries, Shuffling, and an Amazing
                                  Matrix . . . . . . . . . . . . . . . . . 788--803
                Luis Verde-Star   Rational Functions . . . . . . . . . . . 804--827
                   Theo de Jong   Lagrange Multipliers and the Fundamental
                                  Theorem of Algebra . . . . . . . . . . . 828--830
             D. M. Einstein and   
              C. C. Heckman and   
                  T. S. Norfolk   On Sara's Dove Bar Habit . . . . . . . . 831--835
                    Bakir Farhi   An Identity Involving the Least Common
                                  Multiple of Binomial Coefficients and
                                  Its Application  . . . . . . . . . . . . 836--839
             Valerio De Angelis   Stirling's Series Revisited  . . . . . . 839--843
             Cosmin Pohoa\ct\va   Problem 11460  . . . . . . . . . . . . . 844--844
             Panagiote Ligouras   Problem 11461  . . . . . . . . . . . . . 844--844
           Nadezhda Alexandrova   Problem 11462  . . . . . . . . . . . . . 844--844
               Xiang Qian Chang   Problem 11463  . . . . . . . . . . . . . 844--844
                 David Beckwith   Problem 11464  . . . . . . . . . . . . . 845--845
      Pantelimon George Popescu   Problem 11465  . . . . . . . . . . . . . 845--845
                    Tian Yongge   Problem 11466  . . . . . . . . . . . . . 845--845
              Richard Bagby and   
             David Beckwith and   
                 Sag Harbor and   
               Douglas B. Tyler   A Weighted Sample of the Riemann Zeta
                                  Function: 11331 [2007, 926]  . . . . . . 845--846
            Roberto Tauraso and   
              Kenneth Schilling   Irrational Symmetry: 11332 [2007, 926]   846--847
Pablo Fernández Refolio and   
              John B. Zacharias   Baking a Pi with Factorials: 11333
                                  [2007, 926]  . . . . . . . . . . . . . . 847--847
             Jonathan Bober and   
           Jeffrey Lagarias and   
                Byron Schmuland   Very Composite Numbers: 11334 [2008, 71] 847--848
               Donald Knuth and   
     GCHQ Problem Solving Group   Near-de Bruijn Cycles: 11336 [2008, 71]  848--849
       Mihály Bencze and   
                 Julien Grivaux   More AGM Inequalities: 11347 [2008,167]  849--851
                 Victor J. Katz   Book Review: \booktitleMathematical
                                  Masterpieces: Further Chronicles by the
                                  Explorers, by Arthur Knoebel; Reinhard
                                  Laubenbacher; Jerry Lodder; David
                                  Pengelley  . . . . . . . . . . . . . . . 852--856
             Daniel J. Velleman   Editor's Endnotes  . . . . . . . . . . . 857--858
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 116, Number 10, December, 2009

                   Peter D. Lax   Rethinking the Lebesgue Integral . . . . 863--881
      Reinhard Laubenbacher and   
                Bernd Sturmfels   Computer Algebra in Systems Biology  . . 882--891
                 Bob Palais and   
             Richard Palais and   
                   Stephen Rodi   A Disorienting Look at Euler's Theorem
                                  on the Axis of a Rotation  . . . . . . . 892--909
           Bettina Richmond and   
                   Tom Richmond   How to Recognize a Parabola  . . . . . . 910--922
                   Robert Beals   On Orders of Subgroups in Abelian
                                  Groups: An Elementary Solution of an
                                  Exercise of Herstein . . . . . . . . . . 923--926
       Alexander E. Holroyd and   
                      Terry Soo   A Nonmeasurable Set from Coin Flips  . . 926--928
                 John Brillhart   A Note on Euler's Factoring Problem  . . 928--931
           Joseph B. Keller and   
                     Ravi Vakil   $ \pi_p $, the Value of $ \pi $ in $
                                  \ell_p $ . . . . . . . . . . . . . . . . 931--935
               Lucio R. Berrone   The Associativity of the Pythagorean Law 936--939
               Xiang Qian Chang   Problem 11467  . . . . . . . . . . . . . 940--940
                 Cosmin Pohoata   Problem 11468  . . . . . . . . . . . . . 940--940
                   Slavko Simic   Problem 11469  . . . . . . . . . . . . . 940--940
                  Marian Tetiva   Problem 11470  . . . . . . . . . . . . . 941--941
                Finbarr Holland   Problem 11471  . . . . . . . . . . . . . 941--941
                   Mahdi Makhul   Problem 11472  . . . . . . . . . . . . . 941--941
                 Paolo Perfetti   Problem 11473  . . . . . . . . . . . . . 941--941
Juan López González and   
                  O. P. Lossers   Multiples of 6 Whose Successors Have
                                  Greater Divisor Sum: 11335 [2008, 71]    941--942
José Luis Díaz-Barrero and   
                     Mihai Cipu   A Fibonacci Inequality: 11339 [2008, 72] 942--943
           Luis H. Gallardo and   
                Sam Vandervelde   A Square in a Finite Field: 11342 [2008,
                                  166] . . . . . . . . . . . . . . . . . . 943--944
             David Beckwith and   
                        CMC 328   The Number of Balanced Senates from $n$
                                  States: 11343 [2008, 166]  . . . . . . . 944--945
             Albert Stadler and   
                  Allen Stenger   A Möbius Function Identity: 11344 [2008,
                                  166] . . . . . . . . . . . . . . . . . . 945--946
                      Anonymous   Errata and End Notes for 2008  . . . . . 947--947
                  Michael Henle   Book Review: \booktitleMusic: A
                                  Mathematical Offering, by David J.
                                  Benson; Musimathics: The Mathematical
                                  Foundations of Music ~by Gareth Loy  . . 948--955
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                      Anonymous   Volume Information . . . . . . . . . . . ??