Table of contents for issues of American Mathematical Monthly

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Volume 61, Number ??, 1954
Volume 72, Number ??, 1965
Volume 85, Number 2, 1978
Volume 85, Number 9, 1978
Volume 87, Number 1, 1980
Volume 87, Number 2, 1980
Volume 87, Number 3, 1980
Volume 87, Number 4, 1980
Volume 87, Number 5, 1980
Volume 87, Number 6, 1980
Volume 87, Number 7, 1980
Volume 87, Number 8, 1980
Volume 87, Number 9, 1980
Volume 87, Number 10, 1980
Volume 88, Number 1, 1981
Volume 88, Number 2, 1981
Volume 88, Number 3, 1981
Volume 88, Number 4, April, 1981
Volume 88, Number 5, 1981
Volume 88, Number 6, 1981
Volume 88, Number 7, 1981
Volume 88, Number 8, 1981
Volume 88, Number 9, 1981
Volume 88, Number 10, 1981
Volume 89, Number 1, 1982
Volume 89, Number 2, 1982
Volume 89, Number 3, 1982
Volume 89, Number 4, 1982
Volume 89, Number 5, 1982
Volume 89, Number 6, 1982
Volume 89, Number 7, 1982
Volume 89, Number 8, 1982
Volume 89, Number 9, 1982
Volume 89, Number 10, 1982
Volume 90, Number ??, 1983
Volume 90, Number 1, 1983
Volume 90, Number 2, 1983
Volume 90, Number 3, 1983
Volume 90, Number 4, 1983
Volume 90, Number 5, 1983
Volume 90, Number 6, 1983
Volume 90, Number 7, 1983
Volume 90, Number 8, 1983
Volume 90, Number 9, 1983
Volume 90, Number 10, 1983
Volume 91, Number 1, 1984
Volume 91, Number 2, 1984
Volume 91, Number 3, 1984
Volume 91, Number 4, 1984
Volume 91, Number 5, 1984
Volume 91, Number 6, 1984
Volume 91, Number 7, 1984
Volume 91, Number 8, 1984
Volume 91, Number 9, 1984
Volume 91, Number 10, 1984
Volume 92, Number ??, 1985
Volume 92, Number 1, 1985
Volume 92, Number 2, 1985
Volume 92, Number 3, 1985
Volume 92, Number 4, 1985
Volume 92, Number 5, 1985
Volume 92, Number 6, 1985
Volume 92, Number 7, 1985
Volume 92, Number 8, 1985
Volume 92, Number 9, 1985
Volume 92, Number 10, 1985
Volume 93, Number 1, 1986
Volume 93, Number 2, 1986
Volume 93, Number 3, 1986
Volume 93, Number 4, 1986
Volume 93, Number 5, 1986
Volume 93, Number 6, 1986
Volume 93, Number 7, 1986
Volume 93, Number 8, 1986
Volume 93, Number 9, 1986
Volume 93, Number 10, 1986
Volume 93, Number ??, 1987
Volume 94, Number 1, 1987
Volume 94, Number 2, 1987
Volume 94, Number 3, 1987
Volume 94, Number 4, 1987
Volume 94, Number 5, 1987
Volume 94, Number 6, 1987
Volume 94, Number 7, 1987
Volume 94, Number 8, 1987
Volume 94, Number 9, 1987
Volume 94, Number 10, 1987
Volume 95, Number 1, 1988
Volume 95, Number 2, 1988
Volume 95, Number 3, 1988
Volume 95, Number 4, 1988
Volume 95, Number 5, 1988
Volume 95, Number 6, 1988
Volume 95, Number 7, 1988
Volume 95, Number 8, 1988
Volume 95, Number 9, 1988
Volume 95, Number 10, 1988
Volume 96, Number ??, 1989
Volume 96, Number 1, 1989
Volume 96, Number 2, February, 1989
Volume 96, Number 3, 1989
Volume 96, Number 4, 1989
Volume 96, Number 5, 1989
Volume 96, Number 6, 1989
Volume 96, Number 7, 1989
Volume 96, Number 8, 1989
Volume 96, Number 9, 1989
Volume 96, Number 10, 1989
Volume 97, Number ??, 1990
Volume 97, Number 3, March, 1990
Volume 97, Number 5, May, 1990
Volume 97, Number 7, August / September, 1990
Volume 100, Number 3, March, 1993
Volume 104, Number 9, November, 1997
Volume 7, Number 6, June, 1964
Volume 122, 1981
Volume 66, Number 218, April, 1997


American Mathematical Monthly
Volume 61, Number ??, 1954

                     K. Fan and   
                  G. G. Lorentz   An integral inequality . . . . . . . . . 626--631


American Mathematical Monthly
Volume 72, Number ??, 1965

                      Anonymous   Semitopological groups . . . . . . . . . 996--998


American Mathematical Monthly
Volume 85, Number 2, 1978

           A. E. Livingston and   
               M. L. Livingston   The congruence $a^{r+s}\equiv a^{r}
                                  \pmod {m}$ . . . . . . . . . . . . . . . 97--100

American Mathematical Monthly
Volume 85, Number 9, 1978

                   R. L. Wilder   Evolution of the topological concept of
                                  ``connected''  . . . . . . . . . . . . . 720--726
              Solomon W. Golomb   Cyclotomic polynomials and factorization
                                  theorems . . . . . . . . . . . . . . . . 734--737


American Mathematical Monthly
Volume 87, Number 1, 1980

                Malcolm Murrill   On a hyperanalytic geometry for complex
                                  functions  . . . . . . . . . . . . . . . 8--25
                   Yu Ting Shen   A ``natural'' enumeration of nonnegative
                                  rational numbers---an informal
                                  discussion . . . . . . . . . . . . . . . 25--29
                   R. L. Wilder   Correction and addendum to: ``Evolution
                                  of the topological concept of
                                  `connected'\thinspace '' [Amer. Math.
                                  Monthly \bf 85 (1978), no. 9, 720--726,
                                  MR 80f:01019a] . . . . . . . . . . . . . 31--32
             K. W. Thompson and   
                    T. Schonbek   A problem of the Pompeiu type  . . . . . 32--36
                  A. M. Russell   A commutative Banach algebra of
                                  functions of bounded variation . . . . . 39--40
                       D. Kirby   Concurrences for a triangle  . . . . . . 45--47
             Richard S. Millman   The upper half plane model for
                                  hyperbolic geometry  . . . . . . . . . . 48--53
                      Harry Dym   On the absolute convergence of a
                                  multiple integral of ${\rm sin}\,x/x$    53--54

American Mathematical Monthly
Volume 87, Number 2, 1980

                  R. W. Hamming   The unreasonable effectiveness of
                                  mathematics  . . . . . . . . . . . . . . 81--90
            Robert M. MacGregor   Generalizing the notion of a periodic
                                  sequence . . . . . . . . . . . . . . . . 90--102
              Duane W. DeTemple   A geometric method of phase plane
                                  analysis . . . . . . . . . . . . . . . . 102--112
                   Neal Koblitz   The $p$-adic approach to solutions of
                                  equations over finite fields . . . . . . 115--118
                 J. W. Nienhuys   Uniform continuity of derivatives in
                                  convex sets  . . . . . . . . . . . . . . 118--120
             V. L. N. Sarma and   
                   Nand Lal and   
                    V. K. Singh   An example of a locally finite family    121--122
               David P. Robbins   The probability that neighbors remain
                                  neighbors after random rearrangements    122--124
                  Edward Rozema   Estimating the error in the trapezoidal
                                  rule . . . . . . . . . . . . . . . . . . 124--128
              Gabriel Klambauer   Summation of series  . . . . . . . . . . 128--130

American Mathematical Monthly
Volume 87, Number 3, 1980

               Lawrence Zalcman   Offbeat integral geometry  . . . . . . . 161--175
              David D. Bleecker   Infinitesimal deformations of portions
                                  of the standard sphere in $E^{3}$  . . . 175--182
               Calvin H. Wilcox   Positive temperatures with prescribed
                                  initial heat distributions . . . . . . . 183--186
                Antonio Steiner   Plancherel's theorem and the Shannon
                                  series derived simultaneously  . . . . . 193--197
                    Dixon Jones   Quadrangles, butterflies, Pascal's
                                  hexagon, and projective fixed points . . 197--200
                Eric C. Nummela   Cayley's theorem for topological groups  202--203
                  I. Netuka and   
                    J. Vesel\'y   Regions of harmonicity . . . . . . . . . 203--205

American Mathematical Monthly
Volume 87, Number 4, 1980

                    George Miel   Calculator calculus and roundoff errors  243--252
                 R. E. Rice and   
               B. Schweizer and   
                       A. Sklar   When is $f(f(z))=az^{2}+bz+c$  . . . . . 252--263
           Michael A. B. Deakin   Euler's version of the Laplace transform 264--269
                Carlo H. Sequin   Twisted prismatic Klein bottles  . . . . 269--277
                    J. Cobb and   
                      W. Voxman   Dispersion points and fixed points . . . 278--281
                 G. H. Meisters   Principal vertices, exposed points, and
                                  ears . . . . . . . . . . . . . . . . . . 284--285
               Richard B. Darst   The connection between lim sup and
                                  uniform integrability  . . . . . . . . . 285--286
                     H. Groemer   On finite classes of convex sets that
                                  permit space coverings . . . . . . . . . 286--288
              L. C. Martins and   
              P. Podio-Guidugli   An elementary proof of the polar
                                  decomposition theorem  . . . . . . . . . 288--290
                 Khursheed Alam   Bounds on the negative exponential
                                  function . . . . . . . . . . . . . . . . 290--292
            James H. Foster and   
               Jean J. Pedersen   On the reflective property of ellipses   294--297
                William Watkins   Similarity of matrices . . . . . . . . . 300--300

American Mathematical Monthly
Volume 87, Number 5, 1980

              R. Creighton Buck   Sherlock Holmes in Babylon . . . . . . . 335--345
                  Richard Askey   Ramanujan's extensions of the gamma and
                                  beta functions . . . . . . . . . . . . . 346--359
               Stuart S. Antman   The equations for large vibrations of
                                  strings  . . . . . . . . . . . . . . . . 359--370
                  Lee Rubel and   
              Kenneth Stolarsky   Subseries of the power series for
                                  $e^{x}$  . . . . . . . . . . . . . . . . 371--376
               Albert Nijenhuis   Correction to: ``A minimal-path
                                  algorithm for the `money changing
                                  problem' ''  . . . . . . . . . . . . . . 377--377
                   Alan Dow and   
                  John Ginsburg   Integration on $[0,\,1]^{\omega }$ . . . 378--380
                D. R. Brown and   
                 M. J. O'Malley   On $n$th roots of positive operators . . 380--382
                    Wulf Rehder   On the volume of unions of translates of
                                  a convex set . . . . . . . . . . . . . . 382--384
              Péter Kiss   A method for solving Diophantine
                                  equations  . . . . . . . . . . . . . . . 384--387
              Ray Redheffer and   
                    Carey Smith   On a surprising inequality of Goldberg
                                  and Straus . . . . . . . . . . . . . . . 387--390
          Charles Vanden Eynden   Proofs that $\sum 1/p$ diverges  . . . . 394--397
                   Joel Spencer   Counting magic squares . . . . . . . . . 397--399
               Paul R. Chernoff   Pointwise convergence of Fourier series  399--400

American Mathematical Monthly
Volume 87, Number 6, 1980

                 B. H. Pourciau   Modern multiplier rules  . . . . . . . . 433--452
               Michael A. Penna   Total torsion  . . . . . . . . . . . . . 452--461
                   S. N. Maitra   A simple application of the theorem of
                                  composition of accelerations . . . . . . 466--468
                  M. S. Klamkin   Inequalities for inscribed and
                                  circumscribed polygons . . . . . . . . . 469--473
                Gebhard Greiter   Nonunique factorization in subsemigroups
                                  of semigroups with unique prime
                                  factorization  . . . . . . . . . . . . . 473--474
            U. V. Satyanarayana   A note on Riemann-Stieltjes integrals    477--478
               Henry J. Schultz   The sum of the $k$th powers of the first
                                  $n$ integers . . . . . . . . . . . . . . 478--481
             Donald W. Robinson   A proof of the Frobenius rank equality   481--482
                 Hubert Kennedy   The first written examinations at
                                  Harvard College  . . . . . . . . . . . . 483--486

American Mathematical Monthly
Volume 87, Number 7, 1980

                   P. R. Halmos   The heart of mathematics . . . . . . . . 519--524
                   C. A. Rogers   A less strange version of Milnor's proof
                                  of Brouwer's fixed-point theorem . . . . 525--527
   András Prékopa   On the development of optimization
                                  theory . . . . . . . . . . . . . . . . . 527--542
                   I. M. Isaacs   Roots of polynomials in algebraic
                                  extensions of fields . . . . . . . . . . 543--544
           Kenneth B. Stolarsky   The power and generalized logarithmic
                                  means  . . . . . . . . . . . . . . . . . 545--548
                James R. Schatz   On the weight distributions of cosets of
                                  a linear code  . . . . . . . . . . . . . 548--551
               Shinji Yamashita   Cowling's theorem on a Dirichlet finite
                                  holomorphic function in the disk . . . . 551--552
             J. C. Lagarias and   
                  A. M. Odlyzko   Divisibility properties of some
                                  cyclotomic sequences . . . . . . . . . . 561--564
              M. A. Golberg and   
                      H. Bowman   Mikusi\'nski operators without the
                                  Titchmarsh theorem . . . . . . . . . . . 564--567
               George D. Parker   A metric model of plane Euclidean
                                  geometry . . . . . . . . . . . . . . . . 567--572

