Table of contents for issues of American Mathematical Monthly

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Volume 53, Number ??, 1946
Volume 89, Number 5, 1982
Volume 93, Number 4, 1986
Volume 94, Number 9, 1987
Volume 95, Number 2, 1988
Volume 95, Number 5, May, 1988
Volume 95, Number 6, 1988
Volume 95, Number 8, October, 1988
Volume 95, Number 10, 1988
Volume 96, Number ??, 1989
Volume 96, Number 5, 1989
Volume 97, Number ??, 1990
Volume 97, Number 1, January, 1990
Volume 97, Number 2, February, 1990
Volume 97, Number 3, March, 1990
Volume 97, Number 4, April, 1990
Volume 97, Number 5, May, 1990
Volume 97, Number 6, June / July, 1990
Volume 97, Number 7, August / September, 1990
Volume 97, Number 8, October, 1990
Volume 97, Number 9, November, 1990
Volume 97, Number 10, December, 1990
Volume 98, Number ??, 1991
Volume 98, Number 1, January, 1991
Volume 98, Number 2, February, 1991
Volume 98, Number 3, March, 1991
Volume 98, Number 4, April, 1991
Volume 98, Number 5, May, 1991
Volume 98, Number 6, June / July, 1991
Volume 98, Number 7, August / September, 1991
Volume 98, Number 8, October, 1991
Volume 98, Number 9, November, 1991
Volume 98, Number 10, December, 1991
Volume 100, Number ??, 1993
Volume 99, Number ??, 1992
Volume 99, Number 1, January, 1992
Volume 99, Number 2, February, 1992
Volume 99, Number 3, March, 1992
Volume 99, Number 4, April, 1992
Volume 99, Number 5, May, 1992
Volume 99, Number 6, June / July, 1992
Volume 99, Number 7, August / September, 1992
Volume 99, Number 8, October, 1992
Volume 99, Number 9, November, 1992
Volume 99, Number 10, December, 1992
Volume 100, Number ??, 1993
Volume 100, Number 1, January, 1993
Volume 100, Number 2, February, 1993
Volume 100, Number 3, March, 1993
Volume 100, Number 4, April, 1993
Volume 100, Number 5, May, 1993
Volume 100, Number 6, June / July, 1993
Volume 100, Number 7, August / September, 1993
Volume 100, Number 8, October, 1993
Volume 100, Number 9, November, 1993
Volume 100, Number 10, December, 1993
Volume 94, Number 3, March, 1987
Volume 101, Number ??, 1994
Volume 101, Number 1, January, 1994
Volume 101, Number 2, February, 1994
Volume 101, Number 3, March, 1994
Volume 101, Number 4, April, 1994
Volume 101, Number 5, May, 1994
Volume 101, Number 6, June / July, 1994
Volume 101, Number 7, August / September, 1994
Volume 101, Number 8, October, 1994
Volume 101, Number 9, November, 1994
Volume 101, Number 10, December, 1994
Volume 102, Number 1, January, 1995
Volume 102, Number 2, February, 1995
Volume 102, Number 3, March, 1995
Volume 102, Number 4, April, 1995
Volume 102, Number 5, May, 1995
Volume 102, Number 6, June / July, 1995
Volume 102, Number 7, August / September, 1995
Volume 102, Number 8, October, 1995
Volume 102, Number 9, November, 1995
Volume 102, Number 10, December, 1995
Volume 103, Number 1, January, 1996
Volume 103, Number 2, February, 1996
Volume 103, Number 3, March, 1996
Volume 103, Number 4, April, 1996
Volume 103, Number 5, May, 1996
Volume 103, Number 6, June / July, 1996
Volume 103, Number 7, August / September, 1996
Volume 103, Number 8, October, 1996
Volume 103, Number 9, November, 1996
Volume 103, Number 10, December, 1996
Volume 104, Number 1, January, 1997
Volume 104, Number 2, February, 1997
Volume 104, Number 3, March, 1997
Volume 104, Number 4, April, 1997
Volume 104, Number 5, May, 1997
Volume 104, Number 6, June / July, 1997
Volume 104, Number 7, August / September, 1997
Volume 104, Number 8, October, 1997
Volume 104, Number 9, November, 1997
Volume 104, Number 10, December, 1997
Volume 105, Number 1, January, 1998
Volume 105, Number 2, February, 1998
Volume 105, Number 3, March, 1998
Volume 105, Number 4, April, 1998
Volume 105, Number 5, May, 1998
Volume 105, Number 6, June / July, 1998
Volume 105, Number 7, August / September, 1998
Volume 105, Number 8, October, 1998
Volume 105, Number 9, November, 1998
Volume 105, Number 10, December, 1998
Volume 106, Number 1, 1999
Volume 106, Number 2, 1999
Volume 106, Number 3, 1999
Volume 106, Number 4, 1999
Volume 106, Number 5, May, 1999
Volume 106, Number 6, June / July, 1999
Volume 106, Number 7, August / September, 1999
Volume 106, Number 8, October, 1999
Volume 106, Number 9, November, 1999
Volume 106, Number 10, December, 1999
Volume 66, Number 218, April, 1997


American Mathematical Monthly
Volume 53, Number ??, 1946

                  J. Williamson   Determinants whose elements are $0$ and
                                  $1$  . . . . . . . . . . . . . . . . . . 427--434


American Mathematical Monthly
Volume 89, Number 5, 1982

               Bernard Jacobson   On the mean value theorem for integrals  300--301


American Mathematical Monthly
Volume 93, Number 4, 1986

                   D. H. Lehmer   Coloring the Platonic solids . . . . . . 288--292


American Mathematical Monthly
Volume 94, Number 9, 1987

                Arthur Benjamin   The bisection method: which root . . . . 861--863


American Mathematical Monthly
Volume 95, Number 2, 1988

                    John Beebee   Examples of infinite, incongruent exact
                                  covers . . . . . . . . . . . . . . . . . 121--123

American Mathematical Monthly
Volume 95, Number 5, May, 1988

                Barry Hayes and   
            Donald E. Knuth and   
                    Carlos Subi   Elementary problem E3267, a solitaire
                                  game . . . . . . . . . . . . . . . . . . 456--457

American Mathematical Monthly
Volume 95, Number 6, 1988

                  David W. Boyd   The Diophantine equation $ x^2 + y^m =
                                  z^{2n} $ . . . . . . . . . . . . . . . . 544--547

American Mathematical Monthly
Volume 95, Number 8, October, 1988

            Donald E. Knuth and   
                     Ilan Vardi   Advanced problem 6581, the asymptotic
                                  expansion of the middle binomial
                                  coefficient  . . . . . . . . . . . . . . 774

American Mathematical Monthly
Volume 95, Number 10, 1988

              K. D. Magill, Jr.   Universal topological spaces . . . . . . 942--946


American Mathematical Monthly
Volume 96, Number ??, 1989

                Donald E. Knuth   Elementary problem E3303, a binary
                                  summation  . . . . . . . . . . . . . . . 54--54
                Donald E. Knuth   Elementary problem E3309, a binomial
                                  coefficient inequality . . . . . . . . . 154--154
                Donald E. Knuth   Elementary problem E3335, a deranged
                                  recurrence . . . . . . . . . . . . . . . 525--525

American Mathematical Monthly
Volume 96, Number 5, 1989

          George E. Andrews and   
                   R. J. Baxter   A motivated proof of the
                                  Rogers--Ramanujan identities . . . . . . 401--409


American Mathematical Monthly
Volume 97, Number ??, 1990

                Donald E. Knuth   Solution to Elementary problem E3303, a
                                  binary summation . . . . . . . . . . . . 348--349
                Donald E. Knuth   Solution to Elementary problem E3309, a
                                  binomial coefficient inequality  . . . . 614
                Donald E. Knuth   Solution to Elementary problem E3335, a
                                  deranged recurrence  . . . . . . . . . . 927

American Mathematical Monthly
Volume 97, Number 1, January, 1990

             Henry L. Alder and   
                     Ivan Niven   Award for Distinguished Service to Leon
                                  Henkin . . . . . . . . . . . . . . . . . 3--4
            Peter J. Giblin and   
                Donal B. O'Shea   The bitangent sphere problem . . . . . . 5--23
                   Klaus Sutner   The $ \sigma $-game and cellular
                                  automata . . . . . . . . . . . . . . . . 24--34
               Robert Weinstock   Elementary evaluations of $
                                  \int^\infty_0 e^{-x^2} \, d x $ and $
                                  \int^\infty_0 \cos x^2 \, d x, $ and $
                                  \int^\infty_0 \sin x^2 \, d x $  . . . . 39--42
           Donald J. Newman and   
                   J. S. Byrnes   The $ L^4 $ norm of a polynomial with
                                  coefficients $ \pm 1 $ . . . . . . . . . 42--45
         Johannes C. C. Nitsche   Isoptic characterization of a circle
                                  (proof of a conjecture of M. S. Klamkin) 45--47
                    Roy Mathias   Two theorems on singular values and
                                  eigenvalues  . . . . . . . . . . . . . . 47--50
     Teresa L. Santa Coloma and   
                 Ralph P. Tucci   A decomposition theorem for finite
                                  automata . . . . . . . . . . . . . . . . 51--54
           Thomas W. Hungerford   A counterexample in Galois theory  . . . 54--57
                 Tyre A. Newton   A simple algorithm for finding
                                  eigenvalues and eigenvectors for $ 2
                                  \times 2 $ matrices  . . . . . . . . . . 57--60
             Arno van den Essen   Magic squares and linear algebra . . . . 60--62

American Mathematical Monthly
Volume 97, Number 2, February, 1990

                Donald G. Saari   A visit to the Newtonian $N$-body
                                  problem via elementary complex variables 105--119
                   W. S. Anglin   The square pyramid puzzle  . . . . . . . 120--124
                     Stan Wagon   Editor's corner: the Euclidean algorithm
                                  strikes again  . . . . . . . . . . . . . 125--129
                 Kurt Girstmair   A theorem on the numerators of the
                                  Bernoulli numbers  . . . . . . . . . . . 136--138
                Richard G. Swan   Another proof of the quadratic
                                  reciprocity theorem  . . . . . . . . . . 138--139
           Edward A. Bender and   
               Fred Kochman and   
                Douglas B. West   Adding up to powers  . . . . . . . . . . 139--143
                      D. Zagier   A one-sentence proof that every prime $
                                  p \equiv 1 \pmod 4 $ is a sum of two
                                  squares  . . . . . . . . . . . . . . . . 144--144
           Stephen H. Friedberg   Extending the principal axis theorem to
                                  fields other than $ {\bf R} $  . . . . . 147--149

American Mathematical Monthly
Volume 97, Number 3, March, 1990

                 F. Beukers and   
       J.-P. Bézivin and   
                       P. Robba   An alternative proof of the
                                  Lindemann-Weierstrass theorem  . . . . . 193--197
       Richard C. Bollinger and   
            Charles L. Burchard   Lucas's theorem and some related results
                                  for extended Pascal triangles  . . . . . 198--204
             Esteban I. Poffald   The remainder in Taylor's formula  . . . 205--213
            Raphael M. Robinson   Comment to: ``A motivated proof of the
                                  Rogers--Ramanujan identities'' [Amer.
                                  Math. Monthly \bf 96 (1989), no. 5,
                                  401--409, MR 90e:11147] by G. E. Andrews
                                  and R. J. Baxter. With a reply by
                                  Andrews  . . . . . . . . . . . . . . . . 214--215
              Carsten Thomassen   A link between the Jordan curve theorem
                                  and the Kuratowski planarity criterion   216--218
                  John A. Ewell   A new series representation for $ \zeta
                                  (3) $  . . . . . . . . . . . . . . . . . 219--220
                    David Minda   The Dirichlet problem for a disk . . . . 220--223
           R. Bruce Richter and   
             William P. Wardlaw   Diagonalization over commutative rings   223--227
                  Joe Whittaker   Random triangles . . . . . . . . . . . . 228--230
               Daniel Kopel and   
                Michael Schramm   A new extension of the derivative  . . . 230--233
                  G. B. Folland   Remainder estimates in Taylor's theorem  233--235
                Donald E. Knuth   Solution to problem 6575, an identity
                                  involving sums and products  . . . . . . 256

American Mathematical Monthly
Volume 97, Number 4, April, 1990

                   Anatole Beck   Greed is (sometimes) not enough  . . . . 289--294
          Dragan Jankovi\'c and   
                  T. R. Hamlett   New topologies from old via ideals . . . 295--310
     Calixto P. Calderón   Letter to the editor . . . . . . . . . . 311--312
                 Betty Garrison   Polynomials with large numbers of prime
                                  values . . . . . . . . . . . . . . . . . 316--317
                F. B. Cannonito   On inequivalent group extensions . . . . 317--319
                       A. Vince   A rearrangement inequality and the
                                  permutahedron  . . . . . . . . . . . . . 319--323
                 Patrick Morton   Musings on the prime divisors of
                                  arithmetic sequences . . . . . . . . . . 323--328
              Marjorie Senechal   Finding the finite groups of symmetries
                                  of the sphere  . . . . . . . . . . . . . 329--335
                  C. E. Burgess   Continuous functions and connected
                                  graphs . . . . . . . . . . . . . . . . . 337--339
               Robert A. Leslie   The $ l_2 $ matrix norm and the spectral
                                  radius . . . . . . . . . . . . . . . . . 339--341

American Mathematical Monthly
Volume 97, Number 5, May, 1990

                   Peter D. Lax   The ergodic character of sequences of
                                  pedal triangles  . . . . . . . . . . . . 377--381
                     H. Groemer   Stability properties of geometric
                                  inequalities . . . . . . . . . . . . . . 382--394
                   Fred Richman   Separable extensions and
                                  diagonalizability  . . . . . . . . . . . 395--398
               M. D. Hirschhorn   A birthday present for Ramanujan . . . . 398--400
           Yaakov S. Kupitz and   
                Micha A. Perles   A condition for flatness of curves in $
                                  {\bf R}^n $  . . . . . . . . . . . . . . 401--405
          Pieter P. N. de Groen   A counterexample on vector norms and the
                                  subordinate matrix norms . . . . . . . . 406--407
              Marko Petkov\vsek   Ambiguous numbers are dense  . . . . . . 408--411
                  David W. Boyd   Addendum: ``The Diophantine equation $
                                  x^2 + y^m = z^{2n \, } $'' [Amer. Math.
                                  Monthly 95 (1988), no. 6, 544--547, MR
                                  89f:11046] . . . . . . . . . . . . . . . 411--412
                    John Beebee   Errata: ``Examples of infinite,
                                  incongruent exact covers'' [Amer. Math.
                                  Monthly \bf 95 (1988), no. 2, 121--123,
                                  MR 89g:11013]  . . . . . . . . . . . . . 412--412
             Arthur T. Benjamin   Errata: ``The bisection method: which
                                  root?'' [Amer. Math. Monthly \bf 94
                                  (1987), no. 9, 861--863, MR 89c:26016]   412--412
                Hans-J. Kleiner   Errata: ``Coloring the Platonic solids''
                                  [Amer. Math. Monthly \bf 93 (1986), no.
                                  4, 288--292, MR 87e:05072] by D. H.
                                  Lehmer . . . . . . . . . . . . . . . . . 412--412
              K. D. Magill, Jr.   Errata: ``Universal topological spaces''
                                  [Amer. Math. Monthly \bf 95 (1988), no.
                                  10, 942--946, MR 89m:54018]  . . . . . . 412--412
                 Jingcheng Wong   Errata: ``On the mean value theorem for
                                  integrals'' [Amer. Math. Monthly \bf 89
                                  (1982), no. 5, 300--301, MR 83g:26002]
                                  by B. Jacobson . . . . . . . . . . . . . 412--412
                  K. Hoechsmann   Singular values and the spectral theorem 413--414
      Robert Bartoszy\'nski and   
                       Wai Chan   A remark on the shortest confidence
                                  interval of a normal mean  . . . . . . . 415--417
         François Dubeau   Cauchy-Bunyakowski-Schwarz inequality
                                  revisited  . . . . . . . . . . . . . . . 419--421
             Mary Embry-Wardrop   An old max-min problem revisited . . . . 421--423
                J. Aczél   Functional equations and L'Hôpital's rule
                                  in an exact Poisson derivation . . . . . 423--426

American Mathematical Monthly
Volume 97, Number 6, June / July, 1990

               Kenneth R. Meyer   The geometry of harmonic oscillators . . 457--465
                  P. Eisele and   
                  K. P. Hadeler   Game of cards, dynamical systems, and a
                                  characterization of the floor and
                                  ceiling functions  . . . . . . . . . . . 466--477
               R. R. London and   
               H. P. Rogosinski   Decomposition theory in the teaching of
                                  elementary linear algebra  . . . . . . . 478--485
           Andrew Granville and   
                    Yiliang Zhu   Representing binomial coefficients as
                                  sums of squares  . . . . . . . . . . . . 486--493
              Tim Robertson and   
                Carolyn Pillers   A geometric regularity from
                                  order-restricted statistical inference   496--498
               Bertram Ross and   
             Baldev K. Sachdeva   The solution of certain integral
                                  equations by means of operators of
                                  arbitrary order  . . . . . . . . . . . . 498--503
                  Armel Mercier   Relations between $ \omega (n) $ and $
                                  \Omega (n) $ . . . . . . . . . . . . . . 503--505
                 Jerold Mathews   Gear trains and continued fractions  . . 505--510

American Mathematical Monthly
Volume 97, Number 7, August / September, 1990

                 Paul R. Halmos   Has progress in mathematics slowed down  561--588
               Helaman Ferguson   Two theorems, two sculptures, two
                                  posters  . . . . . . . . . . . . . . . . 589--610
                Donald E. Knuth   Solution to Advanced problem 6581, the
                                  asymptotic expansion of the middle
                                  binomial coefficient . . . . . . . . . . 629--630

American Mathematical Monthly
Volume 97, Number 8, October, 1990

                  Marcel Berger   Convexity  . . . . . . . . . . . . . . . 650--678
              Shiing Shen Chern   What is geometry . . . . . . . . . . . . 679--686
                 Ron Graham and   
                    Frances Yao   A whirlwind tour of computational
                                  geometry . . . . . . . . . . . . . . . . 687--701
              David Hoffman and   
          William H. Meeks, III   Minimal surfaces based on the catenoid   702--730
                Robert Osserman   Curvature in the eighties  . . . . . . . 731--756
            William P. Thurston   Conway's tiling groups . . . . . . . . . 757--773

American Mathematical Monthly
Volume 97, Number 9, November, 1990

             Tomás Feder   Toetjes  . . . . . . . . . . . . . . . . 785--794
                Regina B. Cohen   Set isometries and their extensions in
                                  the max metric . . . . . . . . . . . . . 795--808
               A. C. M. Ran and   
                      L. Rodman   On stability of invariant subspaces of
                                  matrices . . . . . . . . . . . . . . . . 809--823
           George Marsaglia and   
           John C. W. Marsaglia   A new derivation of Stirling's
                                  approximation to $ n! $  . . . . . . . . 826--829
                 M. J. Jamieson   Fibonacci numbers and Aitken sequences
                                  revisited  . . . . . . . . . . . . . . . 829--831
           Stephen L. Bloom and   
  Zoltán Ésik and   
                Ernest G. Manes   A Cayley theorem for Boolean algebras    831--833
               Michael Filaseta   Rouché's theorem for polynomials  . . . . 834--835
       Branko Grünbaum and   
                  Jan Mycielski   Some models of plane geometries  . . . . 839--846

