Table of contents for issues of American Mathematical Monthly

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Volume 79, Number 7, September, 1972
Volume 79, Number 8, October, 1972
Volume 79, Number 10, December, 1972
Volume 81, Number ??, April, 1974
Volume 81, 1974
Volume 82, 1975
Volume 83, 1976
Volume 84, 1977
Volume 85, Number 1, 1978
Volume 85, Number 2, 1978
Volume 85, Number 4, 1978
Volume 85, Number 5, 1978
Volume 85, 1978
Volume 85, Number 6, 1978
Volume 85, Number 7, 1978
Volume 85, Number 8, 1978
Volume 85, 1978
Volume 85, Number 9, 1978
Volume 85, Number 10, 1978
Volume 85, Number 2, 1978
Volume 85, Number ??, 1978
Volume 86, Number 1, 1979
Volume 86, Number 2, 1979
Volume 86, Number 3, 1979
Volume 86, Number 4, 1979
Volume 86, Number 5, 1979
Volume 86, Number 6, 1979
Volume 86, Number 7, 1979
Volume 86, Number 8, 1979
Volume 86, Number 9, 1979
Volume 86, Number 10, 1979
Volume 87, Number 10, 1980
Volume 87, Number 1, 1980
Volume 88, Number 5, 1981
Volume 88, Number 10, 1981


American Mathematical Monthly
Volume 79, Number 7, September, 1972

                Donald E. Knuth   Sequences with precisely $k+1$
                                  $k$-blocks: Solution to Problem E2307    773--774

American Mathematical Monthly
Volume 79, Number 8, October, 1972

                Donald E. Knuth   Schröder's problem: Solution to Problem
                                  E2315  . . . . . . . . . . . . . . . . . 910

American Mathematical Monthly
Volume 79, Number 10, December, 1972

                Donald E. Knuth   Groups: Solution to Problem E2328  . . . 1138--1139


American Mathematical Monthly
Volume 81, Number ??, April, 1974

                Donald E. Knuth   Computer Science and its Relation to
                                  Mathematics  . . . . . . . . . . . . . . 323--343

American Mathematical Monthly
Volume 81, 1974

                Donald E. Knuth   Elementary Problem E2492 (binomial
                                  coefficients and mods) . . . . . . . . . 902


American Mathematical Monthly
Volume 82, 1975

                Donald E. Knuth   Solution to Elementary Problem E2492
                                  (binomial coefficients and mods) . . . . 855
                Donald E. Knuth   Problem 6049 (cyclic permutation
                                  generators)  . . . . . . . . . . . . . . 856
                Donald E. Knuth   Problem 6050 (random maximization) . . . 856


American Mathematical Monthly
Volume 83, 1976

                Donald E. Knuth   Elementary Problem E2613 (compact sets)  656


American Mathematical Monthly
Volume 84, 1977

                Donald E. Knuth   Elementary Problem E2636 (diphages and
                                  triphages) . . . . . . . . . . . . . . . 134
                Donald E. Knuth   Solution to Problem 6049 (cyclic
                                  permutation generators)  . . . . . . . . 397
                Donald E. Knuth   Solution to Elementary Problem E2613
                                  (compact sets) . . . . . . . . . . . . . 827--828


American Mathematical Monthly
Volume 85, Number 1, 1978

            Lajos Takács   An increasing continuous singular
                                  function . . . . . . . . . . . . . . . . 35--37

American Mathematical Monthly
Volume 85, Number 2, 1978

                      Anonymous   Extended mean values . . . . . . . . . . 84--90

American Mathematical Monthly
Volume 85, Number 4, 1978

                   P. R. Halmos   Schauder bases . . . . . . . . . . . . . 256--257

American Mathematical Monthly
Volume 85, Number 5, 1978

                 H. S. Bear and   
                     G. N. Hile   Gradient characterizations of
                                  analyticity  . . . . . . . . . . . . . . 333--337
          Michael J. Norris and   
     William Yslas Vélez   A characterization of the splitting of
                                  inseparable algebraic extensions . . . . 338--341
                J. E. Humphreys   Hilbert's fourteenth problem . . . . . . 341--353