American Mathematical Monthly
Volume 87, Number 8, 1980

                      Mina Rees   The mathematical sciences and World War
                                  II . . . . . . . . . . . . . . . . . . . 607--621
                    Ivan Netuka   The Dirichlet problem for harmonic
                                  functions  . . . . . . . . . . . . . . . 621--628
               Robert G. Bartle   An extension of Egorov's theorem . . . . 628--633
              Walter Stromquist   How to cut a cake fairly . . . . . . . . 640--644
                    Leon Gerber   Napoleon's theorem and the parallelogram
                                  inequality for affine-regular polygons   644--648
         Joan P. Hutchinson and   
                   Paul B. Trow   Some pigeonhole principle results
                                  extended . . . . . . . . . . . . . . . . 648--651
              M. S. Klamkin and   
                         A. Liu   Note on a result of Niven on impossible
                                  tessellations  . . . . . . . . . . . . . 651--653
              William J. Knight   Functions with zero right derivatives
                                  are constant . . . . . . . . . . . . . . 657--658
               Albert Nijenhuis   Complete solutions of linear difference
                                  equations  . . . . . . . . . . . . . . . 658--660
                Kenneth A. Ross   Another approach to Riemann-Stieltjes
                                  integrals  . . . . . . . . . . . . . . . 660--662

American Mathematical Monthly
Volume 87, Number 9, 1980

                   D. J. Newman   Simple analytic proof of the prime
                                  number theorem . . . . . . . . . . . . . 693--696
                    E. R. Swart   The philosophical implications of the
                                  four-color problem . . . . . . . . . . . 697--707
                      M. D. Fox   Formulae for the curvatures of circles
                                  in chains  . . . . . . . . . . . . . . . 708--715
               Frank Boesch and   
                  Ralph Tindell   Robbins's theorem for mixed multigraphs  716--719
              Solomon W. Golomb   Iterated binomial coefficients . . . . . 719--727
                A. Galperin and   
                     Z. Waksman   An elementary approach to Jordan theory  728--732
             János Pintz   On Legendre's prime number formula . . . 733--735
                   Zensho Nakao   Polynomial group laws  . . . . . . . . . 735--736
        Miguel de Guzmán   A change-of-variables formula without
                                  continuity . . . . . . . . . . . . . . . 736--739
              Ronald E. Prather   Generating the $k$-subsets of an $n$-set 740--743
              Thomas Whaley and   
               Judson Williford   Differentiability and permutations of
                                  quantifiers  . . . . . . . . . . . . . . 745--748
                    D. R. Smart   When does $T^{n+1}x-T^{n}x\rightarrow 0$
                                  imply convergence  . . . . . . . . . . . 748--749
                  B. R. Johnson   An elementary proof of
                                  inclusion-exclusion formulas . . . . . . 750--751

American Mathematical Monthly
Volume 87, Number 10, 1980

          Duane W. DeTemple and   
              Jack M. Robertson   Constructing Buffon curves from their
                                  distributions  . . . . . . . . . . . . . 779--784
                   Steven Roman   The formula of Fa\`a di Bruno  . . . . . 805--809
            Israel Halperin and   
                Peter Rosenthal   Burnside's theorem on algebras of
                                  matrices . . . . . . . . . . . . . . . . 810--810
                       A. Ecker   Comment on the note: ``The congruence
                                  $a^{r+s}\equiv a^{r} \pmod {m}$'' [Amer.
                                  Math. Monthly 85 (1978), no. 2, 97--100,
                                  MR 57 #12355] by A. E. Livingston and M.
                                  L. Livingston  . . . . . . . . . . . . . 811--814
                    J. M. Henle   Functions with arbitrarily small periods 816--816
                C. C. Cowen and   
             K. R. Davidson and   
                  R. P. Kaufman   Rearranging the alternating harmonic
                                  series . . . . . . . . . . . . . . . . . 817--819
                  R. B. Burckel   A strong converse to Gauss's mean-value
                                  theorem  . . . . . . . . . . . . . . . . 819--820


American Mathematical Monthly
Volume 88, Number 1, 1981

                Bernard Grofman   Fair apportionment and the Banzhaf index 1--5
                        B. Roth   Rigid and flexible frameworks  . . . . . 6--21
                    J. R. Quine   Plücker equations for curves  . . . . . . 21--29
               Kenneth R. Meyer   An application of Poincaré's recurrence
                                  theorem to academic administration . . . 32--33
                  Paul Schaefer   Sum-preserving rearrangements of
                                  infinite series  . . . . . . . . . . . . 33--40
            C. G. Méndez   On the law of large numbers, infinite
                                  games, and category  . . . . . . . . . . 40--42
                Richard A. Dean   A rational polynomial whose group is the
                                  quaternions  . . . . . . . . . . . . . . 42--45
             Douglas S. Bridges   On Montel's proof of the great Picard
                                  theorem  . . . . . . . . . . . . . . . . 45--47
               Tudor Zamfirescu   Most monotone functions are singular . . 47--49
                Herbert S. Wilf   An algorithm-inspired proof of the
                                  spectral theorem in $E^{n}$  . . . . . . 49--50
               Mark D. Meyerson   Every power series is a Taylor series    51--52
                    John Isbell   Submodules of free modules . . . . . . . 53--53

American Mathematical Monthly
Volume 88, Number 2, 1981

               Thomas Zaslavsky   The geometry of root systems and signed
                                  graphs . . . . . . . . . . . . . . . . . 88--105
             Chester J. Salwach   Planes, biplanes, and their codes  . . . 106--125
            Hans Willi Siegberg   Some historical remarks concerning
                                  degree theory  . . . . . . . . . . . . . 125--139
              R. Creighton Buck   Characterization of classes of functions 139--142
          Lindsay N. Childs and   
                  Morris Orzech   On modular group rings, normal bases,
                                  and fixed points . . . . . . . . . . . . 142--145

American Mathematical Monthly
Volume 88, Number 3, 1981

                 G. M. Phillips   Archimedes the numerical analyst . . . . 165--169
             L. J. Ratliff, Jr.   A brief history and survey of the
                                  catenary chain conjectures . . . . . . . 169--178
                 Russell Merris   Pólya's counting theorem via tensors  . . 179--185
              Marcus B. Feldman   A proof of Lusin's theorem . . . . . . . 191--192
                 Adolf Cusmariu   A proof of the arithmetic mean-geometric
                                  mean inequality  . . . . . . . . . . . . 192--194
          S. M. Gagola, Jr. and   
             S. C. Garrison and   
                   M. R. Pettet   On a vanishing product in the integral
                                  group ring . . . . . . . . . . . . . . . 195--196
                  Ernst Snapper   An affine generalization of the Euler
                                  line . . . . . . . . . . . . . . . . . . 196--198
                  Charles Riley   A note on strict convexity . . . . . . . 198--199
               Stanley Kertzner   The linear Diophantine equation  . . . . 200--203
                 Hermann Hueber   On uniform continuity and compactness in
                                  metric spaces  . . . . . . . . . . . . . 204--205
                 Emeric Deutsch   Bounds for the zeros of polynomials  . . 205--206

American Mathematical Monthly
Volume 88, Number 4, April, 1981

              R. Arthur Knoebel   Exponentials reiterated  . . . . . . . . 235--252
              J. L. Brenner and   
                   R. C. Lyndon   Proof of the fundamental theorem of
                                  algebra  . . . . . . . . . . . . . . . . 253--256
                     Ezra Brown   The first proof of the quadratic
                                  reciprocity law, revisited . . . . . . . 257--264
                   Yakar Kannai   An elementary proof of the no-retraction
                                  theorem  . . . . . . . . . . . . . . . . 264--268
                James Kraft and   
                  Michael Rosen   Eisenstein reciprocity and $n$th-power
                                  residues . . . . . . . . . . . . . . . . 269--270
                  John A. Ewell   An easy proof of the triple-product
                                  identity . . . . . . . . . . . . . . . . 270--272
                 W. A. Sentance   Occurrences of consecutive odd powerful
                                  numbers  . . . . . . . . . . . . . . . . 272--274
           Josip E. Pe\vcari\'c   Note on: ``An integral inequality''
                                  [Amer. Math. Monthly \bf 61 (1954),
                                  626--631, MR \bf 16, 342] by K. Fan and
                                  G. G. Lorentz  . . . . . . . . . . . . . 275--276
               Daniel A. Marcus   Classroom Notes: An Alternative to
                                  Euclid's Algorithm . . . . . . . . . . . 280--283
    Arthur H. Copeland, Jr. and   
                 Albert O. Shar   Constructing loops from groups . . . . . 283--285
                   G. J. Porter   New angles on an old game  . . . . . . . 285--286

American Mathematical Monthly
Volume 88, Number 5, 1981

                Philip J. Davis   Are there coincidences in mathematics    311--320
                   W. Hrusa and   
                 J. L. Troutman   Elementary characterization of classical
                                  minima . . . . . . . . . . . . . . . . . 321--327
                H. B. Griffiths   Cayley's version of the resultant of two
                                  polynomials  . . . . . . . . . . . . . . 328--338
              Solomon W. Golomb   Corrections to: ``Cyclotomic polynomials
                                  and factorization theorems'' [Amer.
                                  Math. Monthly \bf 85 (1978), no. 9,
                                  734--737, MR 80e:10011]  . . . . . . . . 338--339
                 Duane Boes and   
              Richard Darst and   
                Paul Erdös   Fat, symmetric, irrational Cantor sets   340--341
                Thomas P. Dence   On the monotonicity of a class of
                                  exponential sequences  . . . . . . . . . 341--344

American Mathematical Monthly
Volume 88, Number 6, 1981

                  Michael Rosen   Abel's theorem on the lemniscate . . . . 387--395
                  R. B. Burckel   Iterating analytic self-maps of discs    396--407
             Frank D. Grosshans   Rigid motions of conics: an introduction
                                  to invariant theory  . . . . . . . . . . 407--413
               Edith H. Luchins   Women and mathematics: fact and fiction  413--419
                 John Bloom and   
                      Lee Whitt   The geometry of rolling curves . . . . . 420--426
            John A. R. Holbrook   Stochastic independence and
                                  space-filling curves . . . . . . . . . . 426--432
                   Y. Sternfeld   Homeomorphisms of cubes into Euclidean
                                  spaces . . . . . . . . . . . . . . . . . 436--439
                Robert D. Small   Modified convergence of Taylor series    439--441
                 Andrew Sobczyk   Equivalence of an identity in vector
                                  analysis to quaternion associativity,
                                  and ramifications  . . . . . . . . . . . 441--443

American Mathematical Monthly
Volume 88, Number 7, 1981

              Saunders Mac Lane   Mathematical models: a sketch for the
                                  philosophy of mathematics  . . . . . . . 462--472
               L. E. Dubins and   
                 D. A. Freedman   Machiavelli and the Gale--Shapley
                                  algorithm  . . . . . . . . . . . . . . . 485--494
            I. Grattan-Guinness   On the development of logics between the
                                  two World Wars . . . . . . . . . . . . . 495--509
                 Edward T. Wong   Polygons, circulant matrices, and
                                  Moore--Penrose inverses  . . . . . . . . 509--515
                 Roger L. Cooke   Almost-periodic functions  . . . . . . . 515--526
                   D. J. Newman   Differentiation of asymptotic formulas   526--527
                Alexander Abian   Generalizing the generalized mean-value
                                  theorem  . . . . . . . . . . . . . . . . 528--530
                     G. Alefeld   On the convergence of Halley's method    530--536

American Mathematical Monthly
Volume 88, Number 8, 1981

              M. Katchalski and   
              M. S. Klamkin and   
                         A. Liu   An experience in problem solving . . . . 551--556
                   W. B. Arthur   Why a population converges to stability  557--563
             Karen D. Rappaport   S. Kovalevsky: a mathematical lesson . . 564--574
                William Abikoff   The uniformization theorem . . . . . . . 574--592
          Patricia C. Kenschaft   Black women in mathematics in the United
                                  States . . . . . . . . . . . . . . . . . 592--604
         Cyril W. L. Garner and   
              Agnes M. Herzberg   On McCarty's queen squares . . . . . . . 612--613
              Walter Stromquist   Addendum to: ``How to cut a cake
                                  fairly'' [Amer. Math. Monthly \bf 87
                                  (1980), no. 8, 640--644, MR 81m:05016]   613--614
               Chantal Shafroth   A generalization of the formula for
                                  computing the inverse of a matrix  . . . 614--616
               I. J. Schoenberg   A direct derivation of a Jacobian
                                  identity from elliptic functions . . . . 616--618

American Mathematical Monthly
Volume 88, Number 9, 1981

               Bhama Srinivasan   Characters of finite groups: some uses
                                  and mathematical applications  . . . . . 639--646
                 J.-P. Delahaye   The set of periodic points . . . . . . . 646--651
                J. W. Bruce and   
               P. J. Giblin and   
                   C. G. Gibson   On caustics of plane curves  . . . . . . 651--667
            Lawrence Narici and   
             Edward Beckenstein   Strange terrain --- non-Archimedean
                                  spaces . . . . . . . . . . . . . . . . . 667--676
                   Eldon Hansen   Sums of functions satisfying recursion
                                  relations  . . . . . . . . . . . . . . . 676--679
              Solomon W. Golomb   Normed division domains  . . . . . . . . 680--686
                  Jozef Dodziuk   Eigenvalues of the Laplacian and the
                                  heat equation  . . . . . . . . . . . . . 686--695
           Richard Johnsonbaugh   The trapezoid rule, Stirling's formula,
                                  and Euler's constant . . . . . . . . . . 696--698
              Elon Kohlberg and   
                 Abraham Neyman   Asymptotic behavior of nonexpansive
                                  mappings in uniformly convex Banach
                                  spaces . . . . . . . . . . . . . . . . . 698--700