American Mathematical Monthly
Volume 97, Number 10, December, 1990

              Joyce Justicz and   
      Edward R. Scheinerman and   
               Peter M. Winkler   Random intervals . . . . . . . . . . . . 881--889
              Gideon E. Schwarz   The dark side of the Moebius strip . . . 890--897
                    Peter Ungar   Mixing property of the pedal mapping . . 898--900
              R. E. Mirollo and   
                 S. H. Strogatz   Integral representation of a finite
                                  spike  . . . . . . . . . . . . . . . . . 901--903
                     D. Desbrow   On the irrationality of $ \pi^2 $  . . . 903--906
            Donald E. Knuth and   
                   Boris Pittel   Elementary problem E3411, two sums over
                                  compositions . . . . . . . . . . . . . . 916--917


American Mathematical Monthly
Volume 98, Number ??, 1991

                Donald E. Knuth   Advanced problem 6649, a generalized
                                  gamma function with independent branches 168
            Donald E. Knuth and   
                  John McCarthy   Elementary problem E3429, small pills    264
                Donald E. Knuth   Elementary problem E3463, points in a
                                  circle . . . . . . . . . . . . . . . . . 852

American Mathematical Monthly
Volume 98, Number 1, January, 1991

               Colin L. Mallows   Conway's challenge sequence  . . . . . . 5--20
               Henri Darmon and   
                     John McKay   A continued fraction and permutations
                                  with fixed points  . . . . . . . . . . . 25--27
             Vítor Neves   Smoothness from finite points  . . . . . 27--31
             Godfried Toussaint   Anthropomorphic polygons . . . . . . . . 31--35
                      W. A. Day   Inequalities for areas associated with
                                  conics . . . . . . . . . . . . . . . . . 36--39
                   Stephen Kuhn   The derivative \`a la Carathéodory  . . . 40--44
              George T. Gilbert   Positive definite matrices and
                                  Sylvester's criterion  . . . . . . . . . 44--46
                  J. Foster and   
                 F. B. Richards   The Gibbs phenomenon for
                                  piecewise-linear approximation . . . . . 47--49
          Philippe Flajolet and   
                Donald E. Knuth   Elementary problem E3415, a
                                  hypergenerating function . . . . . . . . 54

American Mathematical Monthly
Volume 98, Number 2, February, 1991

              Duane W. DeTemple   Carlyle circles and the Lemoine
                                  simplicity of polygon constructions  . . 97--108
                     H. S. Bear   Part metric and hyperbolic metric  . . . 109--123
              Timothy Lance and   
                  Edward Thomas   Arcs with positive measure and a
                                  space-filling curve  . . . . . . . . . . 124--127
      K. P. S. Bhaskara Rao and   
             A. Ramachandra Rao   Unions and common complements of
                                  subspaces  . . . . . . . . . . . . . . . 127--131
               Hans Liebeck and   
                Anthony Osborne   The generation of all rational
                                  orthogonal matrices  . . . . . . . . . . 131--133
                 Norman Richert   Hypocycloids, continued fractions, and
                                  distribution modulo one  . . . . . . . . 133--139
                James P. Butler   The perimeter of a rose  . . . . . . . . 139--143
                   A. R. Meijer   A tree among the stepping stones . . . . 144--146
                        Wen Liu   An analytic technique to prove Borel's
                                  strong law of large numbers  . . . . . . 146--148
                 Ira Rosenholtz   A topological mean value theorem for the
                                  plane  . . . . . . . . . . . . . . . . . 149--154
                  Walter Carlip   Disks and shells revisited . . . . . . . 154--156
                  Donald Hartig   L'Hôpital's rule via integration  . . . . 156--157

American Mathematical Monthly
Volume 98, Number 3, March, 1991

                  E. N. Gilbert   How things float . . . . . . . . . . . . 201--216
          Robert L. Devaney and   
              Marilyn B. Durkin   The exploding exponential and other
                                  chaotic bursts in complex dynamics . . . 217--233
            M. V. Deshpande and   
             Sudhir R. Ghorpade   Algebraic characterization of compact
                                  abelian groups . . . . . . . . . . . . . 235--237
                     G. Myerson   First-class functions  . . . . . . . . . 237--240
                P. D. Barry and   
                   D. J. Hurley   On series of partial fractions . . . . . 240--242
                  Peter A. Loeb   A note on Dixon's proof of Cauchy's
                                  integral theorem . . . . . . . . . . . . 242--244
                Daniel Goffinet   Number systems with a complex base: a
                                  fractal tool for teaching topology . . . 249--255
              Donald R. Chalice   A characterization of the Cantor
                                  function . . . . . . . . . . . . . . . . 255--258
                    L. R. Bragg   Parametric differentiation revisited . . 259--262

American Mathematical Monthly
Volume 98, Number 4, April, 1991

                   C. W. H. Lam   The search for a finite projective plane
                                  of order $ 10 $  . . . . . . . . . . . . 305--318
              N. Metropolis and   
                Gian-Carlo Rota   Symmetry classes: functions of three
                                  variables  . . . . . . . . . . . . . . . 328--332
                 Richard Beigel   Irrationality without number theory  . . 332--335
                     J. I. Hall   Another elementary approach to the
                                  Jordan form  . . . . . . . . . . . . . . 336--340
       Bernt Lindström and   
     Hans-Olov Zetterström   Borromean circles are impossible . . . . 340--341
                   A. G. Miamee   The inclusion $ L^p(\mu) \subseteq
                                  L^q(\nu) $ . . . . . . . . . . . . . . . 342--345
                    Lee Rudolph   The structure of orthogonal
                                  transformations  . . . . . . . . . . . . 349--352
                 Jonathan Lewin   A simple proof of Zorn's lemma . . . . . 353--354
                  Richard Grant   The converse of Liouville's theorem  . . 354--354
                Albert A. Cuoco   Visualizing the $p$-adic integers  . . . 355--364

American Mathematical Monthly
Volume 98, Number 5, May, 1991

               Calvin H. Wilcox   The Cauchy problem for the wave equation
                                  with distribution data: an elementary
                                  approach . . . . . . . . . . . . . . . . 401--410
              Hidefumi Katsuura   Continuous nowhere-differentiable
                                  functions --- an application of
                                  contraction mappings . . . . . . . . . . 411--416
           Daniel Bienstock and   
                  Fan Chung and   
         Michael L. Fredman and   
 Alejandro A. Schäffer and   
              Peter W. Shor and   
                   Subhash Suri   A note on finding a strict saddlepoint   418--419
                Robert Osserman   Circumscribed circles  . . . . . . . . . 419--422
             Elias Y. Deeba and   
            Dennis M. Rodriguez   Stirling's series and Bernoulli numbers  423--426
              J. H. Lindsey, II   A simple proof of the Weierstrass
                                  approximation theorem  . . . . . . . . . 429--430

American Mathematical Monthly
Volume 98, Number 6, June / July, 1991

         Christopher J. Henrich   Magic squares and linear algebra . . . . 481--488
             James V. Whittaker   An analytical description of some simple
                                  cases of chaotic behaviour . . . . . . . 489--504
            Albert Fässler   Multiple Pythagorean number triples  . . 505--517
              Jean-Pierre Rosay   A very elementary proof of the
                                  Malgrange-Ehrenpreis theorem . . . . . . 518--523
                  Li-Chien Shen   On the zeros of $ \tan^{(k)}z $  . . . . 524--527
                  John B. Kelly   Two equal sums of three squares with
                                  equal products . . . . . . . . . . . . . 527--529
                  Ira M. Gessel   A coloring problem . . . . . . . . . . . 530--533
              Man Kam Kwong and   
                       A. Zettl   Norm inequalities for the powers of a
                                  matrix . . . . . . . . . . . . . . . . . 533--538

American Mathematical Monthly
Volume 98, Number 7, August / September, 1991

                       B. Mazur   Number theory as gadfly  . . . . . . . . 593--610
             Lawrence H. Riddle   An occurrence of the ballot numbers in
                                  operator theory  . . . . . . . . . . . . 613--617
             Stephen G. Penrice   Derangements, permanents, and Christmas
                                  presents . . . . . . . . . . . . . . . . 617--620
                Fred Galvin and   
                    S. D. Shore   Distance functions and topologies  . . . 620--623
          Dragan Jankovi\'c and   
         Maximilian Ganster and   
                    Ivan Reilly   A characterization of Baire spaces . . . 624--625
                  Man Keung Siu   Which Latin squares are Cayley tables    625--627
               Marysia T. Weiss   An early introduction to dynamics  . . . 635--641
                  Alan Gluchoff   A simple interpretation of the complex
                                  contour integral . . . . . . . . . . . . 641--644

American Mathematical Monthly
Volume 98, Number 8, October, 1991

                J. P. Jones and   
            Y. V. Matijasevi\vc   Proof of recursive unsolvability of
                                  Hilbert's tenth problem  . . . . . . . . 689--709
        Jerome A. Goldstein and   
                       Mel Levy   Linear algebra and quantum chemistry . . 710--718
                  F. M. Dekking   Branching processes that grow faster
                                  than binary splitting  . . . . . . . . . 728--731
               Robert A. Leslie   How not to repeatedly differentiate a
                                  reciprocal . . . . . . . . . . . . . . . 732--735
        Jonathan M. Borwein and   
                    G. de Barra   Nested radicals  . . . . . . . . . . . . 735--739
               M. A. Berger and   
              A. Felzenbaum and   
             A. S. Fraenkel and   
                     R. Holzman   On infinite and finite covering systems  739--742
            Lajos Takács   A moment convergence theorem . . . . . . 742--746
              Clay C. Ross, Jr.   Why the method of undetermined
                                  coefficients works . . . . . . . . . . . 747--749

American Mathematical Monthly
Volume 98, Number 9, November, 1991

               Carl de Boor and   
              Klaus Höllig   Box-spline tilings . . . . . . . . . . . 793--802
               Steve Alpern and   
                   Anatole Beck   Hex games and twist maps on the annulus  803--811
                  Dan Flath and   
                     Stan Wagon   How to pick out the integers in the
                                  rationals: an application of number
                                  theory to logic  . . . . . . . . . . . . 812--823
               P. R. Garabedian   A simple proof of a simple version of
                                  the Riemann mapping theorem by simple
                                  functional analysis  . . . . . . . . . . 824--826
                Alfonso Villani   On the equality $ L^1 (\mu) = L^1_{\rm
                                  loc}(\mu) $  . . . . . . . . . . . . . . 826--828
                     D. de Caen   The ranks of tournament matrices . . . . 829--831
                   Arthur Smith   Convergence-preserving functions: an
                                  alternative discussion . . . . . . . . . 831--833
                   R. J. Duffin   Lines of best fit by graphics and the
                                  Wald line  . . . . . . . . . . . . . . . 835--839
                    M. Furi and   
                    M. Martelli   On the mean value theorem, inequality,
                                  and inclusion  . . . . . . . . . . . . . 840--846
                 C. W. Groetsch   Differentiation of approximately
                                  specified functions  . . . . . . . . . . 847--850
                   Paul Binding   More on cross products . . . . . . . . . 850--851

American Mathematical Monthly
Volume 98, Number 10, December, 1991

           Kenneth B. Stolarsky   From Wythoff's Nim to Chebyshev's
                                  inequality . . . . . . . . . . . . . . . 889--900
               T. Yung Kong and   
            Ralph Kopperman and   
                  Paul R. Meyer   A topological approach to digital
                                  topology . . . . . . . . . . . . . . . . 901--917
              Scott H. Hochwald   Linear algebra by analogy  . . . . . . . 918--926
              Kenneth P. Bogart   An obvious proof of Burnside's lemma . . 927--928
             J. Král and   
                  W. F. Pfeffer   Poisson integrals of Riemann integrable
                                  functions  . . . . . . . . . . . . . . . 929--931
                 James Chew and   
                Jing Cheng Tong   Some remarks on weak continuity  . . . . 931--934
    Dragomir \vZ. \Dbarokovi\'c   On the product of two alternating
                                  matrices . . . . . . . . . . . . . . . . 935--936
                   M. J. Knight   An ``oceans of zeros'' proof that a
                                  certain non-Liouville number is
                                  transcendental . . . . . . . . . . . . . 947--949


American Mathematical Monthly
Volume 100, Number ??, 1993

                Donald E. Knuth   Solution to Elementary problem E3463,
                                  points in a circle . . . . . . . . . . . 693--694


American Mathematical Monthly
Volume 99, Number ??, 1992

            Donald E. Knuth and   
                  John McCarthy   Solution to Elementary problem E3429,
                                  small pills  . . . . . . . . . . . . . . 684

American Mathematical Monthly
Volume 99, Number 1, January, 1992

                     Mark Lynch   A continuous, nowhere differentiable
                                  function . . . . . . . . . . . . . . . . 8--9
              Robert M. Gethner   Two relatives of Picard's theorem on
                                  entire functions . . . . . . . . . . . . 13--19
          Nathaniel A. Friedman   Replication and stacking in ergodic
                                  theory . . . . . . . . . . . . . . . . . 31--41
                 J. Segercrantz   Improving the Cayley--Hamilton equation
                                  for low-rank transformations . . . . . . 42--44
                  Peter Colwell   Bessel functions and Kepler's equation   45--48
          Richard J. Libera and   
       Eligiusz J. Z\lotkiewicz   Löwner's inverse coefficients theorem for
                                  starlike functions . . . . . . . . . . . 49--50
              Sheldon Axler and   
               Paul Bourdon and   
                     Wade Ramey   Bôcher's theorem  . . . . . . . . . . . . 51--55
                     Ruben Mera   On the determination of the intermediate
                                  point in Taylor's theorem  . . . . . . . 56--58

American Mathematical Monthly
Volume 99, Number 2, February, 1992

         Kenneth M. Hoffman and   
            James R. C. Leitzel   Award for distinguished service to Dr.
                                  Lynn Arthur Steen  . . . . . . . . . . . 99--100
                 Norman Richert   Strang's strange figures . . . . . . . . 101--107
                 Jean E. Taylor   Zonohedra and generalized zonohedra  . . 108--111
                John A. Velling   The uniformization of rectangles, an
                                  exercise in Schwarz's lemma  . . . . . . 112--115
              Carsten Thomassen   The Jordan-Schönflies theorem and the
                                  classification of surfaces . . . . . . . 116--130
                 Ira Rosenholtz   A pigeonhole proof of Kaplansky's
                                  theorem  . . . . . . . . . . . . . . . . 132--133
             A. M. Bruckner and   
          J. Ma\vrík and   
                     C. E. Weil   Some aspects of products of derivatives  134--145
                Chris Brink and   
                  Jan Pretorius   Boolean circulants, groups, and relation
                                  algebras . . . . . . . . . . . . . . . . 146--152
         Brigitte Servatius and   
           Peter R. Christopher   Construction of self-dual graphs . . . . 153--158
         Pawe\l Góra and   
               Abraham Boyarsky   On functions of bounded variation in
                                  higher dimensions  . . . . . . . . . . . 159--160

American Mathematical Monthly
Volume 99, Number 3, March, 1992

                  R. M. Corless   Continued fractions and chaos  . . . . . 203--215
              A. F. Beardon and   
                    T. K. Carne   A strengthening of the Schwarz-Pick
                                  inequality . . . . . . . . . . . . . . . 216--217
                Jerzy Dydak and   
                 Nathan Feldman   Major theorems on compactness: a unified
                                  exposition . . . . . . . . . . . . . . . 220--227
              R. A. Brualdi and   
                       J. Csima   Butterfly embedding proof of a theorem
                                  of König  . . . . . . . . . . . . . . . . 228--230
            Richard J. McIntosh   A generalization of a congruential
                                  property of Lucas  . . . . . . . . . . . 231--238
                Barthel W. Huff   Mixtures and order statistics  . . . . . 239--242
              Michael J. Beeson   Triangles with vertices on lattice
                                  points . . . . . . . . . . . . . . . . . 243--252
              Karl R. Stromberg   Universally nonmeasurable subgroups of $
                                  {\bf R} $  . . . . . . . . . . . . . . . 253--255
        Ömer E\ugecio\uglu   A combinatorial generalization of a
                                  Putnam problem . . . . . . . . . . . . . 256--258
                 David C. Kurtz   A sufficient condition for all the roots
                                  of a polynomial to be real . . . . . . . 259--263
                  Daniel Shanks   Improving an approximation for pi  . . . 263--263

American Mathematical Monthly
Volume 99, Number 4, April, 1992

                 Paul R. Halmos   Large intersections of large sets  . . . 307--312
               Andrew Granville   Zaphod Beeblebrox's brain and the
                                  fifty-ninth row of Pascal's triangle . . 318--331
                   J. Banks and   
                  J. Brooks and   
                  G. Cairns and   
                   G. Davis and   
                      P. Stacey   On Devaney's definition of chaos . . . . 332--334
               Jonathan L. King   Dilemma of the sleeping stockbroker  . . 335--338
                 John E. Wetzel   Converses of Napoleon's theorem  . . . . 339--351
               I. M. Isaacs and   
                 G. R. Robinson   On a theorem of Frobenius: solutions of
                                  $ x^n = 1 $ in finite groups . . . . . . 352--354
          Charles Vanden Eynden   On a problem of Stein concerning
                                  infinite covers  . . . . . . . . . . . . 355--358
           James H. Cliborn and   
                   Blake Jordan   Minimal surfaces . . . . . . . . . . . . 376--376

American Mathematical Monthly
Volume 99, Number 5, May, 1992

                Donald E. Knuth   Two notes on notation  . . . . . . . . . 403--422
          Blair K. Spearman and   
            Kenneth S. Williams   Representing primes by binary quadratic
                                  forms  . . . . . . . . . . . . . . . . . 423--426
Enrique A. González-Velasco   Connections in mathematical analysis:
                                  the case of Fourier series . . . . . . . 427--441
                Chandler Fulton   Tessellations  . . . . . . . . . . . . . 442--445
              J. L. Leavitt and   
              G. J. Sherman and   
                   M. E. Walker   Rewriteability in finite groups  . . . . 446--452

American Mathematical Monthly
Volume 99, Number 6, June / July, 1992

               Blake Temple and   
                 Craig A. Tracy   From Newton to Einstein  . . . . . . . . 507--521
        Michael D. Boshernitzan   Billiards and rational periodic
                                  directions in polygons . . . . . . . . . 522--529
            Edgar M. E. Wermuth   Some elementary properties of infinite
                                  products . . . . . . . . . . . . . . . . 530--537
                Andreas M. Hinz   Pascal's triangle and the Tower of Hanoi 538--544
              Dieter Jungnickel   On the uniqueness of the cyclic group of
                                  order $n$  . . . . . . . . . . . . . . . 545--547
                   Robin Forman   Sequences with many primes . . . . . . . 548--557
                 Mohsen Maesumi   Parabolic mirrors, elliptic and
                                  hyperbolic lenses  . . . . . . . . . . . 558--560
                 Richard Strong   Solution to Elementary problem E3411,
                                  two sums over compositions . . . . . . . 578--579

