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Volume 53, Number ??, 1946J. Williamson Determinants whose elements are $0$ and $1$ . . . . . . . . . . . . . . . . . . 427--434
Bernard Jacobson On the mean value theorem for integrals 300--301
D. H. Lehmer Coloring the Platonic solids . . . . . . 288--292
Arthur Benjamin The bisection method: which root . . . . 861--863
John Beebee Examples of infinite, incongruent exact covers . . . . . . . . . . . . . . . . . 121--123
Barry Hayes and Donald E. Knuth and Carlos Subi Elementary problem E3267, a solitaire game . . . . . . . . . . . . . . . . . . 456--457
David W. Boyd The Diophantine equation $ x^2 + y^m = z^{2n} $ . . . . . . . . . . . . . . . . 544--547
Donald E. Knuth and Ilan Vardi Advanced problem 6581, the asymptotic expansion of the middle binomial coefficient . . . . . . . . . . . . . . 774
K. D. Magill, Jr. Universal topological spaces . . . . . . 942--946
Donald E. Knuth Elementary problem E3303, a binary summation . . . . . . . . . . . . . . . 54--54 Donald E. Knuth Elementary problem E3309, a binomial coefficient inequality . . . . . . . . . 154--154 Donald E. Knuth Elementary problem E3335, a deranged recurrence . . . . . . . . . . . . . . . 525--525
George E. Andrews and R. J. Baxter A motivated proof of the Rogers--Ramanujan identities . . . . . . 401--409
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
Henry L. Alder and Ivan Niven Award for Distinguished Service to Leon Henkin . . . . . . . . . . . . . . . . . 3--4 Peter J. Giblin and Donal B. O'Shea The bitangent sphere problem . . . . . . 5--23 Klaus Sutner The $ \sigma $-game and cellular automata . . . . . . . . . . . . . . . . 24--34 Robert Weinstock Elementary evaluations of $ \int^\infty_0 e^{-x^2} \, d x $ and $ \int^\infty_0 \cos x^2 \, d x, $ and $ \int^\infty_0 \sin x^2 \, d x $ . . . . 39--42 Donald J. Newman and J. S. Byrnes The $ L^4 $ norm of a polynomial with coefficients $ \pm 1 $ . . . . . . . . . 42--45 Johannes C. C. Nitsche Isoptic characterization of a circle (proof of a conjecture of M. S. Klamkin) 45--47 Roy Mathias Two theorems on singular values and eigenvalues . . . . . . . . . . . . . . 47--50 Teresa L. Santa Coloma and Ralph P. Tucci A decomposition theorem for finite automata . . . . . . . . . . . . . . . . 51--54 Thomas W. Hungerford A counterexample in Galois theory . . . 54--57 Tyre A. Newton A simple algorithm for finding eigenvalues and eigenvectors for $ 2 \times 2 $ matrices . . . . . . . . . . 57--60 Arno van den Essen Magic squares and linear algebra . . . . 60--62
Donald G. Saari A visit to the Newtonian $N$-body problem via elementary complex variables 105--119 W. S. Anglin The square pyramid puzzle . . . . . . . 120--124 Stan Wagon Editor's corner: the Euclidean algorithm strikes again . . . . . . . . . . . . . 125--129 Kurt Girstmair A theorem on the numerators of the Bernoulli numbers . . . . . . . . . . . 136--138 Richard G. Swan Another proof of the quadratic reciprocity theorem . . . . . . . . . . 138--139 Edward A. Bender and Fred Kochman and Douglas B. West Adding up to powers . . . . . . . . . . 139--143 D. Zagier A one-sentence proof that every prime $ p \equiv 1 \pmod 4 $ is a sum of two squares . . . . . . . . . . . . . . . . 144--144 Stephen H. Friedberg Extending the principal axis theorem to fields other than $ {\bf R} $ . . . . . 147--149