American Mathematical Monthly
Volume 85, 1978

                Donald E. Knuth   Elementary Problem E2636 (diphages and
                                  triphages) . . . . . . . . . . . . . . . 385--386

American Mathematical Monthly
Volume 85, Number 6, 1978

                     R. P. Boas   Extremal problems for polynomials  . . . 473--475

American Mathematical Monthly
Volume 85, Number 7, 1978

                    John Milnor   Analytic proofs of the ``hairy ball
                                  theorem'' and the Brouwer fixed-point
                                  theorem  . . . . . . . . . . . . . . . . 521--524
               Kenneth I. Gross   On the evolution of noncommutative
                                  harmonic analysis  . . . . . . . . . . . 525--548
                     L. Carlitz   Some product-sum identities  . . . . . . 570--572
                 R. Cignoli and   
                      J. Hounie   Functions with arbitrarily small periods 582--584

American Mathematical Monthly
Volume 85, Number 8, 1978

                 Martha Zelinka   Edward Griffith Begle  . . . . . . . . . 629--631
                    Heinz Bauer   Approximation and abstract boundaries    632--647
                 John E. Wetzel   On the division of the plane by lines    647--656
                E. B. Leach and   
                M. C. Sholander   Corrections to: ``Extended mean values''
                                  [Amer. Math. Monthly \bf 85 (1978), no.
                                  2, 84--90, MR \bf 58 #22428] . . . . . . 656--656
                Calvin C. Moore   Approximately finite von Neumann
                                  algebras . . . . . . . . . . . . . . . . 657--659
                 John E. Wetzel   Dissections of a simply-connected plane
                                  domain . . . . . . . . . . . . . . . . . 660--661
                   A. D. Wadhwa   Some convergent subseries of the
                                  harmonic series  . . . . . . . . . . . . 661--663
            Gérard Letac   Cauchy functional equation again . . . . 663--664

American Mathematical Monthly
Volume 85, 1978

                Donald E. Knuth   Solution to Problem 6050 (random
                                  maximization)  . . . . . . . . . . . . . 686--688

American Mathematical Monthly
Volume 85, Number 9, 1978

                   R. L. Wilder   Evolution of the topological concept of
                                  ``connected''  . . . . . . . . . . . . . 720--726
                J. C. Alexander   Matrices, eigenvalues, and complex
                                  projective space . . . . . . . . . . . . 727--733
              Solomon W. Golomb   Cyclotomic polynomials and factorization
                                  theorems . . . . . . . . . . . . . . . . 734--737
           Cletus O. Oakley and   
               Justine C. Baker   The Morley trisector theorem . . . . . . 737--745
                 L. Carlitz and   
                    Jo Ann Lutz   A characterization of permutation
                                  polynomials over a finite field  . . . . 746--748
                 R. P. Boas and   
                 H. Pollard and   
                   D. V. Widder   The asymptotic behavior of derivatives   749--750
                   Barry Powell   Proof of a special case of Fermat's last
                                  theorem  . . . . . . . . . . . . . . . . 750--751
                H. Guggenheimer   The Jordan and Schoenflies theorems in
                                  axiomatic geometry . . . . . . . . . . . 753--756
                Gebhard Greiter   A simple proof for a theorem of
                                  Kronecker  . . . . . . . . . . . . . . . 756--757

American Mathematical Monthly
Volume 85, Number 10, 1978

                     Ivan Niven   Convex polygons that cannot tile the
                                  plane  . . . . . . . . . . . . . . . . . 785--792
                Donald G. Saari   Apportionment methods and the House of
                                  Representatives  . . . . . . . . . . . . 792--802
                    Leon Gerber   A simple improvement on the binomial
                                  series . . . . . . . . . . . . . . . . . 808--809
                 K. Athreya and   
                D. McDonald and   
                         P. Ney   Coupling and the renewal theorem . . . . 809--814
          Patrick J. O'Hara and   
              Rene S. Rodriguez   Polynomials with zeros uniformly
                                  distributed on the unit circle . . . . . 814--817