American Mathematical Monthly
Volume 99, Number 7, August / September, 1992

           Freeman J. Dyson and   
                    Harold Falk   Period of a discrete cat mapping . . . . 603--614
              David M. Bressoud   Why do we teach calculus . . . . . . . . 615--617
              J. M. Borwein and   
                  P. B. Borwein   Strange series and high precision fraud  622--640
                   Steven Roman   The logarithmic binomial formula . . . . 641--648
                    Bart Braden   Calculating sums of infinite series  . . 649--655
              Sergio A. Alvarez   $ {L}^p $ arithmetic . . . . . . . . . . 656--662

American Mathematical Monthly
Volume 99, Number 8, October, 1992

                   David Fowler   Dedekind's theorem: $ \sqrt 2 \times
                                  \sqrt 3 = \sqrt 6 $  . . . . . . . . . . 725--733
                Ronald J. Knill   A modified Babylonian algorithm  . . . . 734--737
              E. A. Marchisotto   Lines without order  . . . . . . . . . . 738--745
              Solomon W. Golomb   An identity for $ \binom {2n}n $ . . . . 746--748
                     D. G. Mead   Newton's identities  . . . . . . . . . . 749--751
                  John A. Ewell   On sums of triangular numbers and sums
                                  of squares . . . . . . . . . . . . . . . 752--757
             Marco Vianello and   
               Renato Zanovello   On the superlinear convergence of the
                                  secant method  . . . . . . . . . . . . . 758--761
          T. N. Subramaniam and   
              Donald E. G. Malm   How to integrate rational functions  . . 762--772

American Mathematical Monthly
Volume 99, Number 9, November, 1992

           Cathleen S. Morawetz   Giants . . . . . . . . . . . . . . . . . 819--828
             R. B. Eggleton and   
           C. B. Lacampagne and   
                J. L. Selfridge   Euclidean quadratic fields . . . . . . . 829--837
                  K. H. Kim and   
                F. W. Roush and   
             M. D. Intriligator   Overview of mathematical social sciences 838--844
              Mark F. Schilling   Sequential partitioning  . . . . . . . . 846--855
                       Jun Wang   Goldbach's problem in the ring $
                                  M_n({\bf Z}) $ . . . . . . . . . . . . . 856--857
               J.-Cl. Evard and   
                      F. Jafari   A complex Rolle's theorem  . . . . . . . 858--861
              Kenneth A. Brakke   The opaque cube problem  . . . . . . . . 866--871

American Mathematical Monthly
Volume 99, Number 10, December, 1992

           Louis M. Rotando and   
                Edward O. Thorp   The Kelly criterion and the stock market 922--931
               Paul R. Chernoff   A simple proof of Tychonoff's theorem
                                  via nets . . . . . . . . . . . . . . . . 932--934
            David C. Fisher and   
                  Jennifer Ryan   Optimal strategies for a generalized
                                  ``scissors, paper, and stone'' game  . . 935--942
               Scott T. Chapman   A simple example of nonunique
                                  factorization in integral domains  . . . 943--945
                    John Beebee   Bernoulli numbers and exact covering
                                  systems  . . . . . . . . . . . . . . . . 946--948
           Károly Bezdek   Hadwiger's covering conjecture and its
                                  relatives  . . . . . . . . . . . . . . . 954--956


American Mathematical Monthly
Volume 100, Number ??, 1993

                Donald E. Knuth   Problem 10280, a random binary operation 76
                Donald E. Knuth   Problem 10298, a divisibility property
                                  of Stirling numbers  . . . . . . . . . . 400

American Mathematical Monthly
Volume 100, Number 1, January, 1993

                 G. Baley Price   The seventy-fifth anniversary
                                  celebration  . . . . . . . . . . . . . . 4--15
                Leonard Gillman   An axiomatic approach to the integral    16--25
      István Szalkai and   
                   Dan Velleman   Versatile coins  . . . . . . . . . . . . 26--33
                   R. J. Duffin   On seeing progressions of constant cross
                                  ratio  . . . . . . . . . . . . . . . . . 38--47
                      Anonymous   100 years of Monthly editors . . . . . . 48--49
                David Hobby and   
                D. M. Silberger   Quotients of primes  . . . . . . . . . . 50--52
          George C. Donovan and   
           Arnold R. Miller and   
            Timothy J. Moreland   Pathological functions for Newton's
                                  method . . . . . . . . . . . . . . . . . 53--58
              André Avez   A short proof of a theorem of Erd\Hos
                                  and Mordell  . . . . . . . . . . . . . . 60--62
                Evan G. Houston   A linear algebra approach to cyclic
                                  extensions in Galois theory  . . . . . . 64--66
                     Dean Alvis   Solution to Elementary problem E3415, a
                                  hypergenerating function . . . . . . . . 84--85

American Mathematical Monthly
Volume 100, Number 2, February, 1993

    Ramanathan Gnanadesikan and   
                Henry J. Landau   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  award for distinguished service to Henry
                                  O. Pollak  . . . . . . . . . . . . . . . 115--116
                John D. Maxwell   John Marvin Colaw: and the American
                                  Mathematical Monthly . . . . . . . . . . 117--118
                Tristan Needham   Newton and the transmutation of force    119--137
                 Christoph Baxa   A note on Diophantine representations    138--143
           Terence R. Shore and   
               Douglas B. Tyler   Recurrence of simple random walk in the
                                  plane  . . . . . . . . . . . . . . . . . 144--149
       Branko Grünbaum and   
                 G. C. Shephard   Pick's theorem . . . . . . . . . . . . . 150--161
                Ulrich Abel and   
                Hartmut Siebert   Sequences with large numbers of prime
                                  values . . . . . . . . . . . . . . . . . 167--169
                  Horst Martini   Regular simplices in spaces of constant
                                  curvature  . . . . . . . . . . . . . . . 169--171
               John K. Williams   A simple example of little big set . . . 172--174

American Mathematical Monthly
Volume 100, Number 3, March, 1993

                 Edgar R. Lorch   Szeged in 1934 . . . . . . . . . . . . . 219--230
             Stanley Burris and   
                      Simon Lee   Tarski's high school identities  . . . . 231--236
       Steven N. MacEachern and   
               L. Mark Berliner   Aperiodic chaotic orbits . . . . . . . . 237--241
             William J. Gilbert   Bricklaying and the Hermite normal form  242--245
                   Neil Falkner   A characterization of inner product
                                  spaces . . . . . . . . . . . . . . . . . 246--249
                 Gilbert Strang   Polar area is the average of strip areas 250--254
                Alan Durfee and   
          Nathan Kronenfeld and   
               Heidi Munson and   
                   Jeff Roy and   
                     Ina Westby   Counting critical points of real
                                  polynomials in two variables . . . . . . 255--271
                   Peter Walker   Separation of the zeros of polynomials   272--273
          George E. Andrews and   
           Shalosh B. Ekhad and   
               Doron Zeilberger   A short proof of Jacobi's formula for
                                  the number of representations of an
                                  integer as a sum of four squares . . . . 274--276
         Krzysztof Oleszkiewicz   An elementary proof of Hilbert's
                                  inequality . . . . . . . . . . . . . . . 276--280
              Camille Debi\`eve   A note on Fubini's theorem . . . . . . . 281--281
               Albert Nijenhuis   Solution to Elementary problem E3267, a
                                  solitaire game . . . . . . . . . . . . . 292--294

American Mathematical Monthly
Volume 100, Number 4, April, 1993

            Joseph H. Silverman   Taxicabs and sums of two cubes . . . . . 331--340
                  Raymond Ayoub   What is a Napierian logarithm  . . . . . 351--364
                    J. W. Bruce   A really trivial proof of the
                                  Lucas-Lehmer test  . . . . . . . . . . . 370--371
            Gregory S. Call and   
             Daniel J. Velleman   Pascal's matrices  . . . . . . . . . . . 372--376
            Thomas A. Fournelle   Symmetries of the cube and outer
                                  automorphisms of $ S_6 $ . . . . . . . . 377--380
             Timothy A. Murdoch   Isogonal configurations  . . . . . . . . 381--384

American Mathematical Monthly
Volume 100, Number 5, May, 1993

           J. Helen Gardner and   
                Robin J. Wilson   Thomas Archer Hirst---mathematician
                                  xtravagant. I. A Yorkshire surveyor  . . 435--441
            William F. Reynolds   Hyperbolic geometry on a hyperboloid . . 442--455
             Michael Rubinstein   A simple heuristic proof of Hardy and
                                  Littlewood's conjecture B  . . . . . . . 456--460
               H. Turner Laquer   The Pompeiu problem  . . . . . . . . . . 461--467
              Duane W. DeTemple   A quicker convergence to Euler's
                                  constant . . . . . . . . . . . . . . . . 468--470
            William Watkins and   
                   Joel Zeitlin   The minimal polynomial of $ \cos (2 \pi
                                  / n) $ . . . . . . . . . . . . . . . . . 471--474
                B. Richmond and   
                    T. Richmond   The equal area zones property  . . . . . 475--477
                    Mark Copper   Graph theory and the game of sprouts . . 478--482
               Borislav Bojanov   Elementary proof of the Remez inequality 483--485
               T. S. Nanjundiah   A note on an identity of Ramanujan . . . 485--487
               Doron Zeilberger   On an identity of Daubechies . . . . . . 487--487
           Catherine C. McGeoch   Data compression . . . . . . . . . . . . 493--497

American Mathematical Monthly
Volume 100, Number 6, June / July, 1993

           J. Helen Gardner and   
                Robin J. Wilson   Thomas Archer Hirst---mathematician
                                  xtravagant. II. Student days in Germany  531--538
           Robert S. Strichartz   How to make wavelets . . . . . . . . . . 539--556
          William C. Waterhouse   A matrix maximum . . . . . . . . . . . . 557--562
             S. P. Hastings and   
                   J. B. McLeod   Chaotic motion of a pendulum with
                                  oscillatory forcing  . . . . . . . . . . 563--572
          David A. Wagstaff and   
         Theodore A. Norman and   
            Douglas M. Campbell   An application for the curiosity $
                                  (\log_x N)' $  . . . . . . . . . . . . . 573--574
     Miriam Schapiro Grosof and   
               Geraldine Taiani   Vandermonde strikes again  . . . . . . . 575--577
                    Fred Galvin   Embedding countable groups in
                                  $2$-generator groups . . . . . . . . . . 578--580
          Joseph A. Gallian and   
                   Michael Reid   Abelian forcing sets . . . . . . . . . . 580--582

American Mathematical Monthly
Volume 100, Number 7, August / September, 1993

           J. Helen Gardner and   
                Robin J. Wilson   Thomas Archer Hirst---mathematician
                                  xtravagant. III. Göttingen and Berlin . . 619--625
                W. A. Beyer and   
                   Blair Swartz   Bisectors of triangles and tetrahedra    626--640
                 D. G. Mead and   
                    S. K. Stein   More on rectangles tiled by rectangles   641--643
            Bruce C. Berndt and   
                    S. Bhargava   Ramanujan --- for lowbrows . . . . . . . 644--656
                D. Y. Savio and   
             E. R. Suryanarayan   Chebychev polynomials and regular
                                  polygons . . . . . . . . . . . . . . . . 657--661
                   Ren Ding and   
   Krzysztof Ko\lodziejczyk and   
             Grattan Murphy and   
                      John Reay   A fast Pick-type approximation for areas
                                  of $H$-polygons  . . . . . . . . . . . . 669--673

American Mathematical Monthly
Volume 100, Number 8, October, 1993

           J. Helen Gardner and   
                Robin J. Wilson   Thomas Archer Hirst---mathematician
                                  xtravagant. IV. Queenwood, France and
                                  Italy  . . . . . . . . . . . . . . . . . 723--731
           David Mornhinweg and   
          Daniel B. Shapiro and   
                  K. G. Valente   The principal axis theorem over
                                  arbitrary fields . . . . . . . . . . . . 749--754
                Tristan Needham   A visual explanation of Jensen's
                                  inequality . . . . . . . . . . . . . . . 768--771
          Catherine Hassell and   
                     Elmer Rees   The index of a constrained critical
                                  point  . . . . . . . . . . . . . . . . . 772--778
        Norbert Hegyvári   On some irrational decimal fractions . . 779--780
                 Louis Brickman   The symmetry principle for Möbius
                                  transformations  . . . . . . . . . . . . 781--782
             T. von Petersdorff   A short proof for Romberg integration    783--785
                   Ollie Nanyes   An elementary proof that the Borromean
                                  rings are nonsplittable  . . . . . . . . 786--789

American Mathematical Monthly
Volume 100, Number 9, November, 1993

           J. Helen Gardner and   
                Robin J. Wilson   Thomas Archer Hirst---mathematician
                                  xtravagant. V. London in the 1860s . . . 827--834
            Iris Lee Anshel and   
                 Michael Anshel   From the Post-Markov theorem through
                                  decision problems to public-key
                                  cryptography . . . . . . . . . . . . . . 835--844
                 Gilbert Strang   The fundamental theorem of linear
                                  algebra  . . . . . . . . . . . . . . . . 848--855
                  Albrecht Dold   A simple proof of the Jordan-Alexander
                                  complement theorem . . . . . . . . . . . 856--857
              Hansklaus Rummler   Squaring the circle with holes . . . . . 858--860
                    Paul Monsky   Simplifying the proof of Dirichlet's
                                  theorem  . . . . . . . . . . . . . . . . 861--862
                Hiroshi Maehara   Why is $ {\bf P}^2 $ not embeddable in $
                                  {\bf R}^3 $  . . . . . . . . . . . . . . 862--864
                 Bruce Anderson   Polynomial root dragging . . . . . . . . 864--866

American Mathematical Monthly
Volume 100, Number 10, December, 1993

           J. Helen Gardner and   
                Robin J. Wilson   Thomas Archer Hirst---mathematician
                                  xtravagant. VI. Years of decline . . . . 907--915
                  Hans Melissen   Densest packings of congruent circles in
                                  an equilateral triangle  . . . . . . . . 916--925
                 Jan van Yzeren   A simple proof of Pascal's hexagon
                                  theorem  . . . . . . . . . . . . . . . . 930--931
                Andrew T. Hyman   The mathematical relationship between
                                  Kepler's laws and Newton's laws  . . . . 932--936
                 R\uazvan Gelca   A short proof of a result on polynomials 936--937
              Robert A. Proctor   Two amusing Dynkin diagram graph
                                  classifications  . . . . . . . . . . . . 937--941
                    Paul Halmos   Postcards from Max . . . . . . . . . . . 942--944


American Mathematical Monthly
Volume 94, Number 3, March, 1987

                Donald E. Knuth   Solution to problem E3062, A versatile
                                  identity . . . . . . . . . . . . . . . . 376--377


American Mathematical Monthly
Volume 101, Number ??, 1994

                Donald E. Knuth   Problem 103xx, a knight's surprise . . . (to appear)
                Donald E. Knuth   Solution to Advanced problem 6649, a
                                  generalized gamma function with
                                  independent branches . . . . . . . . . . (to appear)
                Donald E. Knuth   Solution to Advanced problem 6649, a
                                  generalized gamma function with
                                  independent branches . . . . . . . . . . 77--78

American Mathematical Monthly
Volume 101, Number 1, January, 1994

                   David A. Cox   Introduction to Fermat's last theorem    3--14
                 John Stillwell   Galois theory for beginners  . . . . . . 22--27
                E. Bruce Pitman   Into the hourglass: reflections on the
                                  forces acting on a granular material . . 28--35
               John Dewey Jones   Orderly currencies . . . . . . . . . . . 36--38
            Robert F. Brown and   
               Robert E. Greene   An interior fixed point property of the
                                  disc . . . . . . . . . . . . . . . . . . 39--47
              J. Michael Steele   Le Cam's inequality and Poisson
                                  approximations . . . . . . . . . . . . . 48--54
              Dorina Mitrea and   
                  Marius Mitrea   A generalization of a theorem of Euler   55--58
            Petru Mironescu and   
         Lauren\ctiu Panaitopol   The existence of a triangle with
                                  prescribed angle bisector lengths  . . . 58--60
               A. Shenitzer and   
                  J. Stepr\=ans   The evolution of integration . . . . . . 66--72

American Mathematical Monthly
Volume 101, Number 2, February, 1994

                David W. Ballew   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for Distinguished Service to J.
                                  Sutherland Frame . . . . . . . . . . . . 107--108
       Branko Grünbaum and   
                 G. C. Shephard   A new look at Euler's theorem for
                                  polyhedra  . . . . . . . . . . . . . . . 109--128
                Philip J. Davis   Otto Neugebauer: reminiscences and
                                  appreciation . . . . . . . . . . . . . . 129--131
               Richard Kavinoky   Correction to: ``From Newton to
                                  Einstein'' [Amer. Math. Monthly \bf 99
                                  (1992), no. 6, 507--521, MR 93c:01001]
                                  by B. Temple and C. A. Tracy . . . . . . 131--131
               Elias Wegert and   
             Lloyd N. Trefethen   From the Buffon needle problem to the
                                  Kreiss matrix theorem  . . . . . . . . . 132--139
          William C. Waterhouse   A counterexample for Germain . . . . . . 140--150
            H. B. Griffiths and   
                    A. E. Hirst   Cubic equations, or Where did the
                                  examination question come from?  . . . . 151--161
               Hellmuth Stachel   On the identity of polyhedra . . . . . . 162--165
               David C. Ullrich   More on the Pompeiu problem  . . . . . . 165--168
                 Richard K. Guy   Every number is expressible as the sum
                                  of how many polygonal numbers  . . . . . 169--172

American Mathematical Monthly
Volume 101, Number 3, March, 1994

       Fernando Q. Gouvêa   A marvelous proof  . . . . . . . . . . . 203--222
                   David Aldous   Triangulating the circle, at random  . . 223--233
           Michael A. B. Deakin   Hypatia and her mathematics  . . . . . . 234--243
             Richard Barshinger   Calculus II and Euler also (with a nod
                                  to series integral remainder bounds) . . 244--249
                    Marc Frantz   A focusing property of the ellipse . . . 250--258
                Roberto Peirone   Reflections can be trapped . . . . . . . 259--260
         Katherine Heinrich and   
             Peter Horák   Euler's theorem  . . . . . . . . . . . . 260--261
            Joan Feigenbaum and   
                  Nick Reingold   Universal traversal sequences  . . . . . 262--265
                 John Stillwell   What are algebraic integers and what are
                                  they for . . . . . . . . . . . . . . . . 266--270