F. Beukers and J.-P. Bézivin and P. Robba An alternative proof of the Lindemann-Weierstrass theorem . . . . . 193--197 Richard C. Bollinger and Charles L. Burchard Lucas's theorem and some related results for extended Pascal triangles . . . . . 198--204 Esteban I. Poffald The remainder in Taylor's formula . . . 205--213 Raphael M. Robinson Comment to: ``A motivated proof of the Rogers--Ramanujan identities'' [Amer. Math. Monthly \bf 96 (1989), no. 5, 401--409, MR 90e:11147] by G. E. Andrews and R. J. Baxter. With a reply by Andrews . . . . . . . . . . . . . . . . 214--215 Carsten Thomassen A link between the Jordan curve theorem and the Kuratowski planarity criterion 216--218 John A. Ewell A new series representation for $ \zeta (3) $ . . . . . . . . . . . . . . . . . 219--220 David Minda The Dirichlet problem for a disk . . . . 220--223 R. Bruce Richter and William P. Wardlaw Diagonalization over commutative rings 223--227 Joe Whittaker Random triangles . . . . . . . . . . . . 228--230 Daniel Kopel and Michael Schramm A new extension of the derivative . . . 230--233 G. B. Folland Remainder estimates in Taylor's theorem 233--235 Donald E. Knuth Solution to problem 6575, an identity involving sums and products . . . . . . 256
Anatole Beck Greed is (sometimes) not enough . . . . 289--294 Dragan Jankovi\'c and T. R. Hamlett New topologies from old via ideals . . . 295--310 Calixto P. Calderón Letter to the editor . . . . . . . . . . 311--312 Betty Garrison Polynomials with large numbers of prime values . . . . . . . . . . . . . . . . . 316--317 F. B. Cannonito On inequivalent group extensions . . . . 317--319 A. Vince A rearrangement inequality and the permutahedron . . . . . . . . . . . . . 319--323 Patrick Morton Musings on the prime divisors of arithmetic sequences . . . . . . . . . . 323--328 Marjorie Senechal Finding the finite groups of symmetries of the sphere . . . . . . . . . . . . . 329--335 C. E. Burgess Continuous functions and connected graphs . . . . . . . . . . . . . . . . . 337--339 Robert A. Leslie The $ l_2 $ matrix norm and the spectral radius . . . . . . . . . . . . . . . . . 339--341
Peter D. Lax The ergodic character of sequences of pedal triangles . . . . . . . . . . . . 377--381 H. Groemer Stability properties of geometric inequalities . . . . . . . . . . . . . . 382--394 Fred Richman Separable extensions and diagonalizability . . . . . . . . . . . 395--398 M. D. Hirschhorn A birthday present for Ramanujan . . . . 398--400 Yaakov S. Kupitz and Micha A. Perles A condition for flatness of curves in $ {\bf R}^n $ . . . . . . . . . . . . . . 401--405 Pieter P. N. de Groen A counterexample on vector norms and the subordinate matrix norms . . . . . . . . 406--407 Marko Petkov\vsek Ambiguous numbers are dense . . . . . . 408--411 David W. Boyd Addendum: ``The Diophantine equation $ x^2 + y^m = z^{2n \, } $'' [Amer. Math. Monthly 95 (1988), no. 6, 544--547, MR 89f:11046] . . . . . . . . . . . . . . . 411--412 John Beebee Errata: ``Examples of infinite, incongruent exact covers'' [Amer. Math. Monthly \bf 95 (1988), no. 2, 121--123, MR 89g:11013] . . . . . . . . . . . . . 412--412 Arthur T. Benjamin Errata: ``The bisection method: which root?'' [Amer. Math. Monthly \bf 94 (1987), no. 9, 861--863, MR 89c:26016] 412--412 Hans-J. Kleiner Errata: ``Coloring the Platonic solids'' [Amer. Math. Monthly \bf 93 (1986), no. 4, 288--292, MR 87e:05072] by D. H. Lehmer . . . . . . . . . . . . . . . . . 412--412 K. D. Magill, Jr. Errata: ``Universal topological spaces'' [Amer. Math. Monthly \bf 95 (1988), no. 10, 942--946, MR 89m:54018] . . . . . . 