American Mathematical Monthly
Volume 88, Number 10, 1981

                Donald E. Knuth   A permanent inequality . . . . . . . . . 731--740, 798
         Geoffrey C. Berresford   Cauchy's theorem . . . . . . . . . . . . 741--744
          Heinrich Guggenheimer   The Hilbert model of hyperbolic geometry 744--748
                  Edwin Buchman   The impossibility of tiling a convex
                                  region with unequal equilateral
                                  triangles  . . . . . . . . . . . . . . . 748--753
        Katherine E. McLain and   
                  Hugh M. Edgar   A note on S. W. Golomb's: ``Cyclotomic
                                  polynomials and factorization theorems''
                                  [Amer. Math. Monthly \bf 85 (1978), no.
                                  9, 734--737, MR 80e:10011] . . . . . . . 753--753
           Tibor \vSalát   On functions that are monotone on no
                                  interval . . . . . . . . . . . . . . . . 754--755
               Richard A. Davis   More on similarity of matrices . . . . . 761--762


American Mathematical Monthly
Volume 89, Number 1, 1982

                  F. F. Bonsall   A down-to-earth view of mathematics  . . 8--15
       A. J. W. Duijvestijn and   
             P. J. Federico and   
                       P. Leeuw   Compound perfect squares . . . . . . . . 15--32
                    John Wavrik   Computers and the multiplicity of
                                  polynomial roots . . . . . . . . . . . . 34--36, 45--56
                  Charles Small   A simple proof of the four-squares
                                  theorem  . . . . . . . . . . . . . . . . 59--61

American Mathematical Monthly
Volume 89, Number 2, 1982

                 G. Baley Price   Award for distinguished service to Dr.
                                  Thornton Carl Fry  . . . . . . . . . . . 81--83 (1 plate)
                   Tony Rothman   Genius and biographers: the
                                  fictionalization of Évariste Galois . . . 84--106
                  F. H. Norwood   Long proofs  . . . . . . . . . . . . . . 110--112
                 Andrew Simoson   An ``Archimedean'' paradox . . . . . . . 114--116, 125
                        M. Nair   On Chebyshev-type inequalities for
                                  primes . . . . . . . . . . . . . . . . . 126--129

American Mathematical Monthly
Volume 89, Number 3, 1982

        Desmond Fearnley-Sander   Hermann Grassmann and the prehistory of
                                  universal algebra  . . . . . . . . . . . 161--166
             Carmen Chicone and   
                Jing Huang Tian   On general properties of quadratic
                                  systems  . . . . . . . . . . . . . . . . 167--178
               Robert C. Reilly   Mean curvature, the Laplacian, and soap
                                  bubbles  . . . . . . . . . . . . . . . . 180--188, 197--198
                  Hong Xiang Li   Elementary quadratures of ordinary
                                  differential equations . . . . . . . . . 198--208
                Mau Hsiang Shih   An analog of Bolzano's theorem for
                                  functions of a complex variable  . . . . 210--211

American Mathematical Monthly
Volume 89, Number 4, 1982

                Wolfgang Walter   Old and new approaches to Euler's
                                  trigonometric expansions . . . . . . . . 225--230
               Azriel Rosenfeld   How a digital computer can tell whether
                                  a line is straight . . . . . . . . . . . 231--235
                    F. K. Hwang   New concepts in seeding knockout
                                  tournaments  . . . . . . . . . . . . . . 235--239
         Andreana S. Madguerova   On Bridges' proof of the great Picard
                                  theorem  . . . . . . . . . . . . . . . . 239--239
                   Walter Rudin   Nonuniqueness and growth in first-order
                                  differential equations . . . . . . . . . 241--244
                     A. K. Bose   Linear differential equations on the
                                  complex plane  . . . . . . . . . . . . . 244--249
                Harley Flanders   On the Fresnel integrals . . . . . . . . 264--266

American Mathematical Monthly
Volume 89, Number 5, 1982

                Herbert S. Wilf   What is an answer  . . . . . . . . . . . 289--292
               Bernard Jacobson   On the mean value theorem for integrals  300--301
            David Challener and   
                      Lee Rubel   A converse to Rouché's theorem  . . . . . 302--305
              Pablo M. Salzberg   A reflection principle for calculating
                                  the derivatives of a polynomial  . . . . 305--307
             Brian M. Scott and   
               Zachary Robinson   The boundary topology of a space . . . . 307--309
                     E. S. Wolk   On the inadequacy of subnets and
                                  transfinite sequences  . . . . . . . . . 310--311
            Alfonso G. Azpeitia   On the Lagrange remainder of the Taylor
                                  formula  . . . . . . . . . . . . . . . . 311--312
                 Norman M. Rice   On $n$th roots of positive operators . . 313--314
                 Achim Clausing   Kantorovich-type inequalities  . . . . . 314, 327--330

American Mathematical Monthly
Volume 89, Number 6, 1982

            Aviezri S. Fraenkel   How to beat your Wythoff games' opponent
                                  on three fronts  . . . . . . . . . . . . 353--361
             William S. Hatcher   Calculus is algebra  . . . . . . . . . . 362--370
           Edwin O. Buchman and   
         Frederick A. Valentine   Any new Helly numbers  . . . . . . . . . 370--375
           Robert S. Strichartz   Radon inversion --- variations on a
                                  theme  . . . . . . . . . . . . . . . . . 377--384, 420--423
                   Fred Richman   Meaning and information in constructive
                                  mathematics  . . . . . . . . . . . . . . 385--388
               Raymond G. Ayoub   On the nonsolvability of the general
                                  polynomial . . . . . . . . . . . . . . . 397--401
                     Dan Kalman   Central functions and fixed points . . . 401--402
               Renfrey B. Potts   Differential and difference equations    402--407
              Gerald Janusz and   
                  Joseph Rotman   Outer automorphisms of $S_{6}$ . . . . . 407--410
             Amitava Bagchi and   
             Edward M. Reingold   A naturally occurring function
                                  continuous only at irrationals . . . . . 411--417
                     G. P. Wene   A little color in abstract algebra . . . 417--419

American Mathematical Monthly
Volume 89, Number 7, 1982

                  Dean S. Clark   On some abstract properties of binomial
                                  coefficients . . . . . . . . . . . . . . 433--443
                    Dawn Fisher   Extending functions to infinitesimals of
                                  finite order . . . . . . . . . . . . . . 443--449
                   W. M. Snyder   Factoring repunits . . . . . . . . . . . 462--466
                    F. S. Cater   Most monotone functions are not singular 466--469

American Mathematical Monthly
Volume 89, Number 8, 1982

                 Gilbert Strang   The width of a chair . . . . . . . . . . 529--534
              Robert L. Devaney   Blowing up singularities in classical
                                  mechanical systems . . . . . . . . . . . 535--552
       Richard Johnsonbaugh and   
                   Tadao Murata   Petri nets and marked graphs ---
                                  mathematical models of concurrent
                                  computation  . . . . . . . . . . . . . . 552--566
           Gregory A. Fredricks   Sylvester's theorem for matrices with
                                  smooth entries . . . . . . . . . . . . . 586--587
              Jean-Pierre Rosay   Injective holomorphic mappings . . . . . 587--588

American Mathematical Monthly
Volume 89, Number 9, 1982

                Robert C. James   Bases in Banach spaces . . . . . . . . . 625--640
             Yung Chow Wong and   
                  Kai Man Tsang   A strong converse of Morley's trisector
                                  theorem  . . . . . . . . . . . . . . . . 642--653
                Robert F. Brown   The fixed point property and Cartesian
                                  products . . . . . . . . . . . . . . . . 654--678
             A. W. Marshall and   
                       I. Olkin   A convexity proof of Hadamard's
                                  inequality . . . . . . . . . . . . . . . 687--688
                  Abraham Ungar   Generalized hyperbolic functions . . . . 688--691
              Donald Duncan and   
                William Barnier   On trisection, quintisection, \ldots,
                                  etc. . . . . . . . . . . . . . . . . . . 693--693

American Mathematical Monthly
Volume 89, Number 10, 1982

              Robert A. Proctor   Solution of two difficult combinatorial
                                  problems with linear algebra . . . . . . 721--734
                  Charles Small   On the equation $xyz=x+y+z=1$  . . . . . 736--749
                Murray Bell and   
                  John Ginsburg   A space which will not go where its
                                  proper subspaces want it to go . . . . . 749--751


American Mathematical Monthly
Volume 90, Number ??, 1983

                Donald E. Knuth   Elementary problem E2982, a double
                                  infinite sum for $\vert x\vert$  . . . . 54--54

American Mathematical Monthly
Volume 90, Number 1, 1983

                E. L. Ortiz and   
                   T. J. Rivlin   Another look at the Chebyshev
                                  polynomials  . . . . . . . . . . . . . . 3--10
                R. Fletcher and   
                 D. C. Sorensen   An algorithmic derivation of the Jordan
                                  canonical form . . . . . . . . . . . . . 12--16
                    George Miel   Of calculations past and present: the
                                  Archimedean algorithm  . . . . . . . . . 17--35
                   Walter Rudin   Well-distributed measurable sets . . . . 41--42
             Bernard R. Gelbaum   An algorithm for the minimal polynomial
                                  of a matrix  . . . . . . . . . . . . . . 43--44

American Mathematical Monthly
Volume 90, Number 2, 1983

                Cleve Moler and   
                Donald Morrison   Singular value analysis of cryptograms   78--87
                     Roger Fenn   What is the geometry of a surface  . . . 87--98
               Richard McIntosh   A necessary and sufficient condition for
                                  the primality of Fermat numbers  . . . . 98--99
           Quentin F. Stout and   
          Patricia A. Woodworth   Relational databases . . . . . . . . . . 101--118
                  J. A. Guthrie   A continuous modulus of continuity . . . 126--127
                 Melvin Hausner   Applications of a simple counting
                                  technique  . . . . . . . . . . . . . . . 127--129
                  Jan Mycielski   The meaning of the conjecture ${\rm
                                  P}\not={\rm NP}$ for mathematical logic  129--130

American Mathematical Monthly
Volume 90, Number 3, 1983

                Keith M. Kendig   Algebra, geometry, and algebraic
                                  geometry: some interconnections  . . . . 161--174
                      Uri Leron   Structuring mathematical proofs  . . . . 174--185
             Judith V. Grabiner   Who gave you the epsilon? Cauchy and the
                                  origins of rigorous calculus . . . . . . 185--194
               L. Richard Duffy   An elementary proof of the isomorphism
                                  ${\bf C}^{*} \approx S^{1}$  . . . . . . 201--202
                   J.-C. Renaud   Matrices with integer entries and
                                  integer eigenvalues  . . . . . . . . . . 202--203
                 Juan L. Romero   When is $L^p(\mu)$ contained in
                                  $L^q(\mu)$?  . . . . . . . . . . . . . . 203--206
           J.-B. Hiriart-Urruty   A short proof of the variational
                                  principle for approximate solutions of a
                                  minimization problem . . . . . . . . . . 206--207

American Mathematical Monthly
Volume 90, Number 4, 1983

                  Joel Franklin   Mathematical methods of economics  . . . 229--244
                    Thomas Jech   The ranking of incomplete tournaments: a
                                  mathematician's guide to popular sports  246--266
                  Morris Marden   Conjectures on the critical points of a
                                  polynomial . . . . . . . . . . . . . . . 267--276
               Donald G. Hartig   The Riesz representation theorem
                                  revisited  . . . . . . . . . . . . . . . 277--280
                E. E. Posey and   
                  J. E. Vaughan   Functions with a proper local maximum in
                                  each interval  . . . . . . . . . . . . . 281--282
                        Liu Wen   A space filling curve  . . . . . . . . . 283--283

American Mathematical Monthly
Volume 90, Number 5, 1983

                  Man Duen Choi   Tricks or treats with the Hilbert matrix 301--312
                     R. Hirshon   A group with constant growth rate  . . . 312--317
             Charles W. Schelin   Calculator function approximation  . . . 317--325
           Allen J. Schwenk and   
                   J. Ian Munro   How small can the mean shadow of a set
                                  be . . . . . . . . . . . . . . . . . . . 325--329
              Charles Blair and   
                   Lee A. Rubel   A universal entire function  . . . . . . 331--332

American Mathematical Monthly
Volume 90, Number 6, 1983

                    John Milnor   On the geometry of the Kepler problem    353--365
                   Joel Spencer   Short theorems with long proofs  . . . . 365--366
             P. C. Fishburn and   
                   H. O. Pollak   Fixed-route cost allocation  . . . . . . 366--378
          William C. Waterhouse   Do symmetric problems have symmetric
                                  solutions  . . . . . . . . . . . . . . . 378--387
            Kenneth R. Davidson   Pointwise limits of analytic functions   391--394
               Lee A. Rubel and   
           Aristomenis Siskakis   A net of exponentials converging to a
                                  nonmeasurable function . . . . . . . . . 394--396
            Jürgen Kindler   A simple proof of the Daniell-Stone
                                  representation theorem . . . . . . . . . 396--397
                A. Keith Austin   An elementary approach to
                                  NP-completeness  . . . . . . . . . . . . 398--399

American Mathematical Monthly
Volume 90, Number 7, 1983

             Geng Zhe Chang and   
                Philip J. Davis   Iterative processes in elementary
                                  geometry . . . . . . . . . . . . . . . . 421--431
               Theodore P. Hill   Determining a fair border  . . . . . . . 438--442
            Harry Appelgate and   
                Hironori Onishi   The slow continued fraction algorithm
                                  via $2\times 2$ integer matrices . . . . 443--455
                   W. A. Coppel   An interesting Cantor set  . . . . . . . 456--460
            Lance L. Littlejohn   Symmetry factors for differential
                                  equations  . . . . . . . . . . . . . . . 462--464
                  H. Haruki and   
                      S. Haruki   Euler's integrals  . . . . . . . . . . . 464--466
                James W. Walker   A homology version of the Borsuk-Ulam
                                  theorem  . . . . . . . . . . . . . . . . 466--468
             John F. Hughes and   
                  J. O. Shallit   On the number of multiplicative
                                  partitions . . . . . . . . . . . . . . . 468--471
       Deborah Tepper Haimo and   
          Franklin Tepper Haimo   Comments and complements . . . . . . . . 472--478