American Mathematical Monthly
Volume 101, Number 4, April, 1994

           Edward A. Bender and   
             Oren Patashnik and   
             Howard Rumsey, Jr.   Pizza slicing, phi's, and the Riemann
                                  hypothesis . . . . . . . . . . . . . . . 307--317
                Ralph Walde and   
                    Paula Russo   Rational periodic points of the
                                  quadratic function $ Q_c(x) = x^2 + c $  318--331
          Ernesto Acosta G. and   
               Cesar Delgado G.   Fréchet vs. Carathéodory . . . . . . . . . 332--338
                 A. C. Thompson   Odd magic powers . . . . . . . . . . . . 339--342
                   Frank Morgan   Mathematicians, including
                                  undergraduates, look at soap bubbles . . 343--351
                    Fred Galvin   A proof of Dilworth's chain
                                  decomposition theorem  . . . . . . . . . 352--353
           Michel Vellekoop and   
                 Raoul Berglund   On intervals, transitivity = chaos . . . 353--355
                  Kiran Kedlaya   Proof of a mixed arithmetic-mean,
                                  geometric-mean inequality  . . . . . . . 355--357

American Mathematical Monthly
Volume 101, Number 5, May, 1994

            Thomas Banchoff and   
                   Peter Giblin   On the geometry of piecewise circular
                                  curves . . . . . . . . . . . . . . . . . 403--416
                  Elliot Linzer   The two envelope paradox . . . . . . . . 417--419
              Stephen B. Maurer   Comment: ``Orderly currencies'' [Amer.
                                  Math. Monthly \bf 101 (1994), no. 1,
                                  36--38] by J. D. Jones . . . . . . . . . 419--419
                   Alain Robert   Fourier series of polygons . . . . . . . 420--428
         Richard P. Savage, Jr.   The paradox of nontransitive dice  . . . 429--436
              Laurent Beeckmans   Squares expressible as sum of
                                  consecutive squares  . . . . . . . . . . 437--442
              Stephen M. Turner   Square roots mod $p$ . . . . . . . . . . 443--449
                Jing Cheng Tong   Kummer's test gives characterizations
                                  for convergence or divergence of all
                                  positive series  . . . . . . . . . . . . 450--452
               Chi-Kwong Li and   
                       Wasin So   Isometries of $ l_p$-norm  . . . . . . . 452--453
               Bo Ying Wang and   
                  Fu Zhen Zhang   A trace inequality for unitary matrices  453--455
                Loukas Grafakos   An elementary proof of the square
                                  summability of the discrete Hilbert
                                  transform  . . . . . . . . . . . . . . . 456--458
                  Abe Shenitzer   How hyperbolic geometry became
                                  respectable  . . . . . . . . . . . . . . 464--470

American Mathematical Monthly
Volume 101, Number 6, June / July, 1994

                 Joe Buhler and   
             David Eisenbud and   
                 Ron Graham and   
                   Colin Wright   Juggling drops and descents  . . . . . . 507--519
                    Gary Gordon   Workable gears, Archimedian solids and
                                  planar bipartite graphs  . . . . . . . . 527--534
               Reese T. Prosser   On the Kummer solutions of the
                                  hypergeometric equation  . . . . . . . . 535--543
              John W. Emert and   
               Kay I. Meeks and   
                Roger B. Nelson   Reflections on a Mira  . . . . . . . . . 544--549
                     Ed Waymire   Buffon noodles . . . . . . . . . . . . . 550--559
           Victor Bronstein and   
            Aviezri S. Fraenkel   On a curious property of counting
                                  sequences  . . . . . . . . . . . . . . . 560--563
                Carsten Knudsen   Chaos without nonperiodicity . . . . . . 563--565
              Josip Pe\vcari\'c   A reverse Stolarsky's inequality . . . . 565--567
                 A. McD. Mercer   A note on some irrational decimal
                                  fractions  . . . . . . . . . . . . . . . 567--568
                   David Callan   A possible permanent formula . . . . . . 571--573

American Mathematical Monthly
Volume 101, Number 7, August / September, 1994

               Jonathan L. King   Three problems in search of a measure    609--628
                 Igor Rivin and   
                 Ilan Vardi and   
                Paul Zimmermann   The $n$-queens problem . . . . . . . . . 629--639
                 Roger L. Kraft   What's the difference between Cantor
                                  sets . . . . . . . . . . . . . . . . . . 640--650
         Jean-Paul Allouche and   
              Dan Astoorian and   
                Jim Randall and   
                Jeffrey Shallit   Morphisms, squarefree strings, and the
                                  Tower of Hanoi puzzle  . . . . . . . . . 651--658
                    A. A. Ageev   Sierpi\'nski's theorem is deducible from
                                  Euler and Dirichlet  . . . . . . . . . . 659--660
              F. Matú\vs   On nonnegativity of symmetric
                                  polynomials  . . . . . . . . . . . . . . 661--664
                  N. Graham and   
            R. C. Entringer and   
           L. A. Székely   New tricks for old trees: maps and the
                                  pigeonhole principle . . . . . . . . . . 664--667
                 Jeffrey Ondich   Do you know the way to vertex $A$  . . . 668--673
                 Erwin Kreyszig   On the calculus of variations and its
                                  major influences on the mathematics of
                                  the first half of our century. I . . . . 674--678

American Mathematical Monthly
Volume 101, Number 8, October, 1994

           Maria S. Terrell and   
              Robert E. Terrell   Behind the scenes of a random dot
                                  stereogram . . . . . . . . . . . . . . . 715--724
                   Goro Shimura   Fractional and trigonometric expressions
                                  for matrices . . . . . . . . . . . . . . 744--758
             Barbara L. Osofsky   Noether Lasker primary decomposition
                                  revisited  . . . . . . . . . . . . . . . 759--768
                   S. Stein and   
                S. Szabó   Elementary infinite sources of
                                  non-unique factorization rings . . . . . 769--770
                Antal E. Fekete   Apropos ``Two notes on notation'' [Amer.
                                  Math. Monthly \bf 99 (1992), no. 5,
                                  403--422, MR 93f:05001] by D. E. Knuth   771--778
                   Lyle Ramshaw   Erratum: ``On the geometry of piecewise
                                  circular curves'' [Amer. Math. Monthly
                                  \bf 101 (1994), no. 5, 403--416, MR
                                  95k:51030a] by T. Banchoff and P. Giblin 778--778
                Leonard Gillman   Congruence of triangles  . . . . . . . . 782--783
      Norbert Hungerbühler   A short elementary proof of the
                                  Mohr-Mascheroni theorem  . . . . . . . . 784--787
                 Folke Eriksson   Which triangles are plane sections of
                                  regular tetrahedra . . . . . . . . . . . 788--789
              Edward C. Waymire   Addendum: ``Buffon noodles'' . . . . . . 791--791

American Mathematical Monthly
Volume 101, Number 9, November, 1994

                    Robert Gray   Georg Cantor and transcendental numbers  819--832
               Milton Sobel and   
           Krzysztof Frankowski   The 500th anniversary of the sharing
                                  problem (the oldest problem in the
                                  theory of probability) . . . . . . . . . 833--847
                  Hugh Thurston   What is wrong with the definition of $ d
                                  y / d x $  . . . . . . . . . . . . . . . 855--857
                   Louis Gordon   A stochastic approach to the gamma
                                  function . . . . . . . . . . . . . . . . 858--865
           Jacob E. Goodman and   
            Richard Pollack and   
             Rephael Wenger and   
               Tudor Zamfirescu   Arrangements and topological planes  . . 866--878
                     Jeff Boyle   An application of Fourier series to the
                                  most significant digit problem . . . . . 879--886
                 Andrew Dittmer   Cross product identities in arbitrary
                                  dimension  . . . . . . . . . . . . . . . 887--891
                 D. H. Armitage   A non-constant continuous function on
                                  the plane whose integral on every line
                                  is zero  . . . . . . . . . . . . . . . . 892--894
               Doron Zeilberger   Chu's 1303 identity implies Bombieri's
                                  1990 norm-inequality (via an identity of
                                  Beauzamy and Dégot) . . . . . . . . . . . 894--896
           Catherine C. McGeoch   How to stay competitive  . . . . . . . . 897--901
                 Erwin Kreyszig   On the calculus of variations and its
                                  major influences on the mathematics of
                                  the first half of our century. II  . . . 902--908

American Mathematical Monthly
Volume 101, Number 10, December, 1994

      Edward R. Scheinerman and   
                Herbert S. Wilf   The rectilinear crossing number of a
                                  complete graph and Sylvester's ``four
                                  point problem'' of geometric probability 939--943
              Ora E. Percus and   
               Jerome K. Percus   String matching for the novice . . . . . 944--947
                   Don Rawlings   Bernoulli trials and number theory . . . 948--952
             William H. Paulsen   What is the shape of a mylar balloon . . 953--958
               Peter Hilton and   
                  Jean Pedersen   Euler's theorem for polyhedra: a
                                  topologist and geometer respond. Comment
                                  to: ``A new look at Euler's theorem for
                                  polyhedra'' [Amer. Math. Monthly \bf 101
                                  (1994), no. 2, 109--128, MR 95c:52032]
                                  by B. Grünbaum and G. C. Shephard. With a
                                  response by Grünbaum and Shephard . . . . 959--962
                 I. Kleiner and   
            N. Movshovitz-Hadar   The role of paradoxes in the evolution
                                  of mathematics . . . . . . . . . . . . . 963--974
         Richard A. Brualdi and   
             Stephen Mellendorf   Regions in the complex plane containing
                                  the eigenvalues of a matrix  . . . . . . 975--985
          Blair K. Spearman and   
            Kenneth S. Williams   Characterization of solvable quintics $
                                  x^5 + a x + b $  . . . . . . . . . . . . 986--992
               John B. Cosgrave   A Halmos problem and a related problem   993--996
                 Kurt Girstmair   A ``popular'' class number formula . . . 997--1001
                     Emre Alkan   Variations on Wolstenholme's theorem . . 1001--1004
                Leonard Gillman   The second-partials test for local
                                  extrema of $ f(x, y) $ . . . . . . . . . 1004--1006


American Mathematical Monthly
Volume 102, Number 1, January, 1995

              Michael Orkin and   
                 Richard Kakigi   What is the worth of free casino credit  3--8
            Steven J. Brams and   
                 Alan D. Taylor   An envy-free cake division protocol  . . 9--18
             Michael E. Hoffman   Derivative polynomials for tangent and
                                  secant . . . . . . . . . . . . . . . . . 23--30
          Thomas M. Liggett and   
                 Peter Petersen   The law of large numbers and $ \sqrt {2}
                                  $  . . . . . . . . . . . . . . . . . . . 31--35
                 R. H. Redfield   Exponentiation in rings  . . . . . . . . 36--40
          Blake E. Peterson and   
                James H. Jordan   Integer hexahedra equivalent to perfect
                                  boxes  . . . . . . . . . . . . . . . . . 41--45
               Richard J. Bagby   Calculating normal probabilities . . . . 46--48
                   Paul Shutler   Constrained critical points  . . . . . . 49--52
                 S. Tabachnikov   A cone eversion  . . . . . . . . . . . . 52--56
            Ran Libeskind-Hadas   Approximation algorithms: good solutions
                                  to hard problems . . . . . . . . . . . . 57--61
            Stefan Mykytiuk and   
                  Abe Shenitzer   Four significant axiomatic systems and
                                  some of the issues associated with them  62--67

American Mathematical Monthly
Volume 102, Number 2, February, 1995

           Deborah Tepper Haimo   Experimentation and conjecture are not
                                  enough . . . . . . . . . . . . . . . . . 102--112
                  Fan Chung and   
                 Ron Graham and   
              John Morrison and   
                 Andrew Odlyzko   Pebbling a chessboard  . . . . . . . . . 113--123
                  S. J. Chapman   Drums that sound the same  . . . . . . . 124--138
                  Sheldon Axler   Down with determinants . . . . . . . . . 139--154
                  Peter Andrews   Where not to find the critical points of
                                  a polynomial---variation on a Putnam
                                  theme  . . . . . . . . . . . . . . . . . 155--158
                   Peter D. Lax   A short path to the shortest path  . . . 158--159
               Dmitry Khavinson   A note on entire solutions of the
                                  eiconal [eikonal] equation . . . . . . . 159--161
              David B. Surowski   The uniqueness aspect of the fundamental
                                  theorem of finite abelian groups . . . . 162--163

American Mathematical Monthly
Volume 102, Number 3, March, 1995

         Stanley Rabinowitz and   
                     Stan Wagon   A spigot algorithm for the digits of $
                                  \pi $  . . . . . . . . . . . . . . . . . 195--203
                Philip J. Davis   The rise, fall, and possible
                                  transfiguration of triangle geometry: a
                                  mini-history . . . . . . . . . . . . . . 204--214
               David Auckly and   
                 John Cleveland   Totally real origami and impossible
                                  paper folding  . . . . . . . . . . . . . 215--226
               Massimo Furi and   
                 Mario Martelli   A multidimensional version of Rolle's
                                  theorem  . . . . . . . . . . . . . . . . 243--249
                  Noga Alon and   
        Melvyn B. Nathanson and   
                     Imre Ruzsa   Adding distinct congruence classes
                                  modulo a prime . . . . . . . . . . . . . 250--255
                Lech Maligranda   A simple proof of the Hölder and the
                                  Minkowski inequality . . . . . . . . . . 256--259
               Irving Kaplansky   Never too late. Addendum to:
                                  ``Determinants whose elements are $0$
                                  and $1$'' [Amer. Math. Monthly 53
                                  (1946), 427--434, MR 8, 128] by J.
                                  Williamson . . . . . . . . . . . . . . . 259--259
           I. G. Bashmakova and   
                  A. N. Rudakov   The evolution of algebra 1800--1870  . . 266--270

American Mathematical Monthly
Volume 102, Number 4, April, 1995

              Alan Hausrath and   
            Bradley Jackson and   
               John Mitchem and   
              Edward Schmeichel   Gale's round-trip jeep problem . . . . . 299--309
            Steven H. Weintraub   Count-wheels: a mathematical problem
                                  arising in horology  . . . . . . . . . . 310--316
              Donald R. Chalice   How to teach a class by the modified
                                  Moore method . . . . . . . . . . . . . . 317--321
               Theodore P. Hill   The significant-digit phenomenon . . . . 322--327
                LaDawn Haws and   
                    Terry Kiser   Exploring the brachistochrone problem    328--336
            William Derrick and   
                  Jack Eidswick   Continued fractions, Chebychev
                                  polynomials, and chaos . . . . . . . . . 337--344
            Zheng Bing Wang and   
             Robert Fokkink and   
                    Wan Fokkink   A relation between partitions and the
                                  number of divisors . . . . . . . . . . . 345--346
                   Paolo Starni   Answers to two questions concerning
                                  quotients of primes  . . . . . . . . . . 347--349
               James W. M. Ford   Avoiding the exchange lemma  . . . . . . 350--351
              Stephen Silverman   Intervals contained in arithmetic
                                  combinations of sets . . . . . . . . . . 351--353
                   D. Flath and   
                      A. Zulauf   Does the Möbius function determine
                                  multiplicative arithmetic  . . . . . . . 354--356

American Mathematical Monthly
Volume 102, Number 5, May, 1995

            I. Grattan-Guinness   Why did George Green write his essay of
                                  1828 on electricity and magnetism  . . . 387--396
                  Susan Bassein   Order and chaos on your desk . . . . . . 409--416
                T. R. Scavo and   
                     J. B. Thoo   On the geometry of Halley's method . . . 417--426
                   A. R. Meijer   The binary expansion of $ 1 / p $  . . . 427--430
               Ricardo Diaz and   
                   Sinai Robins   Pick's formula via the Weierstrass $ \wp
                                  $-function . . . . . . . . . . . . . . . 431--437
                  George Mackiw   Permutations as products of
                                  transpositions . . . . . . . . . . . . . 438--440
                   Bjorn Poonen   Congruences relating the order of a
                                  group to the number of conjugacy classes 440--442
                Peter Andersson   The color invariant for knots and links  442--448
                   Hermann Weyl   Topology and abstract algebra as two
                                  roads of mathematical comprehension. I.
                                  Translated from the German by Abe
                                  Shenitzer  . . . . . . . . . . . . . . . 453--460

American Mathematical Monthly
Volume 102, Number 6, June / July, 1995

                   S. L. Zabell   Alan Turing and the central limit
                                  theorem  . . . . . . . . . . . . . . . . 483--494
               Michael I. Rosen   Niels Hendrik Abel and equations of the
                                  fifth degree . . . . . . . . . . . . . . 495--505
                     John Oprea   Geometry and the Foucault pendulum . . . 515--522
               David P. Robbins   Areas of polygons inscribed in a circle  523--530
               Paul D. Scofield   Curves of constant precession  . . . . . 531--537
               Jeffery C. Allen   Matrix expansion by orthogonal Kronecker
                                  products . . . . . . . . . . . . . . . . 538--540
                   Walter Rudin   Injective polynomial maps are
                                  automorphisms  . . . . . . . . . . . . . 540--543
               Robin J. Chapman   An elementary proof of the simplicity of
                                  the Mathieu groups $ M_{11} $ and $
                                  M_{23} $ . . . . . . . . . . . . . . . . 544--545

American Mathematical Monthly
Volume 102, Number 7, August / September, 1995

Heikki Hämäläinen and   
               Iiro Honkala and   
               Simon Litsyn and   
    Patric Östergård   Football pools --- a game for
                                  mathematicians . . . . . . . . . . . . . 579--588
                   Reuben Hersh   Fresh breezes in the philosophy of
                                  mathematics  . . . . . . . . . . . . . . 589--594
               Nigel Boston and   
          Marshall L. Greenwood   Quadratics representing primes . . . . . 595--599
                 Leslie Lamport   How to write a proof . . . . . . . . . . 600--608
           Kenneth B. Stolarsky   Searching for common generalizations:
                                  the case of hyperbolic functions . . . . 609--619
                 P. Sabinin and   
                    M. G. Stone   Transforming $n$-gons by folding the
                                  plane  . . . . . . . . . . . . . . . . . 620--627
                David A. Singer   Isometries of the plane  . . . . . . . . 628--631
                   V. A. Geyler   One more construction which is
                                  impossible . . . . . . . . . . . . . . . 632--634
                Takashi Matsuda   An inductive proof of a mixed
                                  arithmetic-geometric mean inequality . . 634--637
                  T. S. Michael   The ranks of tournament matrices . . . . 637--639
                 David L. Ranum   On some applications of Fibonacci
                                  numbers  . . . . . . . . . . . . . . . . 640--645
                   Hermann Weyl   Topology and abstract algebra as two
                                  roads of mathematical comprehension. II.
                                  Translated from the German by Abe
                                  Shenitzer  . . . . . . . . . . . . . . . 646--651

American Mathematical Monthly
Volume 102, Number 8, October, 1995

                 G. Myerson and   
          A. J. van der Poorten   Some problems concerning recurrence
                                  sequences  . . . . . . . . . . . . . . . 698--705
                 Dana Mackenzie   A hyperbolic plane coloring and the
                                  simple group of order $ 168 $  . . . . . 706--715
               Kent E. Morrison   Cosine products, Fourier transforms, and
                                  random sums  . . . . . . . . . . . . . . 716--724
                     Geza Schay   How to add fast --- on average . . . . . 725--730
                   H. R. Morton   Fibonacci-like sequences and greatest
                                  common divisors  . . . . . . . . . . . . 731--734
               I. M. Isaacs and   
                Thilo Zieschang   Generating symmetric groups  . . . . . . 734--739
                  Lutz G. Lucht   On the arithmetic-geometric mean
                                  inequality . . . . . . . . . . . . . . . 739--740