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 ??, 1978

                    Emma Lehmer   Rational reciprocity laws  . . . . . . . 467--472


American Mathematical Monthly
Volume 86, Number 1, 1979

                Robert Osserman   Bonnesen-style isoperimetric
                                  inequalities . . . . . . . . . . . . . . 1--29
                     David Gale   Tone perception and decomposition of
                                  periodic functions . . . . . . . . . . . 36--42
              R. Daniel Mauldin   The existence of non-measurable sets . . 45--46
                  B. G. Basmaji   Complex representations of metacyclic
                                  groups . . . . . . . . . . . . . . . . . 47--48

American Mathematical Monthly
Volume 86, Number 2, 1979

                     R. P. Boas   Award for distinguished service to Otto
                                  Neugebauer . . . . . . . . . . . . . . . 77--78
               David P. Roselle   Award of the Chauvenet Prize to Dr. Neil
                                  J. A. Sloane . . . . . . . . . . . . . . 79--79
            Steven J. Brams and   
        Philip D. Straffin, Jr.   Prisoner's dilemma and professional
                                  sports drafts  . . . . . . . . . . . . . 80--88
              George E. Andrews   An introduction to Ramanujan's ``lost''
                                  notebook . . . . . . . . . . . . . . . . 89--108
               James K. Knowles   Universal states of finite anti-plane
                                  shear: Ericksen's problem in miniature   109--113
                 Heiko Harborth   Divisibility of $(^{m}_{k})$ by
                                  $m(m-1)\cdots (m-h+1)$ . . . . . . . . . 115--117
               S. A. Kenton and   
                    S. D. Shore   The Pixley-Roy space is continuously
                                  semimetrizable . . . . . . . . . . . . . 117--119
              Edward T. H. Wang   When is the permanent function convex on
                                  the set of doubly stochastic matrices    119--121
                C. L. Belna and   
                M. J. Evans and   
                    P. D. Humke   Symmetric and strong differentiation . . 121--123

American Mathematical Monthly
Volume 86, Number 3, 1979

                 Karl Stromberg   The Banach-Tarski paradox  . . . . . . . 151--161
               D. B. Oulton and   
             D. J. Wollkind and   
                   R. N. Maurer   A stability analysis of a prototype
                                  moving boundary problem in heat flow and
                                  diffusion  . . . . . . . . . . . . . . . 175--186
              Andrew P. Guinand   The umbral method: a survey of
                                  elementary mnemonic and manipulative
                                  uses . . . . . . . . . . . . . . . . . . 187--195
                Salomon Bochner   Fourier series came first  . . . . . . . 197--199
                   Scott Garten   Corrections to: ``Irregular integers''
                                  (Amer. Math. Monthly \bf 85 (1978), no.
                                  3, 165--172) by M. Schreiber . . . . . . 199--199
               T. M. K. Davison   A generalization of regulated functions  202--204
                Robert Sine and   
 Vladislav Kre\uìnovi\vc   Remarks on billiards . . . . . . . . . . 204--206
            Emad El-Neweihi and   
                 Frank Proschan   Unified treatment of inequalities of the
                                  Weierstrass product type . . . . . . . . 206--208
          William C. Waterhouse   The normal basis theorem . . . . . . . . 212--212
                     G. J. Miel   The Kantorovich theorem with optimal
                                  error bounds . . . . . . . . . . . . . . 212--215