American Mathematical Monthly
Volume 90, Number 8, 1983

                Bruce C. Berndt   The quarterly reports of S. Ramanujan    505--516
                 James T. Cross   The Euler $\varphi$-function in the
                                  Gaussian integers  . . . . . . . . . . . 518--528
                J. W. Bruce and   
                   P. J. Giblin   Generic geometry . . . . . . . . . . . . 529--545
               Steven G. Krantz   Characterization of smooth domains in
                                  ${\bf C}$ by their biholomorphic
                                  self-maps  . . . . . . . . . . . . . . . 555--557
         Michael J. Hoffman and   
                   Richard Katz   The sequence of derivatives of a
                                  $C^{\infty }$ function . . . . . . . . . 557--560
                   P. S. Bullen   An inequality for variations . . . . . . 560--560
                     Z. Kominek   Measure, category, and the sums of sets  561--562

American Mathematical Monthly
Volume 90, Number 9, 1983

              George K. Francis   Drawing Seifert surfaces that fiber the
                                  figure-$8$ knot complement in $S^{3}$
                                  over $S^{1}$ . . . . . . . . . . . . . . 589--599
                     Roger Howe   Very basic Lie theory  . . . . . . . . . 600--623
          Steven C. Althoen and   
             Lawrence D. Kugler   When is ${\bf R}^{2}$ a division algebra 625--635
                  John A. Ewell   A simple proof of Fermat's two-square
                                  theorem  . . . . . . . . . . . . . . . . 635--637
                   G. Ladas and   
               Y. G. Sficas and   
             I. P. Stavroulakis   Necessary and sufficient conditions for
                                  oscillations . . . . . . . . . . . . . . 637--640
                Andrzej Szulkin   ${\bf R}^{3}$ is the union of disjoint
                                  circles  . . . . . . . . . . . . . . . . 640--641

American Mathematical Monthly
Volume 90, Number 10, 1983

             Robert C. Thompson   Author vs. referee: a case history for
                                  middle level mathematicians  . . . . . . 661--668
                   Joel Spencer   Large numbers and unprovable theorems    669--675
                Michael E. Mays   Functions which parametrize means  . . . 677--683
                 K. J. Falconer   Applications of a result on spherical
                                  integration to the theory of convex sets 690--693
                    Denis Higgs   Iterating the derived set function . . . 693--697
                   W. S. Massey   Cross products of vectors in
                                  higher-dimensional Euclidean spaces  . . 697--701
                 Elgin Johnston   A ``counterexample'' for the
                                  Schwarz--Christoffel transform . . . . . 701--703


American Mathematical Monthly
Volume 91, Number 1, 1984

            Donald G. Saari and   
                 John B. Urenko   Newton's method, circle maps, and
                                  chaotic motion . . . . . . . . . . . . . 3--17
             Harvey Diamond and   
               Gregory Gell\`es   Relations among some classes of subsets
                                  of ${\bf R}$ . . . . . . . . . . . . . . 19--22
                  R. B. Burckel   Bishop's Stone-Weierstrass theorem . . . 22--32
               Brad Jackson and   
                 Gerhard Ringel   Colorings of circles . . . . . . . . . . 42--49
                  R. Fuster and   
                    A. Marquina   Geometric series in incomplete normed
                                  algebras . . . . . . . . . . . . . . . . 49--51
                 C. R. MacCluer   A simple proof of the fundamental
                                  theorem on finite abelian groups . . . . 52--52

American Mathematical Monthly
Volume 91, Number 2, 1984

               Joseph Kupka and   
                   Karel Prikry   The measurability of uncountable unions  85--97
              Daniel B. Shapiro   A periodicity problem in plane geometry  97--108
             George M. Phillips   Archimedes and the complex plane . . . . 108--114
                P. G. Laird and   
                      R. McCann   On some characterizations of polynomials 114--116
               Timothy C. Brown   Poisson approximations and the
                                  definition of the Poisson process  . . . 116--123
              Joseph MacDonnell   A ruled Moebius band which
                                  self-intersects in a straight line . . . 125--127
           Thomas L. Miller and   
                 Robert F. Olin   Analytic curves  . . . . . . . . . . . . 127--130
                  G. W. Johnson   An unsymmetric Fubini theorem  . . . . . 131--133
              Joseph A. Gallian   Another proof that $A_{5}$ is simple . . 134--135
                     Hung C. Li   A generalized problem of least squares   135--137

American Mathematical Monthly
Volume 91, Number 3, 1984

            Claude Christen and   
                 Frank K. Hwang   Detection of a defective coin with
                                  partial weight information . . . . . . . 173--179
            Robert S. Boyer and   
              J. Strother Moore   Proof checking the RSA public key
                                  encryption algorithm . . . . . . . . . . 181--189
                 Andrew Simoson   On two halves being two wholes . . . . . 190--193
           Marvin Jay Greenberg   Note on the Cayley--Hamilton theorem . . 193--195
           Josip E. Pe\vcari\'c   A simple proof of the Jensen-Steffensen
                                  inequality . . . . . . . . . . . . . . . 195--196
          Joseph A. Gallian and   
              James Van Buskirk   The number of homomorphisms from $Z_{m}$
                                  into $Z_{n}$ . . . . . . . . . . . . . . 196--197

American Mathematical Monthly
Volume 91, Number 4, 1984

                   J. B. Wilker   Möbius equivalence and Euclidean symmetry 225--247
                     Roger Howe   Correction to: ``Very basic Lie theory'' 247--247
           Kenneth M. Levasseur   A probabilistic proof of the Weierstrass
                                  approximation theorem  . . . . . . . . . 249--250

American Mathematical Monthly
Volume 91, Number 5, 1984

                   Michael Stob   A supplement to: ``A mathematician's
                                  guide to popular sports'' [Amer. Math.
                                  Monthly \bf 90 (1983), no. 4, 246--266,
                                  MR 85i:05122a] by T. Jech  . . . . . . . 277--282
                  Kurt Eisemann   Number-theoretic analysis and extensions
                                  of ``the most complicated and fantastic
                                  card trick ever invented'' . . . . . . . 284--289
              Andrew P. Guinand   Euler lines, tritangent centers, and
                                  their triangles  . . . . . . . . . . . . 290--300
                   Walter Rudin   The inner function problem . . . . . . . 301--302
              Mohsen Pourahmadi   Taylor expansion of ${\rm exp}(\sum
                                  ^{\infty }_{k=0}a_{k}z^{k})$ and some
                                  applications . . . . . . . . . . . . . . 303--307
                    F. S. Cater   On van der Waerden's nowhere
                                  differentiable function  . . . . . . . . 307--308

American Mathematical Monthly
Volume 91, Number 6, 1984

                  John D. Dixon   Factorization and primality tests  . . . 333--352
                 G. M. Phillips   Aitken sequences and Fibonacci numbers   354--357
           Zoltán Magyar   A recursion on quadruples  . . . . . . . 360--362
    I. Bárány and   
              M. Katchalski and   
              János Pach   Helly's theorem with volumes . . . . . . 362--365

American Mathematical Monthly
Volume 91, Number 7, 1984

                 R. J. Stroeker   How to solve a Diophantine equation ---
                                  a number-theoretic excursion . . . . . . 385--392
              B. L. Burrows and   
                   R. F. Talbot   Sums of powers of integers . . . . . . . 394--403
             John V. Baxley and   
              John C. Moorhouse   Lagrange multiplier problems in
                                  economics  . . . . . . . . . . . . . . . 404--412
                     David Avis   The number of furthest neighbour pairs
                                  of a finite planar set . . . . . . . . . 417--420
                    R. P. Lewis   A combinatorial proof of the triple
                                  product identity . . . . . . . . . . . . 420--423
       Doris J. Schattschneider   The taxicab group  . . . . . . . . . . . 423--428
                     B. J. Ball   Arcwise connectedness and the
                                  persistence of errors  . . . . . . . . . 431--433
                    J. M. Henle   Tangent planes with infinitesimals . . . 433--435
            Kenneth S. Williams   Letter to the editor: ``Euler's
                                  integrals'' [Amer. Math. Monthly \bf 90
                                  (1983), no. 7, 464--466, MR 84k:26012],
                                  by H. Haruki and S. Haruki . . . . . . . 455--455

American Mathematical Monthly
Volume 91, Number 8, 1984

                Donald E. Knuth   The toilet paper problem . . . . . . . . 465--470
                  George Boolos   The logic of provability . . . . . . . . 470--480
                   Karl Scherer   Some new types of closure properties in
                                  the plane  . . . . . . . . . . . . . . . 480--487
                 Myron S. Henry   Approximation by polynomials:
                                  interpolation and optimal nodes  . . . . 497--499
                     R. Spigler   Double limits and matched asymptotic
                                  expansions . . . . . . . . . . . . . . . 501--505
                  Nam Kiu Tsing   Infinite-dimensional Banach spaces must
                                  have uncountable basis---an elementary
                                  proof  . . . . . . . . . . . . . . . . . 505--506
           Avraham Feintuch and   
                Matatyahu Rubin   The matrix equation $AX-XB=C$  . . . . . 506--507
          H. G. ter Morsche and   
                 G. W. Veltkamp   A discrete Landau problem  . . . . . . . 508--509

American Mathematical Monthly
Volume 91, Number 9, 1984

              André Weil   Euler  . . . . . . . . . . . . . . . . . 537--542
         Graciela S. Birman and   
                 Katsumi Nomizu   Trigonometry in Lorentzian geometry  . . 543--549
                H. J. ter Horst   Riemann-Stieltjes and Lebesgue-Stieltjes
                                  integrability  . . . . . . . . . . . . . 551--559
               Sidney A. Morris   An elementary proof that the Hilbert
                                  cube is compact  . . . . . . . . . . . . 563--564
                    F. S. Cater   A partition of the unit interval . . . . 564--566
                Stephen Wolfram   Geometry of binomial coefficients  . . . 566--571
                 I. M. Richards   A remark on the number of cyclic
                                  subgroups of a finite group  . . . . . . 571--572
                   Richard Koch   Matrix invariants  . . . . . . . . . . . 573--575

American Mathematical Monthly
Volume 91, Number 10, 1984

                Angus E. Taylor   A life in mathematics remembered . . . . 605--618
                    F. S. Cater   Differentiable, nowhere analytic
                                  functions  . . . . . . . . . . . . . . . 618--624
               Murray Schechter   Summation of divergent series by
                                  computer . . . . . . . . . . . . . . . . 629--632
                 Geng Zhe Chang   Bernstein polynomials via the shifting
                                  operator . . . . . . . . . . . . . . . . 634--638
              Frederick Solomon   A theorem concerning Lorentz
                                  transformations  . . . . . . . . . . . . 638--641
                  Ryuji Maehara   The Jordan curve theorem via the Brouwer
                                  fixed point theorem  . . . . . . . . . . 641--643
                 Hans U. Gerber   Wronski's formula and the resultant of
                                  two polynomials  . . . . . . . . . . . . 644--646
               Bruce R. Johnson   An elementary approach for extending
                                  Poisson processes to the nonstationary
                                  case . . . . . . . . . . . . . . . . . . 646--648


American Mathematical Monthly
Volume 92, Number ??, 1985

                Donald E. Knuth   Problem E3106, A curious sum for Euler's
                                  totient function . . . . . . . . . . . . 590
                    Emma Lehmer   On square-separable primes . . . . . . . 719--720

American Mathematical Monthly
Volume 92, Number 1, 1985

            Jeffrey C. Lagarias   The $3x+1$ problem and its
                                  generalizations  . . . . . . . . . . . . 3--23
            J. Chris Fisher and   
                   D. Ruoff and   
                    J. Shilleto   Perpendicular polygons . . . . . . . . . 23--37
             W. G. Bardsley and   
                  R. M. W. Wood   Critical points and sigmoidicity of
                                  positive rational functions  . . . . . . 37--48
                   Ingram Olkin   A probabilistic proof of a theorem of
                                  Schur  . . . . . . . . . . . . . . . . . 50--51
                David L. Reiner   Enumeration in music theory  . . . . . . 51--54
          David M. Bressoud and   
               Doron Zeilberger   Bijecting Euler's partitions-recurrence  54--55

American Mathematical Monthly
Volume 92, Number 2, 1985

                         L. Wos   Automated reasoning  . . . . . . . . . . 85--92
                Alexander Abian   Solvability of infinite systems of
                                  polynomial equations over the field of
                                  complex numbers  . . . . . . . . . . . . 94--98
                A. O. Pittenger   The logarithmic mean in $n$ variables    99--104
            Aviezri S. Fraenkel   Systems of numeration  . . . . . . . . . 105--114
                Wolfgang Walter   An elementary proof of the
                                  Cauchy-Kowalevsky theorem  . . . . . . . 115--126
                Bruce C. Berndt   The gamma function and the Hurwitz
                                  zeta-function  . . . . . . . . . . . . . 126--130
                  Walter Gander   On Halley's iteration method . . . . . . 131--134
             Carmen Chicone and   
               N. J. Kalton and   
                  Ira J. Papick   A converse for the Cayley--Hamilton
                                  theorem  . . . . . . . . . . . . . . . . 134--136
                  Jerry Johnson   An elementary characterization of weak
                                  convergence of measures  . . . . . . . . 136--137
             Harvey Diamond and   
                 Gregory Gelles   Interlaced second category sets  . . . . 138--140
                  Ernst Snapper   An ingrained error concerning resultants 141--141
                 M. Cosnard and   
                       C. Masse   Letter to the editor: ``Newton's method,
                                  circle maps, and chaotic motion'' [Amer.
                                  Math. Monthly \bf 91 (1984), no. 1,
                                  3--17, MR 85a:58060] by D. Saari and J.
                                  Urenko . . . . . . . . . . . . . . . . . 157--158