American Mathematical Monthly
Volume 102, Number 9, November, 1995

                 Richard K. Guy   My favorite elliptic curve: a tale of
                                  two types of triangles . . . . . . . . . 771--781
                Keith M. Kendig   Stalking the wild ellipse  . . . . . . . 782--787
              Annalisa Crannell   The role of transitivity in Devaney's
                                  definition of chaos  . . . . . . . . . . 788--797
                 David G. Poole   The stochastic group . . . . . . . . . . 798--801
                   J. W. Sander   A story of binomial coefficients and
                                  primes . . . . . . . . . . . . . . . . . 802--807
                  Martin Aigner   Turán's graph theorem . . . . . . . . . . 808--816
                  Hans Samelson   More on Kummer's test  . . . . . . . . . 817--818
                  G. M. Tuynman   The derivation of the exponential map of
                                  matrices . . . . . . . . . . . . . . . . 818--820
          Vlastimil Pták   The Kantorovich inequality . . . . . . . 820--821
              Robert Kalaba and   
                        Rong Xu   On the generalized inverse form of the
                                  equations of constrained motion  . . . . 821--825
                 John Stillwell   Elliptic curves  . . . . . . . . . . . . 831--837

American Mathematical Monthly
Volume 102, Number 10, December, 1995

             George W. Tokarsky   Polygonal rooms not illuminable from
                                  every point  . . . . . . . . . . . . . . 867--879
                Gunnar Blom and   
                 Lars Holst and   
                 Dennis Sandell   Three SING-SING problems . . . . . . . . 880--887
                John E. Morrill   A Nobel Prize in mathematics . . . . . . 888--891
         Richard Blecksmith and   
            Purushottam W. Laud   Some exact number theory computations
                                  via probability mechanisms . . . . . . . 893--903
           Ilse C. F. Ipsen and   
                  Carl D. Meyer   The angle between complementary
                                  subspaces  . . . . . . . . . . . . . . . 904--911
              Serge Tabachnikov   The four-vertex theorem revisited ---
                                  two variations on the old theme  . . . . 912--916
                  R. B. Burckel   Entire functions which vanish at
                                  infinity . . . . . . . . . . . . . . . . 916--918
                      D. Zagier   A converse to Cauchy's inequality  . . . 919--920
             Richard K. Guy and   
          Richard J. Nowakowski   Monthly unsolved problems, 1969--1995    921--926


American Mathematical Monthly
Volume 103, Number 1, January, 1996

                   David Fowler   The binomial coefficient function  . . . 1--17
                      Jim Henle   Classical mathematics. Baroque
                                  mathematics. Romantic mathematics?
                                  Mathematics jazz! Also atonal, New Age,
                                  minimalist, and punk mathematics . . . . 18--29
                  Bruce Solomon   Tantrices of spherical curves  . . . . . 30--39
                 D. Borwein and   
              J. M. Borwein and   
              P. B. Borwein and   
                  R. Girgensohn   Giuga's conjecture on primality  . . . . 40--50
            William M. Faucette   A geometric interpretation of the
                                  solution of the general quartic
                                  polynomial . . . . . . . . . . . . . . . 51--57
            Bruno Codenotti and   
                Luciano Margara   Transitive cellular automata are
                                  sensitive  . . . . . . . . . . . . . . . 58--62
                  Ray Redheffer   Use of a differential inequality in
                                  combinatorics  . . . . . . . . . . . . . 62--64
               V. M. Tikhomirov   The evolution of methods of convex
                                  optimization . . . . . . . . . . . . . . 65--71

American Mathematical Monthly
Volume 103, Number 2, February, 1996

                   H. O. Pollak   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for Distinguished Service to
                                  Andrew Gleason . . . . . . . . . . . . . 105--106
              James T. Sandefur   Using self-similarity to find length,
                                  area, and dimension  . . . . . . . . . . 107--120
               Peter Hilton and   
                  Jean Pedersen   The Euler characteristic and Pólya's
                                  dream  . . . . . . . . . . . . . . . . . 121--131
                  Benno Artmann   A Roman icosahedron discovered . . . . . 132--133
              Manuel Barros and   
                 Oscar J. Garay   Free elastic parallels in a surface of
                                  revolution . . . . . . . . . . . . . . . 149--156
             Israel Gohberg and   
               Seymour Goldberg   A simple proof of the Jordan
                                  decomposition theorem for matrices . . . 157--159
                      A. Caruth   A concise proof of Hilbert's basis
                                  theorem  . . . . . . . . . . . . . . . . 160--161
            Jesús Ferrer   Rolle's theorem fails in $ l_2 $ . . . . 161--165
            Gheorghe P\uaun and   
                   Arto Salomaa   Self-reading sequences . . . . . . . . . 166--168

American Mathematical Monthly
Volume 103, Number 3, March, 1996

                  A. F. Beardon   Sums of powers of integers . . . . . . . 201--213
               Reinhold Remmert   Wielandt's theorem about the $ \Gamma
                                  $-function . . . . . . . . . . . . . . . 214--220
                    Louis Zulli   Charting the $3$-sphere --- an
                                  exposition for undergraduates  . . . . . 221--229
               Doron Zeilberger   The method of undetermined
                                  generalization and specialization.
                                  Illustrated with Fred Galvin's amazing
                                  proof of the Dinitz conjecture . . . . . 233--239
                    Thomas Hull   A note on ``impossible'' paper folding   240--241
                    Gary Lawlor   A new minimization proof for the
                                  brachistochrone  . . . . . . . . . . . . 242--249
              Richard Mansfield   Strategies for the Shannon switching
                                  game . . . . . . . . . . . . . . . . . . 250--252
               Gerald J. Porter   $k$-volume in $ {\bf R}^n$ and the
                                  generalized Pythagorean theorem  . . . . 252--256
                  Abe Shenitzer   A few expository mini-essays . . . . . . 257--263

American Mathematical Monthly
Volume 103, Number 4, April, 1996

              Richard Askey and   
           Deborah Tepper Haimo   Similarities between Fourier and power
                                  series . . . . . . . . . . . . . . . . . 297--304
              Richard H. Warren   Disks on a chessboard  . . . . . . . . . 305--307
          Bennett Eisenberg and   
              Rosemary Sullivan   Random triangles in $n$ dimensions . . . 308--318
                 Adrian Oldknow   The Euler-Gergonne-Soddy triangle of a
                                  triangle . . . . . . . . . . . . . . . . 319--329
              Robert E. Hartwig   Roth's removal rule and the rational
                                  canonical form . . . . . . . . . . . . . 332--335
                 Manfred Krause   A simple proof of the Gale-Ryser theorem 335--337
            Yves Martinez-Maure   A note on the tennis ball theorem  . . . 338--340

American Mathematical Monthly
Volume 103, Number 5, May, 1996

                   Frank Morgan   What is a surface  . . . . . . . . . . . 369--376
                    Ron Perline   Non-Euclidean flashlights  . . . . . . . 377--385
                   Saber Elaydi   On a converse of Sharkovsky's theorem    386--392
                 Kimmo Eriksson   Splitting a polygon into two congruent
                                  pieces . . . . . . . . . . . . . . . . . 393--400
                    John Hannah   A geometric approach to determinants . . 401--409
                Darrell Desbrow   On zero derivatives  . . . . . . . . . . 410--411
                Peter Duren and   
          Walter Hengartner and   
            Richard S. Laugesen   The argument principle for harmonic
                                  functions  . . . . . . . . . . . . . . . 411--415
           Richard B. Darst and   
               Gerald D. Taylor   Differentiating powers of an old friend  415--416
                 Israel Kleiner   The genesis of the abstract ring concept 417--424

American Mathematical Monthly
Volume 103, Number 6, June / July, 1996

          Daniel Henry Gottlieb   All the way with Gauss--Bonnet and the
                                  sociology of mathematics . . . . . . . . 457--469
              Roger A. Horn and   
                   Ingram Olkin   When does $ A^*A = B^*B $ and why does
                                  one want to know . . . . . . . . . . . . 470--482
                  Susan Bassein   A sampler of randomness  . . . . . . . . 483--490
                     Don Fallis   Mathematical proof and the reliability
                                  of DNA evidence  . . . . . . . . . . . . 491--497
              Charles H. Jepsen   Equidissections of trapezoids  . . . . . 498--500
                    Paul Monsky   Calculating a trapezoidal spectrum . . . 500--501
               Doron Zeilberger   Reverend Charles to the aid of Major
                                  Percy and Fields medalist Enrico . . . . 501--502
        József Bukor and   
    János T. Tóth   On accumulation points of ratio sets of
                                  positive integers  . . . . . . . . . . . 502--504

American Mathematical Monthly
Volume 103, Number 7, August / September, 1996

                Paulo Ribenboim   Catalan's conjecture . . . . . . . . . . 529--538
               Roger S. Pinkham   Mathematics and modern technology  . . . 539--545
                 C. W. Groetsch   Tartaglia's Inverse Problem in a
                                  Resistive Medium . . . . . . . . . . . . 546--551
            Donald P. Minassian   The current state of actuarial science   552--561
                  T. Y. Lam and   
                    K. H. Leung   On the cyclotomic polynomial $
                                  \Phi_{pq}(X) $ . . . . . . . . . . . . . 562--564
           Edward B. Burger and   
               Thomas Struppeck   Does $ \sum^\infty_{n = 0}{1} / {n!} $
                                  really converge? Infinite series and
                                  $p$-adic analysis or ``You can sum some
                                  of the series some of the time and some
                                  of the series none of the time$ \ldots $
                                  but can you sum some of the series all
                                  of the time?'' . . . . . . . . . . . . . 565--577
         Charles R. Johnson and   
              Erik A. Schreiner   The relationship between $ A B $ and $ B
                                  A $  . . . . . . . . . . . . . . . . . . 578--582
              Hajrudin Fejzi\'c   On thin sets of circles  . . . . . . . . 582--585
                    Horst Alzer   A proof of the arithmetic mean-geometric
                                  mean inequality  . . . . . . . . . . . . 585--585
                 Joseph L. Doob   The development of rigor in mathematical
                                  probability (1900--1950) [in \it
                                  Development of mathematics 1900--1950
                                  (Luxembourg, 1992), 157--170, Birkhäuser,
                                  Basel, 1994, MR 95i:60001] . . . . . . . 586--595

American Mathematical Monthly
Volume 103, Number 8, October, 1996

               Robert G. Bartle   Return to the Riemann integral . . . . . 625--632
       Richard D. Neidinger and   
             R. John Annen, III   The road to chaos is filled with
                                  polynomial curves  . . . . . . . . . . . 640--653
            Stephen Bedding and   
                   Keith Briggs   Iteration of quaternion functions  . . . 654--664
              Patrick Ahern and   
                   Walter Rudin   Geometric properties of the gamma
                                  function . . . . . . . . . . . . . . . . 678--681
                 Sadahiro Saeki   A proof of the existence of infinite
                                  product probability measures . . . . . . 682--683
                   Leo S. Gurin   A problem  . . . . . . . . . . . . . . . 683--686

American Mathematical Monthly
Volume 103, Number 9, November, 1996

            Paul T. Bateman and   
              Harold G. Diamond   A hundred years of prime numbers . . . . 729--741
              Thomas Burger and   
            Peter Gritzmann and   
                    Victor Klee   Polytope projection and projection
                                  polytopes  . . . . . . . . . . . . . . . 742--755
         Aleksandar Juri\vsi\'c   The Mercedes knot problem  . . . . . . . 756--770
                Arthur T. White   Fabian Stedman: the first group theorist 771--778
           Herbert I. Brown and   
         James W. Burgmeier and   
                David S. Dummit   Functions whose successive tangent lines
                                  enclose proportional areas . . . . . . . 779--787
                    M. H. Eggar   On the discriminant criterion and a
                                  generalization . . . . . . . . . . . . . 788--792
                  Ernst Snapper   Expressing primes as quadratic forms of
                                  integers . . . . . . . . . . . . . . . . 793--794
               Richard J. Bagby   Volumes of cones . . . . . . . . . . . . 794--796
             Edward Bertram and   
                  Marcel Herzog   On regular bases of finite groups  . . . 796--799
                  Freeman Dyson   The scientist as rebel . . . . . . . . . 800--805

American Mathematical Monthly
Volume 103, Number 10, December, 1996

        Shawnee L. McMurran and   
            James J. Tattersall   The mathematical collaboration of M. L.
                                  Cartwright and J. E. Littlewood  . . . . 833--845
                   Roman Kossak   What are infinitesimals and why they
                                  cannot be seen . . . . . . . . . . . . . 846--853
             John Brillhart and   
                 Patrick Morton   A case study in mathematical research:
                                  the Golay--Rudin--Shapiro sequence . . . 854--869
               Edward Aboufadel   A mathematician catches a baseball . . . 870--878
                Victoria Powers   Hilbert's 17th problem and the champagne
                                  problem  . . . . . . . . . . . . . . . . 879--887
                  W. McCune and   
                    A. D. Sands   Computer and human reasoning: single
                                  implicative axioms for groups and for
                                  abelian groups . . . . . . . . . . . . . 888--892
                  Roger Webster   An elementary proof of Horn's theorem    892--894
              James Angelos and   
            George Grossman and   
                 Yury Ionin and   
              Edwin Kaufman and   
               Terry Lenker and   
                   Leela Rakesh   Packability of five spheres on a sphere
                                  implies packability of six . . . . . . . 894--896


American Mathematical Monthly
Volume 104, Number 1, January, 1997

                 Bruce Pourciau   Reading the master: Newton and the birth
                                  of celestial mechanics . . . . . . . . . 1--19
            Jack W. Rogers, Jr.   Applications of linear algebra in
                                  calculus . . . . . . . . . . . . . . . . 20--26
                       A. Vince   Periodicity, quasiperiodicity, and
                                  Bieberbach's theorem on crystallographic
                                  groups . . . . . . . . . . . . . . . . . 27--35
                  John A. Baker   Integration over spheres and the
                                  divergence theorem for balls . . . . . . 36--47
                  R. B. Burckel   Three secrets about harmonic functions   52--56
                Vilmos Komornik   A short proof of the Erd\Hos--Mordell
                                  theorem  . . . . . . . . . . . . . . . . 57--60
                  Don Buckholtz   Inverting the difference of Hilbert
                                  space projections  . . . . . . . . . . . 60--61
           I. G. Bashmakova and   
                 E. I. Slavutin   Glimpses of algebraic geometry.
                                  Introduction to: \booktitleA History of
                                  Diophantine analysis (Russian)
                                  [``Nauka'', Moscow, 1984; MR 85m:01004].
                                  Translated by Abe Shenitzer  . . . . . . 62--67

American Mathematical Monthly
Volume 104, Number 2, February, 1997

           Carole B. Lacampagne   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  award for distinguished service to
                                  Deborah Tepper Haimo . . . . . . . . . . 97--98
            Bryan L. Shader and   
           Chanyoung Lee Shader   Scheduling conflict-free parties for a
                                  dating service . . . . . . . . . . . . . 99--106
          Ralph H. Buchholz and   
             Randall L. Rathbun   An infinite set of Heron triangles with
                                  two rational medians . . . . . . . . . . 107--115
                      T. K. Lam   Connected Sprouts  . . . . . . . . . . . 116--119
              Ronald E. Prather   Regular expressions for program
                                  computations . . . . . . . . . . . . . . 120--130
           R. Bruce Richter and   
              Carsten Thomassen   Relations between crossing numbers of
                                  complete and complete bipartite graphs   131--137
                  John M. Holte   Carries, combinatorics, and an amazing
                                  matrix . . . . . . . . . . . . . . . . . 138--149
                     Walter Nef   A new look at Euler's theorem for
                                  polyhedra: a comment . . . . . . . . . . 150--151
             Tadashi F. Tokieda   The hopping hoop . . . . . . . . . . . . 152--154
                    John Greene   Principal ideal domains are almost
                                  Euclidean  . . . . . . . . . . . . . . . 154--156
                     Shmuel Onn   A colorful determinantal identity, a
                                  conjecture of Rota, and Latin squares    156--159
                W. K. Nicholson   Very semisimple modules  . . . . . . . . 159--162

American Mathematical Monthly
Volume 104, Number 3, March, 1997

                     Jim Pitman   Some probabilistic aspects of set
                                  partitions . . . . . . . . . . . . . . . 201--209
      Karen Hunger Parshall and   
                  Eugene Seneta   Building an international reputation:
                                  the case of J. J. Sylvester (1814--1897) 210--222
            Geoffrey R. Goodson   The inverse-similarity problem for real
                                  orthogonal matrices  . . . . . . . . . . 223--230
               Thomas W. Tucker   Rethinking rigor in calculus: the role
                                  of the mean value theorem  . . . . . . . 231--240
                   Howard Swann   Commentary on rethinking rigor in
                                  calculus: the role of the mean value
                                  theorem  . . . . . . . . . . . . . . . . 241--245
           Edward B. Burger and   
                   Frank Morgan   Fermat's Last Theorem, the Four Color
                                  Conjecture, and Bill Clinton for April
                                  Fools' Day . . . . . . . . . . . . . . . 246--255
                   D. J. Newman   Euler's $ \phi $ function on arithmetic
                                  progressions . . . . . . . . . . . . . . 256--257
                     Steve Fisk   A note on Weyl's inequality  . . . . . . 257--258
                Ming-chang Kang   Minimal polynomials over cyclotomic
                                  fields . . . . . . . . . . . . . . . . . 258--260
                 Wilhelm Magnus   The significance of mathematics: the
                                  mathematicians' share in the general
                                  human condition  . . . . . . . . . . . . 261--269

American Mathematical Monthly
Volume 104, Number 4, April, 1997

              A. J. Berrick and   
                  M. E. Keating   Rectangular invertible matrices  . . . . 297--302
       Maarten C. Boerlijst and   
            Martin A. Nowak and   
                   Karl Sigmund   Equal pay for all prisoners  . . . . . . 303--305
              Jim Sauerberg and   
                  Linghsueh Shu   The long and the short on counting
                                  sequences  . . . . . . . . . . . . . . . 306--317
             Daniel J. Velleman   Characterizing continuity  . . . . . . . 318--322
           A. M. Bruckstein and   
              C. L. Mallows and   
                   I. A. Wagner   Probabilistic pursuits on the grid . . . 323--343
             Richard P. Stanley   Hipparchus, Plutarch, Schröder, and Hough 344--350
                  Gert Almkvist   Many correct digits of $ \pi $,
                                  revisited  . . . . . . . . . . . . . . . 351--353
                Martin L. Jones   A note on a cake cutting algorithm of
                                  Banach and Knaster . . . . . . . . . . . 353--355
                Hassan Sedaghat   The impossibility of unstable, globally
                                  attracting fixed points for continuous
                                  mappings of the line . . . . . . . . . . 356--358