412--412 Jingcheng Wong Errata: ``On the mean value theorem for integrals'' [Amer. Math. Monthly \bf 89 (1982), no. 5, 300--301, MR 83g:26002] by B. Jacobson . . . . . . . . . . . . . 412--412 K. Hoechsmann Singular values and the spectral theorem 413--414 Robert Bartoszy\'nski and Wai Chan A remark on the shortest confidence interval of a normal mean . . . . . . . 415--417 François Dubeau Cauchy-Bunyakowski-Schwarz inequality revisited . . . . . . . . . . . . . . . 419--421 Mary Embry-Wardrop An old max-min problem revisited . . . . 421--423 J. Aczél Functional equations and L'Hôpital's rule in an exact Poisson derivation . . . . . 423--426
Kenneth R. Meyer The geometry of harmonic oscillators . . 457--465 P. Eisele and K. P. Hadeler Game of cards, dynamical systems, and a characterization of the floor and ceiling functions . . . . . . . . . . . 466--477 R. R. London and H. P. Rogosinski Decomposition theory in the teaching of elementary linear algebra . . . . . . . 478--485 Andrew Granville and Yiliang Zhu Representing binomial coefficients as sums of squares . . . . . . . . . . . . 486--493 Tim Robertson and Carolyn Pillers A geometric regularity from order-restricted statistical inference 496--498 Bertram Ross and Baldev K. Sachdeva The solution of certain integral equations by means of operators of arbitrary order . . . . . . . . . . . . 498--503 Armel Mercier Relations between $ \omega (n) $ and $ \Omega (n) $ . . . . . . . . . . . . . . 503--505 Jerold Mathews Gear trains and continued fractions . . 505--510
Paul R. Halmos Has progress in mathematics slowed down 561--588 Helaman Ferguson Two theorems, two sculptures, two posters . . . . . . . . . . . . . . . . 589--610 Donald E. Knuth Solution to Advanced problem 6581, the asymptotic expansion of the middle binomial coefficient . . . . . . . . . . 629--630
Marcel Berger Convexity . . . . . . . . . . . . . . . 650--678 Shiing Shen Chern What is geometry . . . . . . . . . . . . 679--686 Ron Graham and Frances Yao A whirlwind tour of computational geometry . . . . . . . . . . . . . . . . 687--701 David Hoffman and William H. Meeks, III Minimal surfaces based on the catenoid 702--730 Robert Osserman Curvature in the eighties . . . . . . . 731--756 William P. Thurston Conway's tiling groups . . . . . . . . . 757--773
Tomás Feder Toetjes . . . . . . . . . . . . . . . . 785--794 Regina B. Cohen Set isometries and their extensions in the max metric . . . . . . . . . . . . . 795--808 A. C. M. Ran and L. Rodman On stability of invariant subspaces of matrices . . . . . . . . . . . . . . . . 809--823 George Marsaglia and John C. W. Marsaglia A new derivation of Stirling's approximation to $ n! $ . . . . . . . . 826--829 M. J. Jamieson Fibonacci numbers and Aitken sequences revisited . . . . . . . . . . . . . . . 829--831 Stephen L. Bloom and Zoltán Ésik and Ernest G. Manes A Cayley theorem for Boolean algebras 831--833 Michael Filaseta Rouché's theorem for polynomials . . . . 834--835 Branko Grünbaum and Jan Mycielski Some models of plane geometries . . . . 839--846
Joyce Justicz and Edward R. Scheinerman and Peter M. Winkler Random intervals . . . . . . . . . . . . 881--889 Gideon E. Schwarz The dark side of the Moebius strip . . . 890--897 Peter Ungar Mixing property of the pedal mapping . . 898--900 R. E. Mirollo and S. H. Strogatz Integral representation of a finite spike . . . . . . . . . . . . . . . . . 901--903 D. Desbrow On the irrationality of $ \pi^2 $ . . . 903--906 Donald E. Knuth and Boris Pittel Elementary problem E3411, two sums over compositions . . . . . . . . . . . . . . 916--917