American Mathematical Monthly
Volume 92, Number 3, 1985

                  David Roselle   Award for distinguished service to
                                  Professor Everett Pitcher  . . . . . . . 169--170
                Donald E. Knuth   Algorithmic thinking and mathematical
                                  thinking . . . . . . . . . . . . . . . . 170--181
                 Jonathan Britt   The anatomy of low-dimensional stable
                                  singularities  . . . . . . . . . . . . . 183--201
     F. J. Craveiro de Carvalho   Characterizing maximally looped closed
                                  curves . . . . . . . . . . . . . . . . . 202--207
                Ronald J. Leach   On Gelbaum's algorithm for computing the
                                  minimal polynomial of a matrix . . . . . 208--209
            Vladimir Drobot and   
                Micha\l Morayne   Continuous functions with a dense set of
                                  proper local maxima  . . . . . . . . . . 209--211
               Frank Harary and   
             Robert W. Robinson   The diameter of a graph and its
                                  complement . . . . . . . . . . . . . . . 211--212
           Kenneth M. Levasseur   Letter to the editor: ``A probabilistic
                                  proof of the Weierstrass approximation
                                  theorem'' [Amer. Math. Monthly \bf 91
                                  (1984), no. 4, 249--250, MR 85h:41016]   227--227

American Mathematical Monthly
Volume 92, Number 4, 1985

                 Ethan Akin and   
                   Morton Davis   Bulgarian solitaire  . . . . . . . . . . 237--250
                Herbert S. Wilf   Some examples of combinatorial averaging 250--261
                 David Gale and   
              Marilda Sotomayor   Ms. Machiavelli and the stable matching
                                  problem  . . . . . . . . . . . . . . . . 261--268
          William C. Waterhouse   When one equation solves them all  . . . 270--273
                     F. J. Papp   The d'Alembert functional equation . . . 273--275
               L. K. Arnold and   
             S. J. Benkoski and   
                   B. J. McCabe   The discriminator (a simple application
                                  of Bertrand's postulate) . . . . . . . . 275--277
              Seymour Lipschutz   Notes on graphs and matrix inequalities  277--280
                  K. L. Teo and   
                    M. D. Hendy   Letter to the editor: ``Another proof
                                  that $A_5$ is simple'' [Amer. Math.
                                  Monthly 91 (1984), no. 2, 134--135, MR
                                  85h:20020] by J. A. Gallian  . . . . . . 303--303
              Joseph A. Gallian   Letter to the editor: ``Another proof
                                  that $A_5$ is simple'' [Amer. Math.
                                  Monthly 91 (1984), no. 2, 134--135, MR
                                  85h:20020] . . . . . . . . . . . . . . . 303--304

American Mathematical Monthly
Volume 92, Number 5, 1985

               F. J. Bloore and   
                   H. R. Morton   Advice on hanging pictures . . . . . . . 309--321
              B. van Rootselaar   How to solve the system $x'=Ax$  . . . . 321--327
                    A. H. Stone   Trees and power-sums . . . . . . . . . . 328--331
                Robert Osserman   The four-or-more vertex theorem  . . . . 332--337
                 Solomon Leader   The inclusion-exclusion probability
                                  formulas by Taylor's theorem . . . . . . 343--345
                 A. Charnow and   
                     E. Charnow   On transcendental linear operators . . . 345--347
                    Piotr Biler   Dini type theorems on positive series    347--349
                  C. E. Burgess   Classification of surfaces . . . . . . . 349--354
                Boris Kimelfeld   An inequality concerning minors of a
                                  semidefinite matrix  . . . . . . . . . . 354--355
               Paul R. Chernoff   Letter to the editor: ``Pointwise
                                  convergence of Fourier series'' [Amer.
                                  Math. Monthly \bf 87 (1980), no. 5,
                                  399--400, MR 81b:42028]  . . . . . . . . 373--374

American Mathematical Monthly
Volume 92, Number 6, 1985

            Mogens Esrom Larsen   Rubik's revenge: the group theoretical
                                  solution . . . . . . . . . . . . . . . . 381--390
                T. H. MacGregor   Linear methods in geometric function
                                  theory . . . . . . . . . . . . . . . . . 392--406
                  Paul Cull and   
             E. F. Ecklund, Jr.   Towers of Hanoi and analysis of
                                  algorithms . . . . . . . . . . . . . . . 407--420
                    Jeff Connor   A short proof of Steinhaus' theorem on
                                  summability  . . . . . . . . . . . . . . 420--421
                   Robin Thomas   A combinatorial construction of a
                                  nonmeasurable set  . . . . . . . . . . . 421--422
              Paul Bankston and   
                      Ralph Fox   Topological partitions of Euclidean
                                  space by spheres . . . . . . . . . . . . 423--424
                  John D. Dixon   Letter to the editor: ``Factorization
                                  and primality tests''  . . . . . . . . . 444--444

American Mathematical Monthly
Volume 92, Number 7, 1985

                   D. H. Lehmer   Interesting series involving the central
                                  binomial coefficient . . . . . . . . . . 449--457
                    T. A. McKee   The logic of graph-theoretic duality . . 457--464
              Marc Rogalski and   
             Jean Saint-Raymond   Inequalities about symmetric compact
                                  convex sets in the plane . . . . . . . . 466--480
             Lawrence J. Wallen   Modified iteration and probability . . . 481--485
                Alfonso Villani   Another note on the inclusion
                                  $L^p(\mu)\subset L^q(\mu)$ . . . . . . . 485--487
                M. Arala Chaves   Spaces where all continuity is uniform   487--489
                   Walter Rudin   Unique right inverses are two-sided  . . 489--490
                    Gunnar Blom   A simple property of exchangeable random
                                  variables  . . . . . . . . . . . . . . . 491--492
                     N. J. Lord   Simultaneous complements in
                                  finite-dimensional vector spaces . . . . 492--493
               N. Costa Pereira   A short proof of Chebyshev's theorem . . 494--495
                 Geng Zhe Chang   Planar metric inequalities derived from
                                  the Vandermonde determinant  . . . . . . 495--499
                 Jerome L. Paul   Combinatorial proofs of Pascal's formula
                                  for sums of powers of the integers . . . 499--501
                I. N. Baker and   
                   P. J. Rippon   A note on complex iteration  . . . . . . 501--504
                    Warren Page   Compactness and closedness in locally
                                  compact Hausdorff spaces . . . . . . . . 504--506
                James M. Ortega   Comment on: ``Matrices with integer
                                  entries and integer eigenvalues'' by
                                  J.-C. Renaud [Amer. Math. Monthly \bf 90
                                  (1983), no. 3, 202--203, MR 84c:15024 ]
                                  and ``Generation of test matrices by
                                  similarity transformations'' by Ortega
                                  [Comm. ACM \bf 7 (1964), 377--378, MR
                                  \bf 29 #5375]  . . . . . . . . . . . . . 526--526

American Mathematical Monthly
Volume 92, Number 8, 1985

                 N. N. Chan and   
                  Man Kam Kwong   Hermitian matrix inequalities and a
                                  conjecture . . . . . . . . . . . . . . . 533--541
             R. J. MacG. Dawson   Monostatic simplexes . . . . . . . . . . 541--546
                 G. R. Veldkamp   The isoperimetric point and the point(s)
                                  of equal detour in a triangle  . . . . . 546--558
                   I. M. Isaacs   Solution of polynomials by real radicals 571--575
             Haragauri N. Gupta   A theorem in combinatorics and Wilson's
                                  theorem  . . . . . . . . . . . . . . . . 575--576
               Roger C. Alperin   $p$-adic binomial coefficients mod $p$   576--578
          Michael D. Hirschhorn   A simple proof of Jacobi's two-square
                                  theorem  . . . . . . . . . . . . . . . . 579--580
            Donald P. Minassian   A simple structure theorem for
                                  two-generator, one-relation groups . . . 580--583
           Marvin Jay Greenberg   Correction to: ``Note on the
                                  Cayley--Hamilton theorem'' [Amer. Math.
                                  Monthly \bf 91 (1984), no. 3, 193--195,
                                  MR 85c:15023]  . . . . . . . . . . . . . 583--583
                Dale E. Varberg   Pick's theorem revisited . . . . . . . . 584--587
                Charles R. Wall   Unbounded sequences of Euler-Dedekind
                                  means  . . . . . . . . . . . . . . . . . 587--587

American Mathematical Monthly
Volume 92, Number 9, 1985

           Edward C. Turner and   
                  Karen F. Gold   Rubik's groups . . . . . . . . . . . . . 617--629
                      D. Spring   On the second derivative test for
                                  constrained local extrema  . . . . . . . 631--643
                  Morris Marden   The search for a Rolle's theorem in the
                                  complex domain . . . . . . . . . . . . . 643--650
                   Peter Hilton   On all sorts of automorphisms  . . . . . 650--656
                   Alan Shuchat   Generalized least squares and
                                  eigenvalues  . . . . . . . . . . . . . . 656--659
           James C. Owings, Jr.   A combinatorial proof of a criterion for
                                  normality  . . . . . . . . . . . . . . . 662--663

American Mathematical Monthly
Volume 92, Number 10, 1985

               P. J. Giblin and   
                 S. A. Brassett   Local symmetry of plane curves . . . . . 689--707
                   G. Gerla and   
                       R. Volpe   Geometry without points  . . . . . . . . 707--711
                James R. Weaver   Centrosymmetric (cross-symmetric)
                                  matrices, their basic properties,
                                  eigenvalues, and eigenvectors  . . . . . 711--717
                  Dean S. Clark   A combinatorial theorem on circulant
                                  matrices . . . . . . . . . . . . . . . . 725--729
            David E. Penney and   
                 Carl Pomerance   Multiplicative relations for sums of
                                  initial $k$th powers . . . . . . . . . . 729--731
               Eric L. Grinberg   On the smoothness hypothesis in Sard's
                                  theorem  . . . . . . . . . . . . . . . . 733--734


American Mathematical Monthly
Volume 93, Number 1, 1986

               I. J. Schoenberg   A conjectured analogue of Rolle's
                                  theorem for polynomials with real or
                                  complex coefficients . . . . . . . . . . 8--13
          J. M. De Villiers and   
                 P. N. Robinson   The interval of convergence and limiting
                                  functions of a hyperpower sequence . . . 13--23
                  Victor Namias   A simple derivation of Stirling's
                                  asymptotic series  . . . . . . . . . . . 25--29
         Albrecht Beutelspacher   $21-6=15$: a connection between two
                                  distinguished geometries . . . . . . . . 29--41
           Steven G. Krantz and   
                  T. D. Parsons   Antisocial subcovers of self-centered
                                  coverings  . . . . . . . . . . . . . . . 45--48
      Edwin H. Kaufman, Jr. and   
                Terry D. Lenker   Linear convergence and the bisection
                                  algorithm  . . . . . . . . . . . . . . . 48--51
          Ibrahim A. Salama and   
             Lawrence L. Kupper   A geometric interpretation for the
                                  Eulerian numbers . . . . . . . . . . . . 51--52
        Philip D. Straffin, Jr.   Letter to the editor: ``The diameter of
                                  a graph and its complement'' [Amer.
                                  Math. Monthly \bf 92 (1985), no. 3,
                                  211--212, MR 87j:05139a] by F. Harary
                                  and R. W. Robinson . . . . . . . . . . . 76--76

American Mathematical Monthly
Volume 93, Number 2, 1986

            Andrea Laforgia and   
              Martin E. Muldoon   Some consequences of the Sturm
                                  comparison theorem . . . . . . . . . . . 89--94
              William A. Chance   A geometric derivation of the
                                  distribution of the correlation
                                  coefficient $\vert r\vert $ when
                                  $\rho=0$ . . . . . . . . . . . . . . . . 94--98
             Thomas Tracy Allen   Pólya's orchard problem . . . . . . . . . 98--104
              Philip A. Leonard   Cyclic relative difference sets  . . . . 106--111
                    T. L. McCoy   On ``${\rm cos}\,f(x)=f({\rm sin}\,x)$'' 111--115
          Jack M. Robertson and   
               Andrew F. Siegel   Designing Buffon's needle for a given
                                  crossing distribution  . . . . . . . . . 116--119
Mícheál Ó Searcóid and   
                Desmond MacHale   Two elementary generalisations of
                                  Boolean rings  . . . . . . . . . . . . . 121--122
                P. Diaconis and   
                    D. Freedman   An elementary proof of Stirling's
                                  formula  . . . . . . . . . . . . . . . . 123--125
              L. E. Mattics and   
                     F. W. Dodd   A bound for the number of multiplicative
                                  partitions . . . . . . . . . . . . . . . 125--126
                  Curtis Cooper   Geometric series and a probability
                                  problem  . . . . . . . . . . . . . . . . 126--127

American Mathematical Monthly
Volume 93, Number 3, 1986

                 J. A. Eidswick   Cubelike puzzles --- what are they and
                                  how do you solve them  . . . . . . . . . 157--176
         E. J. P. Georg Schmidt   An alternative approach to canonical
                                  forms of matrices  . . . . . . . . . . . 176--184
                 Sandy Grabiner   The Tietze extension theorem and the
                                  open mapping theorem . . . . . . . . . . 190--191
               Joseph B. Keller   The probability of heads . . . . . . . . 191--197
                  T. D. Parsons   Ancestors, cardinals, and
                                  representatives  . . . . . . . . . . . . 197--200
                      A. Lenard   A note on Liouville's theorem  . . . . . 200--201
                  Kurt Eisemann   A self-dual card trick based on
                                  congruences and $k$-shuffles . . . . . . 201--205
                Donald E. Knuth   Solution to problem 6480, A Catalonian
                                  sum  . . . . . . . . . . . . . . . . . . 220--220
                    Peter Ungar   Review of three calculus textbooks . . . 221--230