American Mathematical Monthly
Volume 86, Number 4, 1979

           Dorothy L. Bernstein   The role of applications in pure
                                  mathematics  . . . . . . . . . . . . . . 245--253
                   Keith Harrow   Theoretical and applied computer
                                  science: antagonism or symbiosis . . . . 253--260
                   J. C. Fisher   Geometry according to Euclid . . . . . . 260--270
                   D. V. Widder   The Airy transform . . . . . . . . . . . 271--277
                Ronald J. Evans   Silverman's game on intervals  . . . . . 277--281
                   Erwin Turdza   The solutions of an inequality for the
                                  $n$th iterate of a function  . . . . . . 281--283
              Paul D. Humke and   
          Lawrence L. Krajewski   A characterization of circles which
                                  contain rational points  . . . . . . . . 287--290
                     Y. H. Wang   Dependent random variables with
                                  independent subsets  . . . . . . . . . . 290--292
              David H. Anderson   The application of a classical
                                  inequality to population mathematics . . 294--296
                Robert M. Young   An elementary proof of a trigonometric
                                  identity . . . . . . . . . . . . . . . . 296--297
       Lud\vek Zají\vcek   An elementary proof of the
                                  one-dimensional density theorem  . . . . 297--298

American Mathematical Monthly
Volume 86, Number 5, 1979

              Shiing Shen Chern   From triangles to manifolds  . . . . . . 339--349
                  J. L. Brenner   Student days---1930  . . . . . . . . . . 350--356
                  E. J. Barbeau   Euler subdues a very obstreperous series 356--372
                 Robert Baillie   Sums of reciprocals of integers missing
                                  a given digit  . . . . . . . . . . . . . 372--374
                 Patrick Morton   A generalization of Zolotarev's theorem  374--375
                Denis Higgs and   
                  Paul de Witte   On products of transpositions and their
                                  graphs . . . . . . . . . . . . . . . . . 376--380
            R. Výborn\'y   On the use of a differentiable homotopy
                                  in the proof of the Cauchy theorem . . . 380--382

American Mathematical Monthly
Volume 86, Number 6, 1979

                Steven H. Schot   Geometrical properties of the
                                  penosculating conics of a plane curve    449--457
                T. Bruce McLean   ${V}$-flexing the hexahexaflexagon . . . 457--466
                   Trevor Evans   Universal algebra and Euler's officer
                                  problem  . . . . . . . . . . . . . . . . 466--473
                      E. Lutwak   On isoperimetric inequalities related to
                                  a problem of Moser . . . . . . . . . . . 476--477
              George E. Andrews   A note on partitions and triangles with
                                  integer sides  . . . . . . . . . . . . . 477--478
                Dan Eustice and   
                  M. S. Klamkin   On the coefficients of a partial
                                  fraction decomposition . . . . . . . . . 478--480
                  A. M. Russell   Further comments on the variation
                                  function . . . . . . . . . . . . . . . . 480--482
                Alexander Abian   An ultimate proof of Rolle's theorem . . 484--485
                 A. Day Bradley   Prismatoid, prismoid, generalized
                                  prismoid . . . . . . . . . . . . . . . . 486--490
                  Bertram Walsh   More on gradient characterizations of
                                  analyticity  . . . . . . . . . . . . . . 490--491

American Mathematical Monthly
Volume 86, Number 7, 1979

             Bernard O. Koopman   Search and its optimization  . . . . . . 527--540
             Nicolas D. Goodman   Mathematics as an objective science  . . 540--551
                  Ernst Snapper   What is mathematics  . . . . . . . . . . 551--557
                    R. L. Cooke   The Cantor-Lebesgue theorem  . . . . . . 558--565
              William H. Ruckle   The bounded consistency theorem  . . . . 566--571
           Murray Eisenberg and   
                     Robert Guy   A proof of the hairy ball theorem  . . . 572--574
              John Ginsburg and   
                     Bill Sands   Minimal infinite topological spaces  . . 574--576
                 Shigeru Haruki   A property of quadratic polynomials  . . 577--579
        Samuel S. Wagstaff, Jr.   Some questions about arithmetic
                                  progressions . . . . . . . . . . . . . . 579--582
                 Ira Rosenholtz   There is no differentiable metric for
                                  ${\bf R}^{n}$  . . . . . . . . . . . . . 585--586