American Mathematical Monthly
Volume 104, Number 5, May, 1997

                    Hardy Grant   Reviews: \em Vita Mathematica:
                                  Historical Research and Integration with
                                  Teaching, edited by Ronald Calinger  . . ??
                     Andre Toom   Reviews: \em Mathematical Circles
                                  (Russian Experience), by Dmitri Fomin,
                                  Sergey Genkin, and Ilia Itenberg . . . . ??
             Judith V. Grabiner   Was Newton's calculus a dead end? The
                                  continental influence of Maclaurin's
                                  treatise of fluxions . . . . . . . . . . 393--410
                     Pat Touhey   Yet another definition of chaos  . . . . 411--414
        Scott A. McCullough and   
                   Leiba Rodman   Hereditary classes of operators and
                                  matrices . . . . . . . . . . . . . . . . 415--430
               Clark Kimberling   Major centers of triangles . . . . . . . 431--438
                  M. Laczkovich   On Lambert's proof of the irrationality
                                  of $ \pi $ . . . . . . . . . . . . . . . 439--443
                Winfried Kohnen   A simple congruence modulo $p$ . . . . . 444--445
                Marcelo Polezzi   A geometrical method for finding an
                                  explicit formula for the greatest common
                                  divisor  . . . . . . . . . . . . . . . . 445--446
                Detlef Laugwitz   The Evolution of \ldots: On the
                                  historical development of infinitesimal
                                  mathematics  . . . . . . . . . . . . . . 447--455

American Mathematical Monthly
Volume 104, Number 6, June / July, 1997

                  Sheldon Axler   Reviews: \em The Life of Stefan Banach,
                                  by Roman Kaluza  . . . . . . . . . . . . ??
              J. Kevin Colligan   Reviews: \em 101 Careers in Mathematics,
                                  edited by Andrew Sterrett  . . . . . . . ??
                J. Dénes   Unsolved Problems: When Is There a Latin
                                  Power Set? . . . . . . . . . . . . . . . ??
                Melanie A. King   Lecturing at the `Bored' . . . . . . . . ??
            Rajendra Bhatia and   
                  Peter \vSemrl   Approximate isometries on Euclidean
                                  spaces . . . . . . . . . . . . . . . . . 497--504
        István Nemes and   
          Marko Petkov\vsek and   
            Herbert S. Wilf and   
               Doron Zeilberger   How to do Monthly problems with your
                                  computer . . . . . . . . . . . . . . . . 505--519
        Lawrence W. Baggett and   
          Herbert A. Medina and   
               Kathy D. Merrill   Simultaneously symmetric functions . . . 520--528
                   R. A. Mollin   Prime-producing quadratics . . . . . . . 529--544
                Wladyslaw Kulpa   The Poincaré-Miranda theorem  . . . . . . 545--550
                       M. Bayat   A generalization of Wolstenholme's
                                  theorem  . . . . . . . . . . . . . . . . 557--560
                  Bao-lin Zhang   A note on the mean value theorem for
                                  integrals  . . . . . . . . . . . . . . . 561--562

American Mathematical Monthly
Volume 104, Number 7, August / September, 1997

            J. N. Anthony Danby   Reviews: \em The Sheer Joy of Celestial
                                  Mechanics, by Nathaniel Grossman . . . . ??
           Jennifer R. Galovich   Reviews: \em Strength in Numbers:
                                  Discovering the Joy and Power of
                                  Mathematics in Everyday Life, by Sherman
                                  K. Stein . . . . . . . . . . . . . . . . ??
         Kent G. Merryfield and   
                   Ngo Viet and   
                    Saleem Wats   Notes: The Wallet Paradox  . . . . . . . ??
                 S. C. Coutinho   The many avatars of a simple algebra . . 593--604
                   Tiberiu Trif   Multiple integrals of symmetric
                                  functions  . . . . . . . . . . . . . . . 605--608
                   John Chollet   Some inequalities for principal
                                  submatrices  . . . . . . . . . . . . . . 609--617
                  Eugene Gutkin   Two applications of calculus to
                                  triangular billiards . . . . . . . . . . 618--622
            Steven H. Weintraub   Early transcendentals  . . . . . . . . . 623--631
                   Keith Devlin   The logical structure of computer-aided
                                  mathematical reasoning . . . . . . . . . 632--646
                Henryk Gzyl and   
      José Luis Palacios   Notes: The Weierstrass approximation
                                  theorem and large deviations . . . . . . 651--653
                Detlef Laugwitz   The Evolution of \ldots: On the
                                  historical development of infinitesimal
                                  mathematics. II. The conceptual thinking
                                  of Cauchy. Translated from the German by
                                  Abe Shenitzer with the editorial
                                  assistance of Hardy Grant  . . . . . . . 654--663

American Mathematical Monthly
Volume 104, Number 8, October, 1997

            Norbert Peyerimhoff   Areas and Intersections in Convex
                                  Domains  . . . . . . . . . . . . . . . . 697--704
                      D. Zagier   Newman's Short Proof of the Prime Number
                                  Theorem  . . . . . . . . . . . . . . . . 705--708
                   David Callan   An Exploratory Approach to Kaplansky's
                                  Lemma Leads to a Generalized Resultant   709--712
           Bettina Richmond and   
                Thomas Richmond   Metric Spaces in Which All Triangles Are
                                  Degenerate . . . . . . . . . . . . . . . 713--719
                   Albert Fathi   Partitions of Unity for Countable Covers 720--723
                   Jeff Knisley   Calculus: a Modern Perspective . . . . . 724
                  Paul Zorn and   
                 Arnold Ostebee   Pro Choice . . . . . . . . . . . . . . . 728
                 James J. Kaput   Rethinking Calculus: Learning and
                                  Thinking . . . . . . . . . . . . . . . . 731
                  Richard Askey   What Do We Do About Calculus? First, Do
                                  No Harm  . . . . . . . . . . . . . . . . 738
     Gerald L. Alexanderson and   
       Leonard F. Klosinski and   
                Loren C. Larson   The Fifty-Seventh William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 744
                   Joseph Kupka   Notes: a Quadratic Trio  . . . . . . . . 755--757
              Apoloniusz Tyszka   Notes: a Discrete Form of the
                                  Beckman-Quarles Theorem  . . . . . . . . 757--761
      J. Daniel Christensen and   
                   Mark Tilford   Unsolved Problems: David Gale's Subset
                                  Take-Away Game . . . . . . . . . . . . . 762
              Ronald E. Mickens   Reviews: \em An Introduction to
                                  Difference Equations, by Saber Elyadi    777
                  Wayne Roberts   Reviews: \em Calculus Lite, by Frank
                                  Morgan . . . . . . . . . . . . . . . . . 780

American Mathematical Monthly
Volume 104, Number 9, November, 1997

             George W. Cobb and   
                 David S. Moore   Mathematics, Statistics, and Teaching    801
                    Marco Abate   When is a Linear Operator
                                  Diagonalizable?  . . . . . . . . . . . . 824--830
                      Eric Bach   Energy Arguments in the Theory of
                                  Algorithms . . . . . . . . . . . . . . . 831--837
                 Thomas Forster   Quine's $ {\rm NF} $---60 years on . . . 838--845
            Micha\l Misiurewicz   Remarks on Sharkovsky's Theorem  . . . . 846--847
               Andrew Granville   Correction to: ``Zaphod Beeblebrox's
                                  brain and the fifty-ninth row of
                                  Pascal's triangle'' [Amer. Math. Monthly
                                  \bf 99 (1992), no. 4, 318--331; MR
                                  93a:05008] . . . . . . . . . . . . . . . 848--851
            Victor Adamchik and   
                     Stan Wagon   A Simple Formula for $ \pi $ . . . . . . 852--855
              Francis Edward Su   Borsuk--Ulam Implies Brouwer: a Direct
                                  Construction . . . . . . . . . . . . . . 855--859
           Zdzis\law Pogoda and   
          Leszek M. Soko\lowski   The Evolution of\ldots: Does mathematics
                                  distinguish certain dimensions of
                                  spaces? Translated by Abe Shenitzer  . . 860--869
              William D. Dunbar   Reviews: \em Knots and Surfaces: A Guide
                                  to Discovering Mathematics, by David W.
                                  Farmer and Theodore Stanford & \em Knots
                                  and Surfaces, by N. D. Gilbert and T.
                                  Porter . . . . . . . . . . . . . . . . . 882
                 Andrew Bremner   Reviews: \em The Book of Numbers, by
                                  John Horton Conway and Richard K. Guy    884

American Mathematical Monthly
Volume 104, Number 10, December, 1997

            Bruce C. Berndt and   
             Heng Huat Chan and   
              Liang-Cheng Zhang   Ramanujan's Association with Radicals in
                                  India  . . . . . . . . . . . . . . . . . 905--911
                        Ken Ono   Ramanujan, Taxicabs, Birthdates, ZIP
                                  Codes, and Twists  . . . . . . . . . . . 912--917
              George E. Andrews   Simplicity and Surprise in Ramanujan's
                                  ``Lost'' Notebook  . . . . . . . . . . . 918--925
                Lou Shapiro and   
               D. G. Rogers and   
                   Wen-Jin Woan   The Catalan Numbers, the Lebesgue
                                  Integral, and $ 4^n - 2 $  . . . . . . . 926--931
           R. Bruce Richter and   
             William P. Wardlaw   Good Matrices: Matrices that Preserve
                                  Ideals . . . . . . . . . . . . . . . . . 932--938
             Peter A. Braza and   
                 Jingcheng Tong   A Converse of the Mean Value Theorem . . 939--942
           Andrew Granville and   
               Takashi Agoh and   
                   Paul Erd\Hos   Primes at a (Somewhat Lengthy) Glance    943--945
                          H. Wu   The Mathematics Education Reform: Why
                                  You Should be Concerned and What You Can
                                  Do . . . . . . . . . . . . . . . . . . . 946
              Jeremy Kilpatrick   Confronting Reform . . . . . . . . . . . 955
                  John L. Drost   A Shorter Proof of the Ramanujan
                                  Congruence Modulo 5  . . . . . . . . . . 963--964
              Scott Ahlgren and   
               Lars English and   
                    Ron Winters   An Amusing Representation of $ x / (\sin
                                  x) $ . . . . . . . . . . . . . . . . . . 964--966
      Richard J. Nowakowski and   
                 Richard K. Guy   Monthly Unsolved Problems, 1969--1997    967
              Saunders Mac Lane   \em Conceptual Mathematics: A First
                                  Introduction to Categories, by F.
                                  William Lawvere and Steven Schanuel  . . 985
                     Ezra Brown   \em Early Astronomy, by Hugh Thurston    988


American Mathematical Monthly
Volume 105, Number 1, January, 1998

                Jerry L. Kazdan   Solving Equations, an Elegant Legacy . . 1--21
             Donald W. Robinson   Separation of Subspaces by Volume  . . . 22--27
                  Kai Lai Chung   Probability and Doob . . . . . . . . . . 28--35
              George E. Andrews   The Geometric Series in Calculus . . . . 36--40
                Timothy Y. Chow   The Surprise Examination or Unexpected
                                  Hanging Paradox  . . . . . . . . . . . . 41--51
       Michael David Hirschhorn   Notes: Two or Three Identities of
                                  Ramanujan  . . . . . . . . . . . . . . . 52--55
             Michael E. Hoffman   The Bull and the Silo: An Application of
                                  Curvature  . . . . . . . . . . . . . . . 55--58
                       N. Luzin   The Evolution of \ldots Function: Part I 59--67
                  John Troutman   Reviews: \em Analysis by its History, by
                                  E. Hairer and G. Wanner  . . . . . . . . 79
                Anthony Ralston   Reviews: \em Principles and Practices of
                                  Mathematics, by COMAP  . . . . . . . . . 81
                     Andre Toom   Reviews: \em A Mathematical Mosaic:
                                  Patterns & Problem Solving, by Ravi Vakil 86

American Mathematical Monthly
Volume 105, Number 2, February, 1998

                  Linda R. Sons   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for Distinguished Service to Alice
                                  Turner Schafer . . . . . . . . . . . . . 105
              Russell A. Gordon   The Use of Tagged Partitions in
                                  Elementary Real Analysis . . . . . . . . 107--117
                  Susan Bassein   The Dynamics of a Family of
                                  One-Dimensional Maps . . . . . . . . . . 118--130
          Hunter S. Snevily and   
                Douglas B. West   The Bricklayer Problem and the Strong
                                  Cycle Lemma  . . . . . . . . . . . . . . 131--143
               Craig M. Johnson   A Computer Search for Free Actions on
                                  Surfaces . . . . . . . . . . . . . . . . 144--153
              John C. McConnell   Division Algebras --- Beyond the
                                  Quaternions  . . . . . . . . . . . . . . 154--162
               Brian Gerard and   
               Lawrence Roberts   Graphical Discovery of a New Identity
                                  for Jacobi Polynomials . . . . . . . . . 163--166
                 Philippe Revoy   The Generalized Level of a Non Prime
                                  Finite Field is Two  . . . . . . . . . . 167--168
         Wolfgang Kühn and   
               Zuzana Kühn   Cutting High-Dimensional Cakes . . . . . 168--169
            Joan Hutchinson and   
                     Stan Wagon   Kempe Revisited  . . . . . . . . . . . . 170--174
              Jean Pedersen and   
         Gerald L. Alexanderson   Reviews: \em ``Invertible'' Polyhedron
                                  Models, distributed by Snyder
                                  Engineering  . . . . . . . . . . . . . . 186
                William Goldman   Reviews: \em Topology and Geometry, by
                                  Glen E. Bredon . . . . . . . . . . . . . 192

American Mathematical Monthly
Volume 105, Number 3, March, 1998

    Béla Bollobás   To Prove and Conjecture: Paul Erd\Hos
                                  and His Mathematics  . . . . . . . . . . 209--237
            Ran Libeskind-Hadas   Sorting in Parallel  . . . . . . . . . . 238--245
               Murray Schechter   Integration Over a Polyhedron: An
                                  Application of the Fourier-Motzkin
                                  Elimination Method . . . . . . . . . . . 246--251
                Kenneth A. Ross   Doing and Proving: The Place of
                                  Algorithms and Proofs in School
                                  Mathematics  . . . . . . . . . . . . . . 252--255
                 David Beckwith   Legendre Polynomials and Polygon
                                  Dissections? . . . . . . . . . . . . . . 256--257
            Takayuki Furuta and   
              Masahiro Yanagida   Generalized Means and Convexity of
                                  Inversion for Positive Operators . . . . 258--259
             Mohammad Saleh and   
                   Hasan Yousef   The Number of Ring Homomorphisms from $
                                  {Z}_{m_1} \times \cdots \times {Z}_{m_r}
                                  i n t o {Z}_{k_1} \times \cdots \times
                                  {Z}_{k_s} $  . . . . . . . . . . . . . . 259--260
                  M. Mirzakhani   A Simple Proof of a Theorem of Schur . . 260--262
                       N. Luzin   The Evolution of \ldots Function: Part
                                  II . . . . . . . . . . . . . . . . . . . 263--270
                      Anonymous   Problems and Solutions . . . . . . . . . 271--283
                    Roger Cooke   \em Évariste Galois 1811--1832, by Laura
                                  Toti Rigatelli. Translated from the
                                  Italian by John Denton. Birkhäuser, 1996,
                                  168pp., \$29.50  . . . . . . . . . . . . 284--288
                       Jet Wimp   Reviews: \em The Fast Fourier Transform
                                  Workshop, by Richard and Sandra McPeak   289--292
               Daniel H. Ullman   Reviews: \em Which Way Did the Bicycle
                                  Go?, by Joseph D. E. Konhauser, Dan
                                  Velleman, and Stan Wagon and \em
                                  Problems and Solutions from the
                                  Mathematical Visitor, edited by Stanley
                                  Rabinowitz . . . . . . . . . . . . . . . 292--296
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 297--301

American Mathematical Monthly
Volume 105, Number 4, April, 1998

                     Ilan Vardi   Archimedes' Cattle Problem . . . . . . . 305--319
                 C. W. Groetsch   Lanczos' Generalized Derivative  . . . . 320--326
              Ellen Gethner and   
                 Stan Wagon and   
                     Brian Wick   A Stroll Through the Gaussian Primes . . 327--337
               Herman Erlichson   Galileo's Work on Swiftest Descent from
                                  a Circle and How He Almost Proved the
                                  Circle Itself Was the Minimum Time Path  338--347
                 Michael Sheard   Induction the Hard Way . . . . . . . . . 348--353
              C. Douglas Howard   Good Paths Don't Double Back . . . . . . 354--357
                    Xianfu Wang   A Note on the Clarke Subdifferential . . 357--359
                   Michael Reid   The Number of Conjugacy Classes  . . . . 359--361
           Branko Grünbaum   Which Coronas Are Simple?  . . . . . . . 362--365
                      Anonymous   Problems and Solutions . . . . . . . . . 366--376
        David A. Sánchez   Ordinary Differential Equations Texts    377--383
                    Owen Thomas   \em The Schools We Need, by E. D.
                                  Hirsch, Jr.  . . . . . . . . . . . . . . 384--386
                 Victor J. Katz   \em Force and Geometry in Newton's
                                  Principia, by François De Gandt,
                                  translated by Curtis Wilson  . . . . . . 386--392
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 393--397

American Mathematical Monthly
Volume 105, Number 5, May, 1998

                     James Case   The Modeling and Analysis of Financial
                                  Time Series  . . . . . . . . . . . . . . 401--411
         Franklin Lowenthal and   
             Arnold Langsen and   
                Clark T. Benson   Merton's Partial Differential Equation
                                  and Fixed Point Theory . . . . . . . . . 412--420
                Wilbur R. Knorr   ``Rational Diameters'' and the Discovery
                                  of Incommensurability  . . . . . . . . . 421--429
            Michel Balinski and   
               Guillaume Ratier   Graphs and Marriages . . . . . . . . . . 430--445
          Laurent Habsieger and   
             Maxim Kazarian and   
                   Sergei Lando   On the Second Number of Plutarch . . . . 446--446
             Bruce Anderson and   
            Jeffrey Jackson and   
                 Meera Sitharam   Descartes' Rule of Signs Revisited . . . 447--451
                  Ralph Faudree   A Conjecture of Erd\Hos  . . . . . . . . 451--453
                   R. D. Driver   Toricelli's Law --- An Ideal Example of
                                  an Elementary ODE  . . . . . . . . . . . 453--455
           Zdzis\law Pogoda and   
          Leszek M. Soko\lowski   Does Mathematics Distinguish Certain
                                  Dimensions of Spaces? Part II  . . . . . 456--463
                      Anonymous   Problems and Solutions . . . . . . . . . 464--476
            Daniel Schwalbe and   
                  Hal R. Varian   Computational Economics and Finance:
                                  Modeling and Analysis with Mathematica   477--481
               Peter Hilton and   
                   T. W. Korner   The Pleasures of Counting  . . . . . . . 481--485
            Leonard Gillman and   
            Richard Courant and   
            Herbert Robbins and   
                    Ian Stewart   What is Mathematics? . . . . . . . . . . 485--488
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 489--493
                  Roger A. Horn   Editor's Endnotes  . . . . . . . . . . . 494--494