American Mathematical Monthly
Volume 93, Number 4, 1986

                  Sheldon Axler   Harmonic functions from a complex
                                  analysis viewpoint . . . . . . . . . . . 246--258
                Joan Cleary and   
           Sidney A. Morris and   
                     David Yost   Numerical geometry --- numbers for
                                  shapes . . . . . . . . . . . . . . . . . 260--275
                  Charles Small   Sums of three squares and levels of
                                  quadratic number fields  . . . . . . . . 276--279
                Georges A. Lion   A simple proof of the Dirichlet--Jordan
                                  convergence test . . . . . . . . . . . . 281--282
                       Jan Turk   The fixed divisor of a polynomial  . . . 282--286
                    Rolf Brandl   Integer polynomials that are reducible
                                  modulo all primes  . . . . . . . . . . . 286--288
                   D. H. Lehmer   Coloring the Platonic solids . . . . . . 288--292
                     Ira Gessel   Letter to the editor: ``Trees and
                                  power-sums'' [Amer. Math. Monthly \bf 92
                                  (1985), no. 5, 328--331, MR 87e:05016a]
                                  by A. H. Stone . . . . . . . . . . . . . 323--324
            Steven H. Weintraub   Letter to the editor: ``Tricks or treats
                                  with the Hilbert matrix'' [Amer. Math.
                                  Monthly \bf 90 (1983), no. 5, 301--312,
                                  MR 84h:47031] by M. D. Choi  . . . . . . 324--324

American Mathematical Monthly
Volume 93, Number 5, 1986

               David Aldous and   
                 Persi Diaconis   Shuffling cards and stopping times . . . 333--348
                 Solomon Leader   What is a differential? A new answer
                                  from the generalized Riemann integral    348--356
                  Alan C. Wilde   Transformations leaving the determinant
                                  of circulant matrices invariant  . . . . 356--361
               Jaroslav Han\vcl   A simple proof of the irrationality of
                                  $\pi^4$  . . . . . . . . . . . . . . . . 374--375
            Thomas E. Cecil and   
                Patrick J. Ryan   The principal curvatures of the monkey
                                  saddle . . . . . . . . . . . . . . . . . 380--382
                  Robert Gilmer   Zero divisors in commutative rings . . . 382--387
             Yasuhiko Ikebe and   
              Toshiyuki Inagaki   An elementary approach to the functional
                                  calculus for matrices  . . . . . . . . . 390--392

American Mathematical Monthly
Volume 93, Number 6, 1986

             Sylvan Burgstahler   An algorithm for solving polynomial
                                  equations  . . . . . . . . . . . . . . . 421--430
                 Benjamin Kedem   A stochastic characterization of the
                                  sine function  . . . . . . . . . . . . . 430--440
                I. D. Macdonald   Commutators and their products . . . . . 440--444
                  R. Farwig and   
                       D. Zwick   A variation on the Landau problem  . . . 444--451
               A. W. F. Edwards   A quick route to sums of powers  . . . . 451--455
                  Gary L. Walls   Automorphism groups  . . . . . . . . . . 459--462
                    A. J. Bosch   The factorization of a square matrix
                                  into two symmetric matrices  . . . . . . 462--464
Tomás Domínguez Benavides   How many zeros does a continuous
                                  function have  . . . . . . . . . . . . . 464--466
                       Jet Wimp   Quadrature with generalized means  . . . 466--468
                    C. J. Smyth   A coloring proof of a generalisation of
                                  Fermat's little theorem  . . . . . . . . 469--471
                 A. H. M. Hoare   An involution of blocks in the
                                  partitions of $n$  . . . . . . . . . . . 475--476
              David F. Anderson   Letter to the editor: ``Solvability of
                                  infinite systems of polynomial equations
                                  over the field of complex numbers''
                                  [Amer. Math. Monthly \bf 92 (1985), no.
                                  2, 94--98, MR 86c:12004] by A. Abian . . 496--497
                  M. J. Pelling   Letter to the editor: ``Dini type
                                  theorems on positive series'' [Amer.
                                  Math. Monthly \bf 92 (1985), no. 5,
                                  347--349, MR 86m:40001] by P. Biler  . . 497--498

American Mathematical Monthly
Volume 93, Number 7, 1986

                    J. Korevaar   Ludwig Bieberbach's conjecture and its
                                  proof by Louis de Branges  . . . . . . . 505--514
          Kenneth P. Bogart and   
                 Peter G. Doyle   Nonsexist solution of the ménage problem  514--519
              David Borwein and   
            Jonathan M. Borwein   A note on alternating series in several
                                  dimensions . . . . . . . . . . . . . . . 531--539
         Rade T. \vZivaljevi\'c   Infinitesimals, microsimplexes and
                                  elementary homology theory . . . . . . . 540--544
                     S. Barnett   Forms of the resultant of two
                                  polynomials  . . . . . . . . . . . . . . 551--552
          Eliot T. Jacobson and   
                  Alan E. Parks   Infinite branches of the phi-tree  . . . 552--554
            Richard M. Aron and   
                 Gerd H. Fricke   Homomorphisms on $C({\bf R})$  . . . . . 555--555
                    Ka-Lam Kueh   A note on Kronecker's approximation
                                  theorem  . . . . . . . . . . . . . . . . 555--556
           J.-B. Hiriart-Urruty   When is a point $x$ satisfying $\nabla
                                  f(x)=0$ a global minimum of $f$  . . . . 556--558

American Mathematical Monthly
Volume 93, Number 8, 1986

                   Everett Howe   A new proof of Erdös' theorem on monotone
                                  multiplicative functions . . . . . . . . 593--595
         Richard P. Savage, Jr.   Graphical constructions of means . . . . 595--603
           David Farnsworth and   
                    Richard Orr   Gini means . . . . . . . . . . . . . . . 603--607
                 Robert L. Long   Remarks on the history and philosophy of
                                  mathematics  . . . . . . . . . . . . . . 609--619
                 George Maltese   A simple proof of the fundamental
                                  theorem of finite Markov chains  . . . . 629--630
               Charles S. Allen   A characterization of dimension  . . . . 635--636
                  G. B. Folland   On characterizations of analyticity  . . 640--641
                Richard D. Byrd   Simultaneous complements in
                                  finite-dimensional vector spaces . . . . 641--642
              Thomas L. Markham   Oppenheim's inequality for positive
                                  definite matrices  . . . . . . . . . . . 642--644
                 Colin R. Blyth   Convolutions of Cauchy distributions . . 645--647
                    M. Carchidi   A method for finding the eigenvectors of
                                  an $n\times n$ matrix corresponding to
                                  eigenvalues of multiplicity one  . . . . 647--649

American Mathematical Monthly
Volume 93, Number 9, 1986

                 H. P. Williams   Fourier's method of linear programming
                                  and its dual . . . . . . . . . . . . . . 681--695
                John Clough and   
                 Gerald Myerson   Musical scales and the generalized
                                  circle of fifths . . . . . . . . . . . . 695--701
               James E. Simpson   More trees and power sums  . . . . . . . 701--708
                H. Väliaho   An elementary approach to the Jordan
                                  form of a matrix . . . . . . . . . . . . 711--714
                      Beda Chan   An application of finite difference
                                  algebra  . . . . . . . . . . . . . . . . 716--717
               David Benson and   
                Walter Feit and   
                     Roger Howe   Finite linear groups, the Commodore 64,
                                  Euler and Sylvester  . . . . . . . . . . 717--719
                Erwin Kleinfeld   A class of rings which are very nearly
                                  associative  . . . . . . . . . . . . . . 720--722
                  Alan E. Parks   $\pi$, and $e$, and other irrational
                                  numbers  . . . . . . . . . . . . . . . . 722--723
              Michael W. Botsko   An easy generalization of the Riemann
                                  integral . . . . . . . . . . . . . . . . 728--732

American Mathematical Monthly
Volume 93, Number 10, 1986

                  Howard Hiller   Crystallography and cohomology of groups 765--779
               Barry W. Brunson   The partial order of iterated
                                  exponentials . . . . . . . . . . . . . . 779--786
            Joseph H. Silverman   Points of finite order on elliptic
                                  curves . . . . . . . . . . . . . . . . . 793--795
                   V. Faber and   
                   J. Mycielski   The shortest curve that meets all the
                                  lines that meet a convex body  . . . . . 796--801

American Mathematical Monthly
Volume 93, Number ??, 1987

                Donald E. Knuth   Problem 86-2, a random knockout
                                  tournament (with solution) . . . . . . . 127--129


American Mathematical Monthly
Volume 94, Number 1, 1987

                Herbert S. Wilf   A greeting: and a view of Riemann's
                                  hypothesis . . . . . . . . . . . . . . . 3--6
               Edward A. Bender   The number of three-dimensional convex
                                  polyhedra  . . . . . . . . . . . . . . . 7--21
                 Dan Kalman and   
                  Abraham Ungar   Combinatorial and functional identities
                                  in one-parameter matrices  . . . . . . . 21--35
                     Ranjan Roy   Binomial identities and hypergeometric
                                  series . . . . . . . . . . . . . . . . . 36--46
                Alan F. Beardon   Curvature, circles, and conformal maps   48--53
             William C. Calhoun   Counting the subgroups of some finite
                                  groups . . . . . . . . . . . . . . . . . 54--59
                  Wells Johnson   The Diophantine equation $X^2+7=2^n$ . . 59--62
              Susan Jane Colley   The tumbling box . . . . . . . . . . . . 62--68
                 Donald Sarason   The multiplication theorem for Fredholm
                                  operators  . . . . . . . . . . . . . . . 68--70

American Mathematical Monthly
Volume 94, Number 2, 1987

                    F. K. Hwang   A tale of two coins  . . . . . . . . . . 121--129
          Steven C. Althoen and   
              Renate McLaughlin   Gauss--Jordan reduction: a brief history 130--142
                  Don Pelletier   Merlin's magic square  . . . . . . . . . 143--150
                    Joseph Zaks   Neighborly families of congruent convex
                                  polytopes  . . . . . . . . . . . . . . . 151--155
                   Anatole Beck   Constructing a fair border . . . . . . . 157--162
                Desmond MacHale   An anticommutativity consequence of a
                                  ring commutativity theorem of Herstein   162--165
Mícheál Ó Searcóid   A reordering of the Sylow theorems . . . 165--168
              P. Erdös and   
         P. P. Pálfy and   
                     M. Szegedy   $a\pmod {p}\leq b\pmod {p}$ for all
                                  primes $p$ implies $a=b$ . . . . . . . . 169--170
                 E. B. Saff and   
                  Jon C. Snader   The error for quadrature methods: a
                                  complex variables approach . . . . . . . 175--180
                Donald E. Knuth   Solution to problem E3061, Empty cells   189

American Mathematical Monthly
Volume 94, Number 3, 1987

               Steven G. Krantz   What is several complex variables  . . . 236--256
             Richard A. Brualdi   The Jordan canonical form: an old proof  257--267
                Herbert S. Wilf   Finite lists of obstructions . . . . . . 267--271
                Takayuki Furuta   A counterexample to a conjectured
                                  Hermitian matrix inequality  . . . . . . 271--272
                    R. B. Paris   An asymptotic approximation connected
                                  with the golden number . . . . . . . . . 272--278
            C. E. van der Ploeg   Duality in nonnormal quartic fields  . . 279--284
               Edward R. Rozema   Romberg integration by Taylor series . . 284--288
                  James Rovnyak   Note on characteristic polynomials . . . 289--290
                 I. N. Herstein   A remark on finite fields  . . . . . . . 290--291
          Robert Lee Taylor and   
                  Tien Chung Hu   Sub-Gaussian techniques in proving
                                  strong laws of large numbers . . . . . . 295--299

American Mathematical Monthly
Volume 94, Number 4, 1987

              James F. Epperson   On the Runge example . . . . . . . . . . 329--341
                Peter Rosenthal   The remarkable theorem of Lévy and
                                  Steinitz . . . . . . . . . . . . . . . . 342--351
             Yasuhiko Ikebe and   
          Toshiyuki Inagaki and   
               Sadaaki Miyamoto   The monotonicity theorem, Cauchy's
                                  interlace theorem, and the
                                  Courant-Fischer theorem  . . . . . . . . 352--354
                   J. B. Wilker   The $n$th derivative as a limit  . . . . 354--356
                  Bong Dae Choi   Limiting distribution for the
                                  generalized matching problem . . . . . . 356--360

American Mathematical Monthly
Volume 94, Number 5, 1987

                    Nina M. Roy   Extreme points of convex sets in
                                  infinite-dimensional spaces  . . . . . . 409--422
                  J. G. Mauldon   A matrix with applications to random
                                  walk, Brownian motion, and ring theory   423--436
             Lawrence J. Wallen   All the way with Wirtinger: a short
                                  proof of Bonnesen's inequality . . . . . 440--442
                Gerald Beer and   
              Luzviminda Villar   When is a free union of regular measures
                                  regular  . . . . . . . . . . . . . . . . 443--445
                     John Petro   Real division algebras of dimension $>1$
                                  contain ${\bf C}$  . . . . . . . . . . . 445--449

American Mathematical Monthly
Volume 94, Number 6, 1987

                 William Miller   The maximum order of an element of a
                                  finite symmetric group . . . . . . . . . 497--506
             William S. Zwicker   Playing games with games: the hypergame
                                  paradox  . . . . . . . . . . . . . . . . 507--514
                     John McKay   On computing discriminants . . . . . . . 523--527
                       D. Zwick   Best approximation by convex functions   528--534
            Detlef Laugwitz and   
                 Bernd Rodewald   A simple characterization of the gamma
                                  function . . . . . . . . . . . . . . . . 534--536