Donald E. Knuth Advanced problem 6649, a generalized gamma function with independent branches 168 Donald E. Knuth and John McCarthy Elementary problem E3429, small pills 264 Donald E. Knuth Elementary problem E3463, points in a circle . . . . . . . . . . . . . . . . . 852
Colin L. Mallows Conway's challenge sequence . . . . . . 5--20 Henri Darmon and John McKay A continued fraction and permutations with fixed points . . . . . . . . . . . 25--27 Vítor Neves Smoothness from finite points . . . . . 27--31 Godfried Toussaint Anthropomorphic polygons . . . . . . . . 31--35 W. A. Day Inequalities for areas associated with conics . . . . . . . . . . . . . . . . . 36--39 Stephen Kuhn The derivative \`a la Carathéodory . . . 40--44 George T. Gilbert Positive definite matrices and Sylvester's criterion . . . . . . . . . 44--46 J. Foster and F. B. Richards The Gibbs phenomenon for piecewise-linear approximation . . . . . 47--49 Philippe Flajolet and Donald E. Knuth Elementary problem E3415, a hypergenerating function . . . . . . . . 54
Duane W. DeTemple Carlyle circles and the Lemoine simplicity of polygon constructions . . 97--108 H. S. Bear Part metric and hyperbolic metric . . . 109--123 Timothy Lance and Edward Thomas Arcs with positive measure and a space-filling curve . . . . . . . . . . 124--127 K. P. S. Bhaskara Rao and A. Ramachandra Rao Unions and common complements of subspaces . . . . . . . . . . . . . . . 127--131 Hans Liebeck and Anthony Osborne The generation of all rational orthogonal matrices . . . . . . . . . . 131--133 Norman Richert Hypocycloids, continued fractions, and distribution modulo one . . . . . . . . 133--139 James P. Butler The perimeter of a rose . . . . . . . . 139--143 A. R. Meijer A tree among the stepping stones . . . . 144--146 Wen Liu An analytic technique to prove Borel's strong law of large numbers . . . . . . 146--148 Ira Rosenholtz A topological mean value theorem for the plane . . . . . . . . . . . . . . . . . 149--154 Walter Carlip Disks and shells revisited . . . . . . . 154--156 Donald Hartig L'Hôpital's rule via integration . . . . 156--157
E. N. Gilbert How things float . . . . . . . . . . . . 201--216 Robert L. Devaney and Marilyn B. Durkin The exploding exponential and other chaotic bursts in complex dynamics . . . 217--233 M. V. Deshpande and Sudhir R. Ghorpade Algebraic characterization of compact abelian groups . . . . . . . . . . . . . 235--237 G. Myerson First-class functions . . . . . . . . . 237--240 P. D. Barry and D. J. Hurley On series of partial fractions . . . . . 240--242 Peter A. Loeb A note on Dixon's proof of Cauchy's integral theorem . . . . . . . . . . . . 242--244 Daniel Goffinet Number systems with a complex base: a fractal tool for teaching topology . . . 249--255 Donald R. Chalice A characterization of the Cantor function . . . . . . . . . . . . . . . . 255--258 L. R. Bragg Parametric differentiation revisited . . 259--262
C. W. H. Lam The search for a finite projective plane of order $ 10 $ . . . . . . . . . . . . 305--318 N. Metropolis and Gian-Carlo Rota Symmetry classes: functions of three variables . . . . . . . . . . . . . . . 328--332 Richard Beigel Irrationality without number theory . . 332--335 J. I. Hall Another elementary approach to the Jordan form . . . . . . . . . . . . . . 336--340 Bernt Lindström and Hans-Olov Zetterström Borromean circles are impossible . . . . 340--341 A. G. Miamee The inclusion $ L^p(\mu) \subseteq L^q(\nu) $ . . . . . . . . . . . . . . . 342--345 Lee Rudolph The structure of orthogonal transformations . . . . . . . . . . . . 349--352 Jonathan Lewin A simple proof of Zorn's lemma . . . . . 353--354 Richard Grant The converse of Liouville's theorem . . 354--354 Albert A. Cuoco Visualizing the $p$-adic integers . . . 355--364