American Mathematical Monthly
Volume 105, Number 6, June / July, 1998

                 Guershon Harel   Two Dual Assertions: The First on
                                  Learning and the Second on Teaching (Or
                                  Vice Versa)  . . . . . . . . . . . . . . 497
              Alan Gluchoff and   
             Frederick Hartmann   Univalent polynomials and non-negative
                                  trigonometric sums . . . . . . . . . . . 508--522
               Peter M. Neumann   Reflections on reflection in a spherical
                                  mirror . . . . . . . . . . . . . . . . . 523--528
         Richard Blecksmith and   
           Michael McCallum and   
                J. L. Selfridge   $3$-smooth representations of integers   529--543
                 C. W. Groetsch   Aristotle's fall . . . . . . . . . . . . 544--547
                B. Banaschewski   On proving the existence of complete
                                  ordered fields . . . . . . . . . . . . . 548--551
              Charles Kicey and   
                    Sudhir Goel   A Series for $ \ln k $ . . . . . . . . . 552--554
                    Gerd Herzog   $ C^1 $-solutions of $ x = f(x') $ are
                                  convex or concave  . . . . . . . . . . . 554--555
         Douglas E. Lampert and   
                Peter J. Slater   Parallel knockouts in the complete graph 556--558
                Frank A. Farris   \em Visual Complex Analysis, by Tristan
                                  Needham  . . . . . . . . . . . . . . . . 570
                  Robert Messer   \em Linear Algebra Problem Book, by Paul
                                  R. Halmos  . . . . . . . . . . . . . . . 577
               David Singmaster   \em After Math. Puzzles and
                                  Brainteasers, by Ed Barbeau; \em The
                                  Chicken from Minsk, by Yuri B. Chernyak
                                  and Robert M. Rose; \em New Mathematical
                                  Diversions, revised edition, by Martin
                                  Gardner  . . . . . . . . . . . . . . . . 579

American Mathematical Monthly
Volume 105, Number 7, August / September, 1998

            Robert A. Bosch and   
                 Jason A. Smith   Separating hyperplanes and the
                                  authorship of the disputed Federalist
                                  papers . . . . . . . . . . . . . . . . . 601--608
                    Marc Frantz   Two functions whose powers make fractals 609--617
                    M. H. Eggar   Pinhole cameras, perspective, and
                                  projective geometry  . . . . . . . . . . 618--630
                  Kosta Do\vsen   Functions redefined  . . . . . . . . . . 631--635
            Vilmos Komornik and   
                   Paola Loreti   Unique developments in non-integer bases 636--639
                  R. W. Hamming   Mathematics on a distant planet  . . . . 640--650
                      T. Y. Lam   A theorem of Burnside on matrix rings    651--653
              Peter Dierolf and   
                 Volker Schmidt   A proof of the change of variable
                                  formula for $d$-dimensional integrals    654--656
                   Hong Bing Yu   On the Diophantine Equation $ (x + 1)^y
                                  - x^z = 1 $  . . . . . . . . . . . . . . 656--657
                  Ira M. Gessel   Wolstenholme revisited . . . . . . . . . 657--658
                 F. A. Medvedev   Nonstandard analysis and the history of
                                  classical analysis . . . . . . . . . . . 659--664
               Steven G. Krantz   \em Introduction to Calculus and
                                  Classical Analysis, by Omar Hijab; \em
                                  Introduction to Mathematical Structures
                                  and Proofs, by Larry J. Gerstein . . . . 677
              Joby Milo Anthony   \em Mathematical Reflections: In a Room
                                  with Many Mirrors, by Peter Hilton,
                                  Derek Holton, and Jean Pedersen  . . . . 682
              Robert L. Devaney   \em Interactive Differential Equations,
                                  by Beverly West, Steven Strogatz, Jean
                                  Marie McDill, and John Cantwell;
                                  software designer Hubert Hohn  . . . . . 687

American Mathematical Monthly
Volume 105, Number 8, October, 1998

             Tadashi F. Tokieda   Mechanical Ideas in Geometry . . . . . . 697--703
                   R. Cheng and   
                A. Dasgupta and   
               B. R. Ebanks and   
                L. F. Kinch and   
               L. M. Larson and   
                 R. B. McFadden   When Does $ f - 1 = 1 / f $ ?  . . . . . 704--717
                 Roger L. Kraft   A Golden Cantor Set  . . . . . . . . . . 718--725
                Darrell Desbrow   On evaluating $ \int^{+ \infty }_{-
                                  \infty }e^{ax(x - 2b)}d x $ by contour
                                  integration round a parallelogram  . . . 726--731
              C. Groß and   
                 T.-K. Strempel   On Generalizations of Conics and on a
                                  Generalization of the Fermat--Torricelli
                                  Problem  . . . . . . . . . . . . . . . . 732--743
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Fifty-Eighth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 744
              T. W. Körner   Butterfly Hunting and the Symmetry of
                                  Mixed Partial Derivatives  . . . . . . . 756--758
         Stephen M. Gagola, Jr.   A Note on the Non-existence of Regular
                                  Bases for Finite Groups  . . . . . . . . 759--761
             Joseph Amal Nathan   The Irrationality of $ e^x $ for Nonzero
                                  Rational $x$ . . . . . . . . . . . . . . 762--763
                  Giles Warrack   A Note on Variable Replacement Rates in
                                  Urn Models . . . . . . . . . . . . . . . 764--765
             Richard K. Guy and   
              John L. Selfridge   Factoring Factorial $n$  . . . . . . . . 766
              Gerald B. Folland   \em Handbook of Writing for the
                                  Mathematical Sciences, by Nicholas J.
                                  Higham; \em A Primer of Mathematical
                                  Writing, by Steven G. Krantz . . . . . . 779
                 Robert V. Hogg   \em Leading Personalities in Statistical
                                  Sciences, edited by Norman L. Johnson
                                  and Samuel Kotz  . . . . . . . . . . . . 782

American Mathematical Monthly
Volume 105, Number 9, November, 1998

             Alfred B. Manaster   Some Characteristics of Eighth Grade
                                  Mathematics Classes in the TIMSS
                                  Videotape Study  . . . . . . . . . . . . 793
                   Lily Yau and   
                 Adi Ben-Israel   The Newton and Halley Methods for
                                  Complex Roots  . . . . . . . . . . . . . 806--818
           Kiran S. Kedlaya and   
                  Lenhard L. Ng   The Rook on the Half-Chessboard, or How
                                  Not to Diagonalize a Matrix  . . . . . . 819--824
                   Jack Cassidy   The Last Round of Betting in Poker . . . 825--831
                 Yoav Benyamini   Applications of the Universal
                                  Surjectivity of the Cantor Set . . . . . 832--839
                Apostolos Thoma   The Group $ {Z}_2 \times {Z}_n $ and
                                  Regular Polygonal Paths  . . . . . . . . 840--841
              Busiso P. Chisala   A Quick Cayley--Hamilton . . . . . . . . 842--844
                J. Marshall Ash   The Probability of a Tie in an $n$-Game
                                  Match  . . . . . . . . . . . . . . . . . 844--846
              J. M. Borwein and   
                    Xianfu Wang   The Converse of the Mean Value Theorem
                                  May Fail Generically . . . . . . . . . . 847--848
                  John A. Ewell   A Trio of Triangular Number Theorems . . 848--849
                 John Stillwell   Exceptional Objects  . . . . . . . . . . 850--858
                   Dan Schnabel   \em Goodbye, Descartes, by Keith Devlin  870
             Jeffrey Nunemacher   \em Fourier Analysis and Boundary Value
                                  Problems, by Enrique A. González-Velasco  874
               William F. Lucas   \em Fair Division: From Cake-Cutting to
                                  Dispute Resolution, by Steven J. Brams
                                  and Alan D. Taylor . . . . . . . . . . . 877

American Mathematical Monthly
Volume 105, Number 10, December, 1998

           Ilse C. F. Ipsen and   
                  Carl D. Meyer   The Idea Behind Krylov Methods . . . . . 889--899
               Kiran S. Kedlaya   Product-Free Subsets of Groups . . . . . 900--906
                Bernd Sturmfels   Polynomial Equations and Convex
                                  Polytopes  . . . . . . . . . . . . . . . 907--922
            Aviezri S. Fraenkel   Multivision: An Intractable Impartial
                                  Game With a Linear Winning Strategy  . . 923--928
              Brian J. McCartin   Seven Deadly Sins of Numerical
                                  Computation  . . . . . . . . . . . . . . 929--941
                     S. C. Woon   Generating Integrals and an Elementary
                                  Proof of the Finite Harmonic Series
                                  Theorem by Fractional Calculus . . . . . 942--945
           Raymond M. Redheffer   Monotonicity of the Maxima . . . . . . . 945--948
                Vilmos Komornik   A Simple Proof of Farkas' Lemma  . . . . 949--950
                 Richard K. Guy   Nothing's New in Number Theory?  . . . . 951--954
                    Lenore Blum   \em Julia, A Life in Mathematics, by
                                  Constance Reid . . . . . . . . . . . . . 964
                 Daniel P. Maki   \em Would-be Worlds, by John L. Casti    972
                   Reuben Hersh   \em The Number Sense: How the Mind
                                  Creates Mathematics, by Stanislas
                                  Dehaene  . . . . . . . . . . . . . . . . 975


American Mathematical Monthly
Volume 106, Number 1, 1999

                  P. J. McKenna   Large torsional oscillations in
                                  suspension bridges revisited: fixing an
                                  old approximation  . . . . . . . . . . . 1--18
            Geoffrey R. Goodson   Inverse conjugacies and reversing
                                  symmetry groups  . . . . . . . . . . . . 19--26
               Dmitry Fuchs and   
              Serge Tabachnikov   More on paperfolding . . . . . . . . . . 27--35
                    L. R. Bragg   Trigonometric integrals and Hadamard
                                  products . . . . . . . . . . . . . . . . 36--42
         Richard Blecksmith and   
               Paul Erd\Hos and   
                J. L. Selfridge   Cluster primes . . . . . . . . . . . . . 43--48
                John A. Zuehlke   Fermat's last theorem for Gaussian
                                  integer exponents  . . . . . . . . . . . 49--49
                 M. J. Jamieson   On rational function approximations to
                                  square roots . . . . . . . . . . . . . . 50--52
      A. J. van der Poorten and   
                    P. G. Walsh   A note on Jacobi symbols and continued
                                  fractions  . . . . . . . . . . . . . . . 52--56
           I. G. Bashmakova and   
                 G. S. Smirnova   The birth of literal algebra. Translated
                                  from the Russian and edited by Abe
                                  Shenitzer  . . . . . . . . . . . . . . . 57--66

American Mathematical Monthly
Volume 106, Number 2, 1999

                Kenneth A. Ross   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for Distinguished Service to
                                  Leonard Gillman  . . . . . . . . . . . . 97--98
               Solomon Feferman   Does mathematics need new axioms . . . . 99--111
              Gerald S. Goodman   Statistical independence and normal
                                  numbers: an aftermath to Mark Kac's
                                  Carus Monograph  . . . . . . . . . . . . 112--126
               Lyle N. Long and   
                   Howard Weiss   The velocity dependence of aerodynamic
                                  drag: a primer for mathematicians  . . . 127--135
                  D. M. Cannell   George Green: an enigmatic mathematician 136--151
         Arthur T. Benjamin and   
                     Kan Yasuda   Magic ``squares'' indeed . . . . . . . . 152--156
   Zoltán Sasvári   An elementary proof of Binet's formula
                                  for the gamma function . . . . . . . . . 156--158
                Richard G. Swan   A simple proof of Rankin's
                                  campanological theorem . . . . . . . . . 159--161

American Mathematical Monthly
Volume 106, Number 3, 1999

                  Junpei Sekino   $n$-ellipses and the minimum distance
                                  sum problem  . . . . . . . . . . . . . . 193--202
           Arcadii Z. Grinshpan   The Bieberbach conjecture and Milin's
                                  functionals  . . . . . . . . . . . . . . 203--214
       Dimitris A. Sardelis and   
           Theodoros M. Valahas   Decision making: a golden rule . . . . . 215--226
                   Vilmos Totik   A tale of two integrals  . . . . . . . . 227--240
       Jaume Paradís and   
      Pelegrí Viader and   
          Lluís Bibiloni   A mathematical excursion: from the
                                  three-door problem to a Cantor-type set  241--251

American Mathematical Monthly
Volume 106, Number 4, 1999

              Robert L. Devaney   The Mandelbrot set, the Farey tree, and
                                  the Fibonacci sequence . . . . . . . . . 289--302
                   Fred Richman   Existence proofs . . . . . . . . . . . . 303--308
                   Paul Corazza   Introduction to metric-preserving
                                  functions  . . . . . . . . . . . . . . . 309--323
           Bernard D. Flury and   
              Robert Irving and   
                    M. N. Goria   Magic dice . . . . . . . . . . . . . . . 324--337
           Andrew Granville and   
              Friedrich Roesler   The set of differences of a given set    338--344
                S. Anoulova and   
                 J. Bennies and   
                 J. Lenhard and   
                 D. Metzler and   
                    Y. Sung and   
                       A. Weber   Six ways of looking at Burtin's lemma    345--351
                Hiroshi Maehara   Lexell's Theorem via an Inscribed Angle
                                  Theorem  . . . . . . . . . . . . . . . . 352--353
             Khristo Boyadzhiev   A Characteristic Property of
                                  Differentiation  . . . . . . . . . . . . 353--355
               Kiran S. Kedlaya   A Weighted Mixed-Mean Inequality . . . . 355--358
                 Ian Caines and   
               Carrie Gates and   
             Richard K. Guy and   
          Richard J. Nowakowski   Periods in Taking and Splitting Games    359--361
                   Vasile Mihai   Problem 10725  . . . . . . . . . . . . . 362--362
                Donald E. Knuth   Problem 10726  . . . . . . . . . . . . . 362--362
                  Jean Anglesio   Problem 10727  . . . . . . . . . . . . . 362--362
                 Titu Andreescu   Problem 10728  . . . . . . . . . . . . . 362--362
           David P. Bellamy and   
                 Felix Lazebnik   Problem 10729  . . . . . . . . . . . . . 362--362
                 Walther Janous   Problem 10730  . . . . . . . . . . . . . 363--363
                  M. J. Pelling   Problem 10731  . . . . . . . . . . . . . 363--363
            Daniel Goffinet and   
           Kiran S. Kedlaya and   
          Kenneth Schilling and   
            Arlo W. Schurle and   
           Fredric D. Ancel and   
                Phil Bowers and   
                    John Bryant   Connected Sets of Periodic Functions:
                                  10434  . . . . . . . . . . . . . . . . . 363--364
             Marius Cavachi and   
            Sam Northshield and   
         Simeon T. Stefanov and   
                    Victor Klee   The Plane Covered by Disks: 10440  . . . 364--365
          Joaquin Gomez Rey and   
               Jose Heber Nieto   Random Perfect Matchings: 10587  . . . . 365--365
                   Marcin Mazur   Characterizations of the Medial
                                  Triangle: 10588  . . . . . . . . . . . . 365--366
               Paul Bateman and   
              David Bradley and   
               David Callan and   
                  Richard Stong   Binary Expansions and $k$ th Powers:
                                  10596  . . . . . . . . . . . . . . . . . 366--367
          Joseph Rosenblatt and   
             Thomas Hermann and   
            John H. Lindsey, II   A Supremum of Sine Differences: 10604    368--368
           Jovan Vukmirovic and   
              Kenneth Schilling   A Convergent Series: 10657 . . . . . . . 368--368
                   Tony Rothman   Book Review: \booktitleThe French
                                  Mathematician, by Tom Petsinis . . . . . 369--373
                    Bonnie Gold   Book Review: \booktitleSocial
                                  Constructivism as a Philosophy of
                                  Mathematics, by Paul Ernest; What is
                                  Mathematics, Really? by Reuben Hersh . . 373--380
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 381--384
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 106, Number 5, May, 1999

          George K. Francis and   
               Jeffrey R. Weeks   Conway's ZIP Proof . . . . . . . . . . . 393--399
                 Roger L. Kraft   Chaos, Cantor Sets, and Hyperbolicity
                                  for the Logistic Maps  . . . . . . . . . 400--408
                 Tom M. Apostol   An Elementary View of Euler's Summation
                                  Formula  . . . . . . . . . . . . . . . . 409--418
              David B. Leep and   
                  Gerry Myerson   Marriage, Magic, and Solitaire . . . . . 419--429
               Hugh Howards and   
          Michael Hutchings and   
                   Frank Morgan   The Isoperimetric Problem on Surfaces    430--439
                 Timothy . Chow   What is a Closed-Form Number?  . . . . . 440--448
                    Greg Martin   The Smallest Solution of $ \phi (30 n +
                                  1) $ Is \ldots . . . . . . . . . . . . . 449--451
                Frank K. Kenter   A Matrix Representation for Euler's
                                  Constant, $ \gamma $ . . . . . . . . . . 452--454
                  H. Fejzic and   
                       D. Rinne   More on a Mean Value Theorem Converse    454--455
                    L. J. Lange   An Elegant Continued Fraction for $ \pi
                                  $  . . . . . . . . . . . . . . . . . . . 456--458
                  Matthias Beck   The Reciprocity Law for Dedekind Sums
                                  via the Constant Ehrhart Coefficient . . 459--462
                Detlef Laugwitz   Riemann's Dissertation and Its Effect on
                                  the Evolution of Mathematics . . . . . . 463--469
                M. N. Deshpande   Problems: 10732  . . . . . . . . . . . . 470--470
                   Sung Soo Kim   Problems: 10733  . . . . . . . . . . . . 470--470
               Floor van Lamoen   Problems: 10734  . . . . . . . . . . . . 470--470
            Gustavus J. Simmons   Problems: 10735  . . . . . . . . . . . . 470--470
                  Mizan R. Khan   Problems: 10736  . . . . . . . . . . . . 470--470
            Hassan Ali Shah Ali   Problems: 10737  . . . . . . . . . . . . 471--471
               Radu Theodorescu   Problems: 10738  . . . . . . . . . . . . 471--471
             Fu-Chuen Chang and   
             Paul Deiermann and   
          Walter Van Assche and   
         Franz Peherstorfer and   
                Johannes Kepler   Moments of Roots of Chebyshev
                                  Polynomials: 10448 . . . . . . . . . . . 471--472
                 Tim Keller and   
     Gchq Problem Solving Group   Indecomposable Numbers: 10589  . . . . . 473--473
            Donald E. Knuth and   
     Gchq Problem Solving Group   Negatively Correlated Vectors of Signs:
                                  10593  . . . . . . . . . . . . . . . . . 473--474
                  David Cox and   
     Gchq Problem Solving Group   $n$-Tuples Whose Elements Divide Their
                                  Sum: 10597 . . . . . . . . . . . . . . . 474--475
                Olaf Krafft and   
            Martin Schaefer and   
              Nora Thornber and   
The National Security Agency Problems Group and   
                    Ulrich Abel   Binomial Ratios: 10625 . . . . . . . . . 475--476
              Mihaly Bencze and   
            Gchq Problems Group   A Triangle Inequality: 10644 . . . . . . 476--476
                   N. P. Bhatia   Limit of a Recurrence: 10648 . . . . . . 476--477
           Colin L. Mallows and   
              Kenneth Schilling   Random Polynomials with Real Roots:
                                  10660  . . . . . . . . . . . . . . . . . 477--477
                   Dan Schnabel   Book Review: \booktitleLife's Other
                                  Secret, by Ian Stewart; \booktitleThe
                                  Magical Maze, by Ian Stewart . . . . . . 478--481
               Cynthia Woodburn   Book Review: \booktitleAn Introductory
                                  Course in Commutative Algebra. by A. W.
                                  Chatters, C. R. Hajarnavis;
                                  \booktitleIntroduction to Algebra, by
                                  Peter J. Cameron . . . . . . . . . . . . 481--483
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 484--487
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 106, Number 6, June / July, 1999