American Mathematical Monthly
Volume 86, Number 8, 1979

               Azriel Rosenfeld   Digital topology . . . . . . . . . . . . 621--630
                  John W. Pratt   Finding how many roots a polynomial has
                                  in $(0,\,1)$ or $(0,\,\infty )$  . . . . 630--637
           Richard Johnsonbaugh   Summing an alternating series  . . . . . 637--648
                 Emil Grosswald   Recent applications of some old work of
                                  Laguerre . . . . . . . . . . . . . . . . 648--658
                  Karel Hrbacek   Nonstandard set theory . . . . . . . . . 659--677
                 J. R. Nurcombe   A sequence of convergence tests  . . . . 679--681
               Richard J. Bagby   Taylor polynomials and difference
                                  quotients  . . . . . . . . . . . . . . . 681--684
                 C. David Minda   Conformal automorphisms of circular
                                  regions  . . . . . . . . . . . . . . . . 684--686
               J. H. Jordan and   
                  Ray Walch and   
                   R. J. Wisner   Triangles with integer sides . . . . . . 686--689
                Walter Leighton   A useful lemma in the theory of
                                  second-order linear differential
                                  equations  . . . . . . . . . . . . . . . 693--694
                    George Miel   An algorithm for the calculation of
                                  $\pi$  . . . . . . . . . . . . . . . . . 694--697

American Mathematical Monthly
Volume 86, Number 9, 1979

               D. H. Lehmer and   
                    Emma Lehmer   Picturesque exponential sums. I  . . . . 725--733
              Wendell Mills and   
           Boris Weisfeiler and   
                 Allan M. Krall   Discovering theorems with a computer:
                                  the case of $y^{\prime} ={\rm sin}(xy)$  733--739
                    John Dawson   The Gödel incompleteness theorem from a
                                  length-of-proof perspective  . . . . . . 740--747
           Marvin Jay Greenberg   Euclidean and non-Euclidean geometries
                                  without continuity . . . . . . . . . . . 757--764
               I. J. Schoenberg   On a problem of Steinhaus on lattice
                                  points . . . . . . . . . . . . . . . . . 765--766
                    A. L. Brown   The Borsuk-Ulam theorem and
                                  orthogonality in normed linear spaces    766--767
                  C. H. Heiberg   Extrema for functions of several
                                  variables  . . . . . . . . . . . . . . . 767--770
           Phyllis Joan Cassidy   Products of commutators are not always
                                  commutators: an example  . . . . . . . . 772--772

American Mathematical Monthly
Volume 86, Number 10, 1979

        Desmond Fearnley-Sander   Hermann Grassmann and the creation of
                                  linear algebra . . . . . . . . . . . . . 809--817
                     David Gale   The game of Hex and the Brouwer
                                  fixed-point theorem  . . . . . . . . . . 818--827
           Marvin Jay Greenberg   The ``real'' projective plane without
                                  continuity . . . . . . . . . . . . . . . 827--832
               Albert Nijenhuis   A minimal-path algorithm for the ``money
                                  changing problem'' . . . . . . . . . . . 832--835
       Deborah Tepper Haimo and   
          Franklin Tepper Haimo   Comments and complements . . . . . . . . 836--841
           David W. Kammler and   
              Robert J. McGlinn   Local conditioning of parametric forms
                                  used to approximate continuous functions 841--845
                   R. D. Nelson   Perfect quadrilaterals . . . . . . . . . 845--847
            James M. Briggs and   
               Thomas Schaffter   Measure and cardinality  . . . . . . . . 852--855


American Mathematical Monthly
Volume 87, Number 10, 1980

                       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

American Mathematical Monthly
Volume 87, Number 1, 1980

                   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


American Mathematical Monthly
Volume 88, Number 5, 1981

              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

American Mathematical Monthly
Volume 88, Number 10, 1981

        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