Calvin H. Wilcox The Cauchy problem for the wave equation with distribution data: an elementary approach . . . . . . . . . . . . . . . . 401--410 Hidefumi Katsuura Continuous nowhere-differentiable functions --- an application of contraction mappings . . . . . . . . . . 411--416 Daniel Bienstock and Fan Chung and Michael L. Fredman and Alejandro A. Schäffer and Peter W. Shor and Subhash Suri A note on finding a strict saddlepoint 418--419 Robert Osserman Circumscribed circles . . . . . . . . . 419--422 Elias Y. Deeba and Dennis M. Rodriguez Stirling's series and Bernoulli numbers 423--426 J. H. Lindsey, II A simple proof of the Weierstrass approximation theorem . . . . . . . . . 429--430
Christopher J. Henrich Magic squares and linear algebra . . . . 481--488 James V. Whittaker An analytical description of some simple cases of chaotic behaviour . . . . . . . 489--504 Albert Fässler Multiple Pythagorean number triples . . 505--517 Jean-Pierre Rosay A very elementary proof of the Malgrange-Ehrenpreis theorem . . . . . . 518--523 Li-Chien Shen On the zeros of $ \tan^{(k)}z $ . . . . 524--527 John B. Kelly Two equal sums of three squares with equal products . . . . . . . . . . . . . 527--529 Ira M. Gessel A coloring problem . . . . . . . . . . . 530--533 Man Kam Kwong and A. Zettl Norm inequalities for the powers of a matrix . . . . . . . . . . . . . . . . . 533--538
B. Mazur Number theory as gadfly . . . . . . . . 593--610 Lawrence H. Riddle An occurrence of the ballot numbers in operator theory . . . . . . . . . . . . 613--617 Stephen G. Penrice Derangements, permanents, and Christmas presents . . . . . . . . . . . . . . . . 617--620 Fred Galvin and S. D. Shore Distance functions and topologies . . . 620--623 Dragan Jankovi\'c and Maximilian Ganster and Ivan Reilly A characterization of Baire spaces . . . 624--625 Man Keung Siu Which Latin squares are Cayley tables 625--627 Marysia T. Weiss An early introduction to dynamics . . . 635--641 Alan Gluchoff A simple interpretation of the complex contour integral . . . . . . . . . . . . 641--644
J. P. Jones and Y. V. Matijasevi\vc Proof of recursive unsolvability of Hilbert's tenth problem . . . . . . . . 689--709 Jerome A. Goldstein and Mel Levy Linear algebra and quantum chemistry . . 710--718 F. M. Dekking Branching processes that grow faster than binary splitting . . . . . . . . . 728--731 Robert A. Leslie How not to repeatedly differentiate a reciprocal . . . . . . . . . . . . . . . 732--735 Jonathan M. Borwein and G. de Barra Nested radicals . . . . . . . . . . . . 735--739 M. A. Berger and A. Felzenbaum and A. S. Fraenkel and R. Holzman On infinite and finite covering systems 739--742 Lajos Takács A moment convergence theorem . . . . . . 742--746 Clay C. Ross, Jr. Why the method of undetermined coefficients works . . . . . . . . . . . 747--749