American Mathematical Monthly
Volume 94, Number 7, 1987

                     Stan Wagon   Fourteen proofs of a result about tiling
                                  a rectangle  . . . . . . . . . . . . . . 601--617
            Mark E. Kidwell and   
               R. Bruce Richter   Trees and Euler tours in a planar graph
                                  and its relatives  . . . . . . . . . . . 618--630
                Peter M. Maurer   A rose is a rose$\ldots$ . . . . . . . . 631--645
              Susan Jane Colley   Correction: ``The tumbling box'' [Amer.
                                  Math. Monthly \bf 94 (1987), no. 1,
                                  62--68, MR 88b:53010]  . . . . . . . . . 646--646
                Lyle E. Pursell   Comment: ``Homomorphisms on $C({\bf
                                  R})$'' [Amer. Math. Monthly 93 (1986),
                                  no. 7, 555, MR 87i:46109] by R. M. Aron
                                  and G. H. Fricke . . . . . . . . . . . . 646--646
               Helaman Ferguson   Generalization of some algorithms of
                                  Euler  . . . . . . . . . . . . . . . . . 647--652
          Charles Vanden Eynden   Applications of a product identity to
                                  sums of squares and partitions . . . . . 652--656
                   T. M. Cronin   The construction of matrices with
                                  required properties over the integers    656--662
                   Boo Rim Choe   An elementary proof of
                                  $\sum^\infty_{n=1}1/n^2=\pi^2/6$ . . . . 662--663
                Michael Hoffman   An invariant of finite abelian groups    664--666

American Mathematical Monthly
Volume 94, Number 8, 1987

                Arthur T. White   Ringing the cosets . . . . . . . . . . . 721--746
                  Paul R. Scott   The fascination of the elementary  . . . 759--768
            Melvyn B. Nathanson   A generalization of the
                                  Goldbach-Shnirel\cprimeman theorem . . . 768--771
                   I. Korec and   
               \vS. Znám   A note on the $3x+1$ problem . . . . . . 771--772

American Mathematical Monthly
Volume 94, Number 9, 1987

     Claudio Martins Mendes and   
    Maria Aparecida Soares Ruas   Hyperbolic motions of conics . . . . . . 825--845
                Dennis Kletzing   Rational representations of finite
                                  groups: the story of $\gamma$  . . . . . 846--854
                Herbert S. Wilf   The editor's corner: strings,
                                  substrings, and the ``nearest integer''
                                  function . . . . . . . . . . . . . . . . 855--860
                Arthur Benjamin   The bisection method: which root . . . . 861--863
                Alfonso Villani   Spaces with locally compact completions
                                  are compact  . . . . . . . . . . . . . . 863--865
                  R. J. Simpson   Disjoint covering systems of congruences 865--868
                 C. Johnson and   
               G. Wolkowicz and   
                   H. Wolkowicz   Elem. Prob. E. 3234  . . . . . . . . . . 877

American Mathematical Monthly
Volume 94, Number 10, 1987

                 Barry A. Cipra   An introduction to the Ising model . . . 937--959
                David E. Freund   Selecting estimators for the standard
                                  deviation of a normal distribution . . . 971--975
               Philippe Tondeur   Barycentric representation for the
                                  incenter and excenters of a triangle . . 975--976
            Donald P. Minassian   The arithmetic-geometric mean inequality
                                  revisited: elementary calculus and
                                  negative numbers . . . . . . . . . . . . 977--978
                Henry Heatherly   Matrices satisfying $AB-BA=I$  . . . . . 979--980
                Roger B. Nelsen   Consequences of the memoryless property
                                  for random variables . . . . . . . . . . 981--984
               Edward A. Bender   Errata: ``The number of
                                  three-dimensional convex polyhedra''
                                  [Amer. Math. Monthly \bf 94 (1987), no.
                                  1, 7--21, MR 88b:52010]  . . . . . . . . 994--994
             S. Elwood Bohn and   
                       Jong Lee   Errata: ``Semitopological groups''
                                  [Amer. Math. Monthly \bf 72 (1965),
                                  996--998, MR \bf 32 #7672] . . . . . . . 994--994
            C. E. van der Ploeg   Errata: ``Duality in nonnormal quartic
                                  fields'' [Amer. Math. Monthly \bf 94
                                  (1987), no. 3, 279--284] . . . . . . . . 994--994


American Mathematical Monthly
Volume 95, Number 1, 1988

         Gerald L. Alexanderson   Award for distinguished service to
                                  Professor Murray Klamkim . . . . . . . . 1--4
       Branko Grünbaum and   
                 G. C. Shephard   Isonemal fabrics . . . . . . . . . . . . 5--30
              Gary S. Bloom and   
            John W. Kennedy and   
               Louis V. Quintas   A characterization of graphs of diameter
                                  two  . . . . . . . . . . . . . . . . . . 37--38
                   Elon L. Lima   The Jordan-Brouwer separation theorem
                                  for smooth hypersurfaces . . . . . . . . 39--42
                Peter A. Fowler   The Königsberg bridges---250 years later  42--43
           Donald J. Newman and   
                  T. D. Parsons   On monotone subsequences . . . . . . . . 44--45

American Mathematical Monthly
Volume 95, Number 2, 1988

                Ralph Kopperman   All topologies come from generalized
                                  metrics  . . . . . . . . . . . . . . . . 89--97
              George W. Polites   Prime desert $n$-tuplets . . . . . . . . 98--104
          Klaus E. Eldridge and   
                    Seok Sagong   The determination of Kaprekar
                                  convergence and loop convergence of all
                                  three-digit numbers  . . . . . . . . . . 105--112
                  I. Bouwer and   
                        Z. Star   A question of protocol . . . . . . . . . 118--121
                    John Beebee   Examples of infinite, incongruent exact
                                  covers . . . . . . . . . . . . . . . . . 121--123
        David J. Hallenbeck and   
         Katarzyna Tkaczy\'nska   The absolute and uniform convergence of
                                  infinite improper integrals  . . . . . . 124--126
             Ashok K. Arora and   
             Sudhir K. Goel and   
            Dennis M. Rodriguez   Special integration techniques for
                                  trigonometric integrals  . . . . . . . . 126--130

American Mathematical Monthly
Volume 95, Number 3, 1988

              Andrew M. Gleason   Angle trisection, the heptagon, and the
                                  triskaidecagon . . . . . . . . . . . . . 185--194
              Louis H. Kauffman   New invariants in the theory of knots    195--242
          Joseph A. Gallian and   
            Douglas S. Jungreis   Homomorphisms from $Z_m[i]$ into
                                  $Z_n[i]$ and $Z_m[\rho]$ into
                                  $Z_n[\rho],$ where $i^2+1=0$ and
                                  $\rho^2+\rho+1=0$  . . . . . . . . . . . 247--249
              Michael W. Botsko   An elementary proof that a bounded a.e.
                                  continuous function is Riemann
                                  integrable . . . . . . . . . . . . . . . 249--252

American Mathematical Monthly
Volume 95, Number 4, 1988

                Jon Froemke and   
            Jerrold W. Grossman   An algebraic approach to some
                                  number-theoretic problems arising from
                                  paper-folding regular polygons . . . . . 289--307
                     Ilan Vardi   Integrals, an introduction to analytic
                                  number theory  . . . . . . . . . . . . . 308--315
         Lewis C. Robertson and   
         Rae Michael Shortt and   
              Stephen G. Landry   Dice with fair sums  . . . . . . . . . . 316--328
            Lawrence Neff Stout   Two discrete forms of the Jordan curve
                                  theorem  . . . . . . . . . . . . . . . . 332--336
               Mohd. Ashraf and   
          Murtaza A. Quadri and   
                Daniel Zelinsky   Some polynomial identities that imply
                                  commutativity for rings  . . . . . . . . 336--339
                Hale F. Trotter   An overlooked example of nonunique
                                  factorization  . . . . . . . . . . . . . 339--342
               P. V. Krishnaiah   Two counterexamples in general topology  342--343
                  Benno Artmann   A simple proof for the simplicity of
                                  $A_5$  . . . . . . . . . . . . . . . . . 344--349

American Mathematical Monthly
Volume 95, Number 5, 1988

                   S. P. Lalley   The ``prime number theorem'' for the
                                  periodic orbits of a Bernoulli flow  . . 385--398
            Wm. Douglas Withers   Folding polynomials and their dynamics   399--413
                  I. E. Leonard   More on Fresnel integrals  . . . . . . . 431--433
                 Gary A. Martin   A class of abelian groups arising from
                                  an analysis of a proof . . . . . . . . . 433--436
                     John Schue   The Wedderburn theorem of finite
                                  division rings . . . . . . . . . . . . . 436--437
               Theodore P. Hill   Common hyperplane medians for random
                                  vectors  . . . . . . . . . . . . . . . . 437--441
                   David A. Cox   Quadratic reciprocity: its conjecture
                                  and application  . . . . . . . . . . . . 442--448
                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

                   Jane Day and   
                 Brian Peterson   Growth in Gaussian elimination . . . . . 489--513
              Stephen D. Fisher   The Möbius group and invariant spaces of
                                  analytic functions . . . . . . . . . . . 514--527
               Brian Conrey and   
                     Amit Ghosh   On the zeros of the Taylor polynomials
                                  associated with the exponential function 528--533
                   J. G. Wendel   Shanks' identity is elementary . . . . . 534--534
                  M. J. Pelling   Letter to the editor . . . . . . . . . . 535--536
                 J. Fabrykowski   On continued fractions and a certain
                                  example of a sequence of continuous
                                  functions  . . . . . . . . . . . . . . . 537--539
                   W. S. Anglin   Using Pythagorean triangles to
                                  approximate angles . . . . . . . . . . . 540--541
              Gerald Wildenberg   Convergence-preserving functions . . . . 542--544
                  David W. Boyd   The Diophantine equation
                                  $x^2+y^m=z^{2n}$ . . . . . . . . . . . . 544--547

American Mathematical Monthly
Volume 95, Number 7, 1988

              Gert Almkvist and   
                   Bruce Berndt   Gauss, Landen, Ramanujan, the
                                  arithmetic-geometric mean, ellipses,
                                  $\pi$, and the Ladies diary  . . . . . . 585--608
           John G. Kingston and   
                  John L. Synge   The sequence of pedal triangles  . . . . 609--620
                  Charles Small   Magic squares over fields  . . . . . . . 621--625
         Janet Crandell Tremain   The Jerusalem ticket problem . . . . . . 626--630
          Kiran B. Chilakamarri   Decomposition of bipartite graphs into
                                  paths  . . . . . . . . . . . . . . . . . 634--636
                    W. V. Quine   Fermat's last theorem in combinatorial
                                  form . . . . . . . . . . . . . . . . . . 636--636
                 Andrew Simoson   A difference equation for strings of
                                  ones . . . . . . . . . . . . . . . . . . 636--638
                    Alec Norton   Continued fractions and
                                  differentiability of functions . . . . . 639--643
                Donald E. Knuth   Solution to problem E3166, A polynomial
                                  identity . . . . . . . . . . . . . . . . 662--663

American Mathematical Monthly
Volume 95, Number 8, 1988

         Nicholas D. Kazarinoff   Special functions and the Bieberbach
                                  conjecture . . . . . . . . . . . . . . . 689--696
                 Richard K. Guy   The strong law of small numbers  . . . . 697--712
              John Mitchell and   
                   Lee A. Rubel   Every smooth map of Euclidean space into
                                  itself is an expansion followed by a
                                  contraction  . . . . . . . . . . . . . . 713--716
                G. L. Cohen and   
                    G. H. Smith   A simple verification of Ilieff's
                                  conjecture for polynomials with three
                                  zeros  . . . . . . . . . . . . . . . . . 734--737
                    Gerald Beer   UC spaces revisited  . . . . . . . . . . 737--739
                 G. N. Hile and   
                      R. Z. Yeh   Line integrals of higher-order
                                  derivatives  . . . . . . . . . . . . . . 739--744
                     James Chew   A note on closure continuity . . . . . . 744--745
            Donald E. Knuth and   
                     Ilan Vardi   Advanced problem 6581, the asymptotic
                                  expansion of the middle binomial
                                  coefficient  . . . . . . . . . . . . . . 774

American Mathematical Monthly
Volume 95, Number 9, 1988

                   Olga Taussky   How I became a torchbearer for matrix
                                  theory . . . . . . . . . . . . . . . . . 801--812
                   Frank Morgan   Area-minimizing surfaces, faces of
                                  Grassmannians, and calibrations  . . . . 813--822
                  Robert Brooks   Constructing isospectral manifolds . . . 823--839
               V. J. Baston and   
                  F. A. Bostock   A simple cover-up game . . . . . . . . . 850--854
                   Fa Sheng Liu   A note on probabilities in proofreading  854--854
               Michael I. Rosen   A proof of the Lucas-Lehmer test . . . . 855--856
            J. Aczél and   
               Zs. Páles   The behaviour of means under equal
                                  increments of their variables  . . . . . 856--860
                  Peter Andrews   The classification of surfaces . . . . . 861--867
        Oscar A. Cámpoli   A principal ideal domain that is not a
                                  Euclidean domain . . . . . . . . . . . . 868--871

American Mathematical Monthly
Volume 95, Number 10, 1988

                   D. H. Lehmer   A new approach to Bernoulli polynomials  905--911
              Andrew M. Gleason   Addenda: ``Angle trisection, the
                                  heptagon, and the triskaidecagon''
                                  [Amer. Math. Monthly \bf 95 (1988), no.
                                  3, 185--194, MR 89d:51028] . . . . . . . 911--911
                   Doug Hensley   Errata: ``On continued fractions and a
                                  certain example of a sequence of
                                  continuous functions'' [Amer. Math.
                                  Monthly \bf 95 (1988), no. 6, 537--539,
                                  MR 89i:40001] by J. Fabrykowski  . . . . 911--911
    Donna Crystal Llewellyn and   
                Craig Tovey and   
                  Michael Trick   Finding saddlepoints of two-person, zero
                                  sum games  . . . . . . . . . . . . . . . 912--918
                 Ronald V. Book   Dehn's algorithm and the complexity of
                                  word problems  . . . . . . . . . . . . . 919--925
                      X.-B. Lin   Another brief proof of the Sylvester
                                  theorem  . . . . . . . . . . . . . . . . 932--933
                Takayuki Furuta   $A\geq B\geq 0$ ensures
                                  $(BA^2B)^{1/2}\geq B^2$---solution to a
                                  conjecture on operator inequalities  . . 933--934
                   Steven Landy   A generalization of Ceva's theorem to
                                  higher dimensions  . . . . . . . . . . . 936--939
            S. Ramakrishnan and   
                 W. D. Sudderth   A sequence of coin toss variables for
                                  which the strong law fails . . . . . . . 939--941
             Jonathan Lewin and   
                   Myrtle Lewin   A simple test for the $n$th term of a
                                  series to approach zero  . . . . . . . . 942--942
              K. D. Magill, Jr.   Universal topological spaces . . . . . . 942--946
             Richard C. Gilbert   Companion matrices with integer entries
                                  and integer eigenvalues and eigenvectors 947--950
              Larry J. Gerstein   A new algorithm for computing the rank
                                  of a matrix  . . . . . . . . . . . . . . 950--952