                   Peter D. Lax   Change of Variables in Multiple
                                  Integrals  . . . . . . . . . . . . . . . 497--501
           Louis J. Billera and   
           Kenneth S. Brown and   
                 Persi Diaconis   Random Walks and Plane Arrangements in
                                  Three Dimensions . . . . . . . . . . . . 502--524
                  Mizan R. Khan   A Counting Formula for Primitive
                                  Tetrahedra in $ Z^3 $  . . . . . . . . . 525--533
                    Adrian Rice   What Makes a Great Mathematics Teacher?
                                  The Case of Augustus De Morgan . . . . . 534--552
                Frank Gerth Iii   The TEAM Approach to Investing . . . . . 553--558
         William J. Schwind and   
                     Jun Ji and   
           Daniel E. Koditschek   A Physically Motivated Further Note on
                                  the Mean Value Theorem for Integrals . . 559--564
                James P. Butler   Hopping Hoops Don't Hop  . . . . . . . . 565--568
                    Peter Mathe   Approximation of Holder Continuous
                                  Functions by Bernstein Polynomials . . . 568--574
               Miguel de Guzman   An Extension of the Wallace--Simson
                                  Theorem: Projecting in Arbitrary
                                  Directions . . . . . . . . . . . . . . . 574--580
          Michael D. Hirschhorn   Another Short Proof of Ramanujan's $
                                  \bmod 5 $ Partition Congruence, and More 580--583
              Hunter S. Snevily   The Cayley Addition Table of $ Z_n $ . . 584--585
                  Oscar Ciaurri   Problems: 10739  . . . . . . . . . . . . 586--586
          Charles Vanden Eynden   Problems: 10740  . . . . . . . . . . . . 586--586
                     Tim Keller   Problems: 10741  . . . . . . . . . . . . 586--586
                     Emre Alkan   Problems: 10742  . . . . . . . . . . . . 586--586
                C\ualin Popescu   Problems: 10743  . . . . . . . . . . . . 586--586
                Peter Lindqvist   Problems: 10744  . . . . . . . . . . . . 587--587
                  M. J. Pelling   Problems: 10745  . . . . . . . . . . . . 587--587
               Jordan Tabov and   
              Murray S. Klamkin   Using the Walls to Find the Center:
                                  10386  . . . . . . . . . . . . . . . . . 587--587
             Seung-Jin Bang and   
           Jeremy E. Dawson and   
             A. N. 't Woord and   
              O. P. Lossers and   
               Victor Hernandez   A Reciprocal Summation Identity: 10490   588--590
              Yury J. Ionin and   
                 Robin R. Lewis   A Limit of Periods: 10603  . . . . . . . 590--590
           Thomas Zaslavsky and   
         Stephen M. Gagola, Jr.   Avoiding the Identity: 10606 . . . . . . 590--591
              Brian Conolly and   
              Allen Stenger and   
                 Thomas Hermann   Some Sums Require Care: 10638  . . . . . 591--592
                   Ricardo Diaz   Book Review: \booktitleAn Imaginary
                                  Tale: The Story of $ \sqrt {-1} $, by
                                  Paul J. Nahin  . . . . . . . . . . . . . 593--594
                John Beebee and   
                 Karen Willmore   Book Review: \booktitleLeaning towards
                                  Infinity, by Sue Woolfe  . . . . . . . . 594--596
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 597--600
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 106, Number 7, August / September, 1999

              Timothy Pritchett   The Hopping Hoop Revisited . . . . . . . 609--617
         Della Dumbaugh Fenster   Why Dickson Left Quadratic Reciprocity
                                  out of His History of the Theory of
                                  Numbers  . . . . . . . . . . . . . . . . 618--627
               Mark Bridger and   
            Gabriel Stolzenberg   Uniform Calculus and the Law of Bounded
                                  Change . . . . . . . . . . . . . . . . . 628--635
                    Gary Gordon   The Answer is $ 2^n. n! $ What's the
                                  Question?  . . . . . . . . . . . . . . . 636--645
              William F. Trench   Conditional Convergence of Infinite
                                  Products . . . . . . . . . . . . . . . . 646--651
               F. W. Clarke and   
              W. N. Everitt and   
           L. L. Littlejohn and   
               S. J. R. Vorster   H. J. S. Smith and the Fermat Two
                                  Squares Theorem  . . . . . . . . . . . . 652--665
            Melvyn B. Nathanson   Number Theory and Semigroups of
                                  Intermediate Growth  . . . . . . . . . . 666--669
             Randall McCutcheon   The Gottschalk--Hedlund Theorem  . . . . 670--672
             Tadashi F. Tokieda   A Mean Value Theorem . . . . . . . . . . 673--674
                        B. Sury   On an Example of Jacobson  . . . . . . . 675--676
                 Israel Kleiner   Field Theory: From Equations to
                                  Axiomatization . . . . . . . . . . . . . 677--684
                C\ualin Popescu   Problems: 10743  . . . . . . . . . . . . 685--685
                 Stepan Tersian   Problems: 10746  . . . . . . . . . . . . 685--685
             Athanasios Kalakos   Problems: 10747  . . . . . . . . . . . . 685--685
              Itshak Borosh and   
         Douglas A. Hensley and   
                      Joel Zinn   Problems: 10748  . . . . . . . . . . . . 685--685
                   Alain Grigis   Problems: 10749  . . . . . . . . . . . . 685--685
                 Leonard Smiley   Problems: 10750  . . . . . . . . . . . . 686--686
                 Emeric Deutsch   Problems: 10751  . . . . . . . . . . . . 686--686
                  Gh. Costovici   Problems: 10752  . . . . . . . . . . . . 686--686
        Joseph H. Silverman and   
              David Bradley and   
              Donald A. Darling   A Zeta Function over a Recurrent
                                  Sequence: 10486  . . . . . . . . . . . . 686--688
                Fred Galvin and   
                Frank Jelen and   
               Eberhard Triesch   A Matrix of Inequalities: 10599  . . . . 688--688
                 Wen-Xiu Ma and   
           Robin J. Chapman and   
             Joseph J. Rushanan   A Complex Determinant: 10601 . . . . . . 688--689
            Donald E. Knuth and   
                   David Callan   On a Convolution of Eulerian Numbers:
                                  10609  . . . . . . . . . . . . . . . . . 690--691
               Richard Hall and   
National Security Agency Problems Group and   
            Gchq Problems Group   A Variation on Additive Bases: 10610 . . 691--692
          Joaquin Gomez Rey and   
Anchorage Math Solutions Group and   
            Gchq Problems Group   An Identity Involving Rooted Trees:
                                  10615  . . . . . . . . . . . . . . . . . 692--693
          James G. Merickel and   
              John P. Robertson   Divisors of Sums of Divisors: 10617  . . 693--693
               Albert A. Mullin   Book Review: \booktitleMy Brain is Open:
                                  The Mathematical Journeys of Paul
                                  Erd\Hos, by Bruce Schechter;
                                  \booktitleThe Man Who Loved Only
                                  Numbers: The Story of Paul Erd\Hos and
                                  the Search for Mathematical Truth, by
                                  Paul Hoffman . . . . . . . . . . . . . . 694--696
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 697--700
                      Anonymous   Lester R. Ford Awards for 1998 . . . . . 701--702
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 106, Number 8, October, 1999

             William J. Terrell   Some Fundamental Control Theory I:
                                  Controllability, Observability, and
                                  Duality  . . . . . . . . . . . . . . . . 705--719
                 Bruce Pourciau   The Education of a Pure Mathematician    720--732
             Daniel J. Velleman   Multivariable Calculus and the Plus
                                  Topology . . . . . . . . . . . . . . . . 733--740
                John H. Hubbard   The Forced Damped Pendulum: Chaos,
                                  Complication and Control . . . . . . . . 741--758
               Abraham A. Ungar   The Hyperbolic Pythagorean Theorem in
                                  the Poincaré Disc Model of Hyperbolic
                                  Geometry . . . . . . . . . . . . . . . . 759--763
                       Jitan Lu   Is the Composite Function Integrable?    763--766
                  Jianhong Shen   On the Generalized ''Lanczos'
                                  Generalized Derivative'' . . . . . . . . 766--768
                   Walter Rudin   A Stability Theorem  . . . . . . . . . . 768--770
               Roger C. Alperin   Rationals and the Modular Group  . . . . 771--773
                Thomas J. Osler   The Union of Vieta's and Wallis's
                                  Products for Pi  . . . . . . . . . . . . 774--776
                  Louis Shapiro   Problems: 10753  . . . . . . . . . . . . 777--777
                   Paul Bracken   Problems: 10754  . . . . . . . . . . . . 777--777
                    Jiro Fukuta   Problems: 10755  . . . . . . . . . . . . 777--777
               Douglas Iannucci   Problems: 10756  . . . . . . . . . . . . 778--778
                   Mark Kidwell   Problems: 10757  . . . . . . . . . . . . 778--778
                     Mark Sapir   Problems: 10758  . . . . . . . . . . . . 778--778
                C\ualin Popescu   Problems: 10759  . . . . . . . . . . . . 778--778
           Kiran S. Kedlaya and   
                  Alain Tissier   Common Eigenvector of Commuting
                                  Matrices: 10633  . . . . . . . . . . . . 778--779
                C. F. Parry and   
                Robert L. Young   Reflected Concurrent Lines: 10637  . . . 779--780
        Hassan Ali Shah Ali and   
              Patrick A. Staley   A Constrained Maximization: 10646  . . . 780--781
             Zoltan Sasvari and   
              William F. Trench   A Pólya--Szegö Exercise Revisited: 10650   781--782
               W. K. Hayman and   
        Tewodros Amdeberhan and   
                  Irl C. Bivens   Harmonic Products of Harmonic Functions:
                                  10651  . . . . . . . . . . . . . . . . . 782--782
           David P. Bellamy and   
             Felix Lazebnik and   
           Jeffrey Lagarias and   
         Stephen M. Gagola, Jr.   Large Values of Tangent: 10656 . . . . . 782--784
            Vasile A. Mihai and   
                      J. Schaer   The Ellipse in a Paper Cup: 10664  . . . 784--784
                   John A. Koch   Book Review: \booktitleThe Four-Color
                                  Theorem. by Rudolf Fritsch, Gerda
                                  Fritsch, J. Peschke  . . . . . . . . . . 785--787
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 788--791
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 106, Number 9, November, 1999

                Aaron F. Archer   A Modern Treatment of the 15 Puzzle  . . 793--799
            James F. Hurley and   
                  Uwe Koehn and   
                Susan L. Ganter   Effects of Calculus Reform: Local and
                                  National . . . . . . . . . . . . . . . . 800--811
             William J. Terrell   Some Fundamental Control Theory II:
                                  Feedback Linearization of Single Input
                                  Nonlinear Systems  . . . . . . . . . . . 812--828
                  John A. Baker   The Dirichlet Problem for Ellipsoids . . 829--834
                David A. Singer   Curves Whose Curvature Depends on
                                  Distance from the Origin . . . . . . . . 835--841
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Fifty-Ninth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 842--849
              Carsten Thomassen   On the Nelson Unit Distance Coloring
                                  Problem  . . . . . . . . . . . . . . . . 850--853
              David J. Grabiner   Descartes' Rule of Signs: Another
                                  Construction . . . . . . . . . . . . . . 854--856
          Jonathan P. McCammond   Integrating Polynomials in Secant and
                                  Tangent  . . . . . . . . . . . . . . . . 856--858
                 Israel Kleiner   Field Theory: From Equations to
                                  Axiomatization . . . . . . . . . . . . . 859--863
                  Bruce Reznick   Problems: 10760  . . . . . . . . . . . . 864--864
                    Fred Galvin   Problems: 10761  . . . . . . . . . . . . 864--864
                     Leroy Quet   Problems: 10762  . . . . . . . . . . . . 864--864
                  Jean Anglesio   Problems: 10763  . . . . . . . . . . . . 864--864
                  Ray Redheffer   Problems: 10764  . . . . . . . . . . . . 864--864
               Peter J. Ferraro   Problems: 10765  . . . . . . . . . . . . 864--864
                 Szilard Andras   Problems: 10766  . . . . . . . . . . . . 865--865
        S. Lakshminarayanan and   
                 S. L. Shah and   
              K. Nandakumar and   
            Gchq Problems Group   Cramer's Rule for Non-Square Matrices:
                                  10618  . . . . . . . . . . . . . . . . . 865--865
                    James Propp   An Identity for Strongly Connected
                                  Digraphs: 10620  . . . . . . . . . . . . 865--867
            M. N. Deshpande and   
           Hansruedi Widmer and   
                 Zachary Franco   Simultaneous Squares from Arithmetic
                                  Progressions: 10622  . . . . . . . . . . 867--868
                Roy Barbara and   
              Nasha Komanda and   
               Robin J. Chapman   The Divisibility Poset inside Itself:
                                  10623  . . . . . . . . . . . . . . . . . 868--869
               Florian Luca and   
                  Nasha Komanda   An Equation Involving the Totient: 10626 869--870
                Jiro Fukuta and   
        Gchq Problems Group and   
                C\ualin Popescu   Three Congruent Circles between Two
                                  Triangles: 10659 . . . . . . . . . . . . 870--870
          Harold G. Diamond and   
             Nathaniel Grossman   Logarithmic Convexity of Stirling's
                                  Ratio: 10680 . . . . . . . . . . . . . . 871--871
     Joseph D. E. Konhauser and   
                 Stan Wagon and   
       Con Amore Problems Group   Quadrilateral Center of Gravity: 10662   871--871
                 James V. Rauff   Book Review: \booktitleAfrican Fractals:
                                  Modern Computing and Indigenous Design.
                                  by Ron Eglash  . . . . . . . . . . . . . 872--875
                 Arnold Ostebee   Telegraphic Reviews  . . . . . . . . . . 876--879
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 106, Number 10, December, 1999

        Jonathan M. Borwein and   
              Robert M. Corless   Emerging Tools for Experimental
                                  Mathematics  . . . . . . . . . . . . . . 889--909
               Thomas W. Tucker   Reform, Tradition, and Synthesis . . . . 910--914
               Steven G. Krantz   You Don't Need a Weatherman to Know
                                  Which Way the Wind Blows . . . . . . . . 915--918
                 Helene Shapiro   The Weyr Characteristic  . . . . . . . . 919--929
              Francis Edward Su   Rental Harmony: Sperner's Lemma in Fair
                                  Division . . . . . . . . . . . . . . . . 930--942
                Leonid G. Hanin   Which Tanks Empty Faster?  . . . . . . . 943--947
                   David Callan   Two Uniformly Distributed Parameters
                                  Defining Catalan Numbers . . . . . . . . 948--949
              Istvan Kovacs and   
           Daniel S. Silver and   
              Susan G. Williams   Determinants of Commuting-Block Matrices 950--952
                        Paul iu   Mixtilinear Incircles  . . . . . . . . . 952--955
                 David N. Etter   The Area of the Medial Parallelogram of
                                  a Tetrahedron  . . . . . . . . . . . . . 956--958
             Richard Nowakowski   Unsolved Problems, 1969--1999  . . . . . 959--962
              Bruce Dearden and   
                  Jerry Metzger   Problems: 10767  . . . . . . . . . . . . 963--963
                   Sung Soo Kim   Problems: 10768  . . . . . . . . . . . . 963--963
              Christian Blatter   Problems: 10769  . . . . . . . . . . . . 963--963
                C\ualin Popescu   Problems: 10770  . . . . . . . . . . . . 963--963
             Mowaffaq Hajja and   
                   Peter Walker   Problems: 10771  . . . . . . . . . . . . 963--963
          William C. Waterhouse   Problems: 10772  . . . . . . . . . . . . 963--963
                  Jean Anglesio   Problems: 10773  . . . . . . . . . . . . 964--964
                 Greg Huber and   
            Gchq Problems Group   Tracking the Incenters: 10631  . . . . . 964--965
          William F. Trench and   
                Ronald A. Kopas   An Appearance of the Beta Function:
                                  10632  . . . . . . . . . . . . . . . . . 965--965
         Nicholas R. Farnum and   
                  Alain Tissier   Apery's Constant: 10635  . . . . . . . . 965--966
                Abram Kagan and   
                Larry Shepp and   
              Kenneth Schilling   Essentially Discontinuous Functions:
                                  10668  . . . . . . . . . . . . . . . . . 966--967
          Salomon Benchimol and   
              Elliott Cohen and   
       Con Amore Problems Group   Two Recurrence Relations, One Easy, One
                                  Hard: 10670  . . . . . . . . . . . . . . 967--968
                   F. Rothe and   
                   Sung Soo Kim   The Number of Zeros of a Maclaurin
                                  Polynomial: 10671  . . . . . . . . . . . 968--968
              V. Anil Kumar and   
            John H. Lindsey, II   An AM--GM Variation: 10672 . . . . . . . 969--969
             Harry Tamvakis and   
            Gchq Problems Group   Functions with a Polynomial Addition
                                  Formula: 10675 . . . . . . . . . . . . . 969--969
                Horst Alzer and   
                  M. J. Pelling   An Unsettled Inequality: 10337 . . . . . 970--970
           Edward Aboufadel and   
           Matthew Boelkins and   
               Steven Schlicker   Book Review: \booktitleWavelets: A
                                  Primer. by Christian Blatter, A. K.
                                  Peters; \booktitleWavelets in a Box, by
                                  Charles K. Chui, Andrew K. Chan, C.
                                  Steve Liu; \booktitleA Primer on
                                  Wavelets for Scientists and Engineers,
                                  by James S. Walker; \booktitleWavelet
                                  Analysis: The Scalable Structure of
                                  Information, by Howard L. Resnikoff,
                                  Raymond O. Wells, Jr.  . . . . . . . . . 971--977
          Daniel Henry Gottlieb   Book Review: \booktitlePoincaré and the
                                  Three Body Problem. by June Barrow-Green 977--980
                      Anonymous   Volume Information . . . . . . . . . . . 981--992
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Front Matter . . . . . . . . . . . . . . ??


Mathematics of Computation
Volume 66, Number 218, April, 1997

               David Bailey and   
              Peter Borwein and   
                  Simon Plouffe   On the rapid computation of various
                                  polylogarithmic constants  . . . . . . . 903--913