Carl de Boor and Klaus Höllig Box-spline tilings . . . . . . . . . . . 793--802 Steve Alpern and Anatole Beck Hex games and twist maps on the annulus 803--811 Dan Flath and Stan Wagon How to pick out the integers in the rationals: an application of number theory to logic . . . . . . . . . . . . 812--823 P. R. Garabedian A simple proof of a simple version of the Riemann mapping theorem by simple functional analysis . . . . . . . . . . 824--826 Alfonso Villani On the equality $ L^1 (\mu) = L^1_{\rm loc}(\mu) $ . . . . . . . . . . . . . . 826--828 D. de Caen The ranks of tournament matrices . . . . 829--831 Arthur Smith Convergence-preserving functions: an alternative discussion . . . . . . . . . 831--833 R. J. Duffin Lines of best fit by graphics and the Wald line . . . . . . . . . . . . . . . 835--839 M. Furi and M. Martelli On the mean value theorem, inequality, and inclusion . . . . . . . . . . . . . 840--846 C. W. Groetsch Differentiation of approximately specified functions . . . . . . . . . . 847--850 Paul Binding More on cross products . . . . . . . . . 850--851
Kenneth B. Stolarsky From Wythoff's Nim to Chebyshev's inequality . . . . . . . . . . . . . . . 889--900 T. Yung Kong and Ralph Kopperman and Paul R. Meyer A topological approach to digital topology . . . . . . . . . . . . . . . . 901--917 Scott H. Hochwald Linear algebra by analogy . . . . . . . 918--926 Kenneth P. Bogart An obvious proof of Burnside's lemma . . 927--928 J. Král and W. F. Pfeffer Poisson integrals of Riemann integrable functions . . . . . . . . . . . . . . . 929--931 James Chew and Jing Cheng Tong Some remarks on weak continuity . . . . 931--934 Dragomir \vZ. \Dbarokovi\'c On the product of two alternating matrices . . . . . . . . . . . . . . . . 935--936 M. J. Knight An ``oceans of zeros'' proof that a certain non-Liouville number is transcendental . . . . . . . . . . . . . 947--949
Donald E. Knuth Solution to Elementary problem E3463, points in a circle . . . . . . . . . . . 693--694
Donald E. Knuth and John McCarthy Solution to Elementary problem E3429, small pills . . . . . . . . . . . . . . 684
Mark Lynch A continuous, nowhere differentiable function . . . . . . . . . . . . . . . . 8--9 Robert M. Gethner Two relatives of Picard's theorem on entire functions . . . . . . . . . . . . 13--19 Nathaniel A. Friedman Replication and stacking in ergodic theory . . . . . . . . . . . . . . . . . 31--41 J. Segercrantz Improving the Cayley--Hamilton equation for low-rank transformations . . . . . . 42--44 Peter Colwell Bessel functions and Kepler's equation 45--48 Richard J. Libera and Eligiusz J. Z\lotkiewicz Löwner's inverse coefficients theorem for starlike functions . . . . . . . . . . . 49--50 Sheldon Axler and Paul Bourdon and Wade Ramey Bôcher's theorem . . . . . . . . . . . . 51--55 Ruben Mera On the determination of the intermediate point in Taylor's theorem . . . . . . . 56--58
Kenneth M. Hoffman and James R. C. Leitzel Award for distinguished service to Dr. Lynn Arthur Steen . . . . . . . . . . . 99--100 Norman Richert Strang's strange figures . . . . . . . . 101--107 Jean E. Taylor Zonohedra and generalized zonohedra . . 108--111 John A. Velling The uniformization of rectangles, an exercise in Schwarz's lemma . . . . . . 112--115 Carsten Thomassen The Jordan-Schönflies theorem and the classification of surfaces . . . . . . . 116--130 Ira Rosenholtz A pigeonhole proof of Kaplansky's theorem . . . . . . . . . . . . . . . . 132--133 A. M. Bruckner and J. Ma\vrík and C. E. Weil Some aspects of products of derivatives 134--145 Chris Brink and Jan Pretorius Boolean circulants, groups, and relation algebras . . . . . . . . . . . . . . . . 146--152 Brigitte Servatius and Peter R. Christopher Construction of self-dual graphs . . . . 153--158 Pawe\l Góra and Abraham Boyarsky On functions of bounded variation in higher dimensions . . . . . . . . . . . 159--160