American Mathematical Monthly
Volume 96, Number ??, 1989

                Donald E. Knuth   Elementary problem E3303, a binary
                                  summation  . . . . . . . . . . . . . . . 54
                Donald E. Knuth   Elementary problem E3309, a binomial
                                  coefficient inequality . . . . . . . . . 154
                Donald E. Knuth   Elementary problem E3335, a deranged
                                  recurrence . . . . . . . . . . . . . . . 525
                Donald E. Knuth   Solution to Elementary problem E2982, a
                                  double infinite sum for $\vert x\vert$   525--526

American Mathematical Monthly
Volume 96, Number 1, 1989

                   Kenneth Ross   Award for distinguished service to Ivan
                                  Niven  . . . . . . . . . . . . . . . . . 3--4
          Stavros Busenberg and   
               David Fisher and   
                 Mario Martelli   Minimal periods of discrete and smooth
                                  orbits . . . . . . . . . . . . . . . . . 5--17
              Andrew J. Lazarus   Letter to the editor: ``Duality in
                                  nonnormal quartic fields'' [Amer. Math.
                                  Monthly \bf 94 (1987), no. 3, 279--284,
                                  MR 88j:11064 and errata, MR 89c:11156]
                                  by C. E. van der Ploeg . . . . . . . . . 17--17
              T. W. Gamelin and   
                   D. Khavinson   The isoperimetric inequality and
                                  rational approximation . . . . . . . . . 18--30
   Lillian E. Peters Hupert and   
                   Anne Leggett   On the square roots of infinite matrices 34--38
                   Lewis Pakula   A note on Venn diagrams  . . . . . . . . 38--39
                 Steve Ligh and   
                      Jiang Luh   Direct sum of $J$-rings and zero rings   40--41
                    J. M. Patin   A very short proof of Stirling's formula 41--42
                    Adolf Mader   A Euclidean model for Euclidean geometry 43--49
            Anthony Osborne and   
                   Hans Liebeck   Orthogonal bases of ${\bf {R}}^3$ with
                                  integer coordinates and integer lengths  49--53

American Mathematical Monthly
Volume 96, Number 2, February, 1989

                 Gilbert Strang   Patterns in linear algebra . . . . . . . 105--117
           Curtis N. Cooper and   
              Robert E. Kennedy   Chebyshev's inequality and natural
                                  density  . . . . . . . . . . . . . . . . 118--124
              P. T. Bateman and   
            J. L. Selfridge and   
            S. S. Wagstaff, Jr.   The new Mersenne conjecture  . . . . . . 125--128
                  S. F. Bockman   Generalizing the formula for areas of
                                  polygons to moments  . . . . . . . . . . 131--132
      Luise-Charlotte Kappe and   
                   Bette Warren   An elementary test for the Galois group
                                  of a quartic polynomial  . . . . . . . . 133--137
                    R. B. Bapat   Comparing the spectral radii of two
                                  nonnegative matrices . . . . . . . . . . 137--139

American Mathematical Monthly
Volume 96, Number 3, 1989

              J. M. Borwein and   
              P. B. Borwein and   
                   D. H. Bailey   Ramanujan, modular equations, and
                                  approximations to pi, or How to compute
                                  one billion digits of pi . . . . . . . . 201--219
                J. Lawrence and   
                   G. E. Simons   Equations in division rings --- a survey 220--232
               Gerald Leibowitz   Letters to the editor: ``Special
                                  integration techniques for trigonometric
                                  integrals'' [Amer. Math. Monthly \bf 95
                                  (1988), no. 2, 126--130, MR 89e:26004]
                                  by A. K. Arora, S. K. Goel and D. M.
                                  Rodriguez  . . . . . . . . . . . . . . . 232--232
           J. R. Sangwine-Yager   The missing boundary of the Blaschke
                                  diagram  . . . . . . . . . . . . . . . . 233--237
                S. J. Blank and   
           Nishan Krikorian and   
                   David Spring   A geometrically inspired proof of the
                                  singular value decomposition . . . . . . 238--239
               Craig Bailey and   
               R. Bruce Richter   Sum zero (mod $n$), size $n$ subsets of
                                  integers . . . . . . . . . . . . . . . . 240--242
                 John Crowe and   
               Dominick Samperi   On open maps . . . . . . . . . . . . . . 242--243
               Doron Zeilberger   On a conjecture of R. J. Simpson about
                                  exact covering congruences: ``Disjoint
                                  covering systems of congruences'' [Amer.
                                  Math. Monthly \bf 94 (1987), no. 9,
                                  865--868, MR 89b:11006]  . . . . . . . . 243--243

American Mathematical Monthly
Volume 96, Number 4, 1989

                   Narain Gupta   On groups in which every element has
                                  finite order . . . . . . . . . . . . . . 297--308
               Ani Adhikari and   
                     Jim Pitman   The shortest planar arc of width $1$ . . 309--327
              Michael W. Botsko   The use of full covers in real analysis  328--333
             Persi Diaconis and   
               Joseph B. Keller   Fair dice  . . . . . . . . . . . . . . . 337--339
               John B. Cosgrave   A remark on Euclid's proof of the
                                  infinitude of primes . . . . . . . . . . 339--341
              Felipe Cucker and   
      Antonio Gonzalez Corbalan   An alternate proof of the continuity of
                                  the roots of a polynomial  . . . . . . . 342--345
                 H. B. Thompson   Taylor's theorem using the generalized
                                  Riemann integral . . . . . . . . . . . . 346--350

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
                  John McCleary   How not to prove Fermat's last theorem   410--420
                   Lee A. Rubel   The editor's corner: summability theory:
                                  a neglected tool of analysis . . . . . . 421--423
                  Guy David and   
                   Carlos Tomei   The problem of the calissons . . . . . . 429--431
          Jean-Pierre Rosay and   
                   Walter Rudin   Arakelian's approximation theorem  . . . 432--434
                   I. J. Maddox   The norm of a linear functional  . . . . 434--436
             Richard C. Bradley   An elementary treatment of the
                                  Radon--Nikodým derivative . . . . . . . . 437--440
                Albert Wilansky   On the proof of the Radon--Nikodým
                                  theorem  . . . . . . . . . . . . . . . . 441--441
        Christopher L. Thompson   Nonstandard continuity and uniform
                                  convergence  . . . . . . . . . . . . . . 443--444

American Mathematical Monthly
Volume 96, Number 6, 1989

           Richard Anderson and   
László Lovász and   
                 Peter Shor and   
               Joel Spencer and   
          Éva Tardos and   
                Shmuel Winograd   Disks, balls, and walls: analysis of a
                                  combinatorial game . . . . . . . . . . . 481--493
           Jacob E. Goodman and   
          János Pach and   
                    Chee-K. Yap   Mountain climbing, ladder moving, and
                                  the ring-width of a polygon  . . . . . . 494--510
                   David Callan   Letter to the editor: ``A new approach
                                  to Bernoulli polynomials'' [Amer. Math.
                                  Monthly \bf 95 (1988), no. 10, 905--911,
                                  MR 90c:11014] by D. H. Lehmer  . . . . . 510--510
                Roger B. Nelsen   Letter to the editor: ``A very short
                                  proof of Stirling's formula'' [Amer.
                                  Math. Monthly \bf 96 (1989), no. 1,
                                  41--42, MR 90e:33005a] by J. M. Patin    510--511
               Albert A. Mullin   Letter to the editor: ``The new Mersenne
                                  conjecture'' [Amer. Math. Monthly \bf 96
                                  (1989), no. 2, 125--128, MR 90c:11009]
                                  by P. T. Bateman, J. L. Selfridge and S.
                                  S. Wagstaff, Jr  . . . . . . . . . . . . 511--511
                  Roger Pinkham   Letter to the editor: ``A simple test
                                  for the $n$th term of a series to
                                  approach zero'' [Amer. Math. Monthly \bf
                                  95 (1988), no. 10, 942] by J. Lewin and
                                  M. Lewin . . . . . . . . . . . . . . . . 511--511
                  Joel M. Cohen   Monotone multiplicative functions  . . . 512--513
                     W. J. Wong   Powers of a prime dividing binomial
                                  coefficients . . . . . . . . . . . . . . 513--517
                   Derming Wang   The polar decomposition and a matrix
                                  inequality . . . . . . . . . . . . . . . 517--519

American Mathematical Monthly
Volume 96, Number 7, 1989

            Paul Erdös and   
             Dean Hickerson and   
              János Pach   A problem of Leo Moser about repeated
                                  distances on the sphere  . . . . . . . . 569--575
        Faruk F. Abi-Khuzam and   
            Artin B. Boghossian   Some recent geometric inequalities . . . 576--589
               Doron Zeilberger   Kathy O'Hara's constructive proof of the
                                  unimodality of the Gaussian polynomials  590--602
         David R. Arterburn and   
             William Dean Stone   A Cantor set of nonconvergence . . . . . 604--608
                Daniel L. Stock   Merlin's magic square revisited  . . . . 608--610
                David C. Fisher   The number of words of length $n$ in a
                                  graph monoid . . . . . . . . . . . . . . 610--614
       Herbert Edelsbrunner and   
               Steven S. Skiena   On the number of furthest neighbour
                                  pairs in a point set . . . . . . . . . . 614--618
                   E. T. Y. Lee   A remark on divided differences  . . . . 618--622

American Mathematical Monthly
Volume 96, Number 8, 1989

              J. M. Borwein and   
              P. B. Borwein and   
                     K. Dilcher   Pi, Euler numbers, and asymptotic
                                  expansions . . . . . . . . . . . . . . . 681--687
                    M. C. Irwin   Geometry of continued fractions  . . . . 696--703
                Herbert S. Wilf   The editor's corner: the white screen
                                  problem  . . . . . . . . . . . . . . . . 704--707
                  Peter F. Zoll   Letter to the editor . . . . . . . . . . 709--710
            Larry W. Cusick and   
               Peter Tannenbaum   Fixed points of the twisted cyclic shift
                                  operator . . . . . . . . . . . . . . . . 713--717
             Eric K. van Douwen   Fubini's theorem for null sets . . . . . 718--721
                Richard Bassein   An optimization problem  . . . . . . . . 721--725
                R. E. Lewkowicz   A characterization of a class of
                                  composition operators  . . . . . . . . . 725--726

American Mathematical Monthly
Volume 96, Number 9, 1989

                   Lee A. Rubel   A survey of transcendentally
                                  transcendental functions . . . . . . . . 777--788
                  K. Bezdek and   
                    R. Connelly   Covering curves by translates of a
                                  convex set . . . . . . . . . . . . . . . 789--806
                   Alan Horwitz   Reconstructing a function from its set
                                  of tangent lines . . . . . . . . . . . . 807--813
                  Hugh Thurston   Can a graph be both continuous and
                                  discontinuous  . . . . . . . . . . . . . 814--815
                  Shmuel Rosset   Normalized symmetric functions, Newton's
                                  inequalities and a new set of stronger
                                  inequalities . . . . . . . . . . . . . . 815--819
                    N. Alon and   
                I. Krasikov and   
                       Y. Peres   Reflection sequences . . . . . . . . . . 820--823
                   Yoram Sagher   Counting the rationals . . . . . . . . . 823--823
                 Isom H. Herron   The radius of convergence of power
                                  series solutions to linear differential
                                  equations  . . . . . . . . . . . . . . . 824--827
              James F. Epperson   On the use of iteration methods for
                                  approximating the natural logarithm  . . 831--835
             William F. Dowling   There are no safe virus tests  . . . . . 835--836

American Mathematical Monthly
Volume 96, Number 10, 1989

                J. Marshall Ash   Uniqueness of representation by
                                  trigonometric series . . . . . . . . . . 873--885
                John S. Lew and   
         Donald A. Quarles, Jr.   Optimal inscribed polygons in convex
                                  curves . . . . . . . . . . . . . . . . . 886--902
                  A. Tsarpalias   A version of Rouché's theorem of
                                  continuous functions . . . . . . . . . . 911--913
              Victor Pambuccian   Another example of an exotic function    913--914
              Kenneth P. Bogart   A fresh(man) treatment of determinants   915--920
             Joseph J. Rushanan   On the Vandermonde matrix  . . . . . . . 921--924
                    F. C. Leary   Rings with invertible regular elements   924--926


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--927

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

            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

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

                  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

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

                Donald E. Knuth   Solution to Advanced problem 6581, the
                                  asymptotic expansion of the middle
                                  binomial coefficient . . . . . . . . . . 629--630


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

               Albert Nijenhuis   Solution to Elementary problem E3267, a
                                  solitaire game . . . . . . . . . . . . . 292--294


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

            Victor Adamchik and   
                     Stan Wagon   A Simple Formula for $\pi$ . . . . . . . 852--855


Communications of the ACM
Volume 7, Number 6, June, 1964

                James M. Ortega   Generation of test matrices by
                                  similarity transformations . . . . . . . 377--378


Lecture Notes in Computer Science
Volume 122, 1981

                Donald E. Knuth   Algorithms in modern mathematics and
                                  computer science . . . . . . . . . . . . 82--99


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