R. M. Corless Continued fractions and chaos . . . . . 203--215 A. F. Beardon and T. K. Carne A strengthening of the Schwarz-Pick inequality . . . . . . . . . . . . . . . 216--217 Jerzy Dydak and Nathan Feldman Major theorems on compactness: a unified exposition . . . . . . . . . . . . . . . 220--227 R. A. Brualdi and J. Csima Butterfly embedding proof of a theorem of König . . . . . . . . . . . . . . . . 228--230 Richard J. McIntosh A generalization of a congruential property of Lucas . . . . . . . . . . . 231--238 Barthel W. Huff Mixtures and order statistics . . . . . 239--242 Michael J. Beeson Triangles with vertices on lattice points . . . . . . . . . . . . . . . . . 243--252 Karl R. Stromberg Universally nonmeasurable subgroups of $ {\bf R} $ . . . . . . . . . . . . . . . 253--255 Ömer E\ugecio\uglu A combinatorial generalization of a Putnam problem . . . . . . . . . . . . . 256--258 David C. Kurtz A sufficient condition for all the roots of a polynomial to be real . . . . . . . 259--263 Daniel Shanks Improving an approximation for pi . . . 263--263
Paul R. Halmos Large intersections of large sets . . . 307--312 Andrew Granville Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle . . 318--331 J. Banks and J. Brooks and G. Cairns and G. Davis and P. Stacey On Devaney's definition of chaos . . . . 332--334 Jonathan L. King Dilemma of the sleeping stockbroker . . 335--338 John E. Wetzel Converses of Napoleon's theorem . . . . 339--351 I. M. Isaacs and G. R. Robinson On a theorem of Frobenius: solutions of $ x^n = 1 $ in finite groups . . . . . . 352--354 Charles Vanden Eynden On a problem of Stein concerning infinite covers . . . . . . . . . . . . 355--358 James H. Cliborn and Blake Jordan Minimal surfaces . . . . . . . . . . . . 376--376
Donald E. Knuth Two notes on notation . . . . . . . . . 403--422 Blair K. Spearman and Kenneth S. Williams Representing primes by binary quadratic forms . . . . . . . . . . . . . . . . . 423--426 Enrique A. González-Velasco Connections in mathematical analysis: the case of Fourier series . . . . . . . 427--441 Chandler Fulton Tessellations . . . . . . . . . . . . . 442--445 J. L. Leavitt and G. J. Sherman and M. E. Walker Rewriteability in finite groups . . . . 446--452
Blake Temple and Craig A. Tracy From Newton to Einstein . . . . . . . . 507--521 Michael D. Boshernitzan Billiards and rational periodic directions in polygons . . . . . . . . . 522--529 Edgar M. E. Wermuth Some elementary properties of infinite products . . . . . . . . . . . . . . . . 530--537 Andreas M. Hinz Pascal's triangle and the Tower of Hanoi 538--544 Dieter Jungnickel On the uniqueness of the cyclic group of order $n$ . . . . . . . . . . . . . . . 545--547 Robin Forman Sequences with many primes . . . . . . . 548--557 Mohsen Maesumi Parabolic mirrors, elliptic and hyperbolic lenses . . . . . . . . . . . 558--560 Richard Strong Solution to Elementary problem E3411, two sums over compositions . . . . . . . 578--579
Freeman J. Dyson and Harold Falk Period of a discrete cat mapping . . . . 603--614 David M. Bressoud Why do we teach calculus . . . . . . . . 615--617 J. M. Borwein and P. B. Borwein Strange series and high precision fraud 622--640 Steven Roman The logarithmic binomial formula . . . . 641--648 Bart Braden Calculating sums of infinite series . . 649--655 Sergio A. Alvarez $ {L}^p $ arithmetic . . . . . . . . . . 656--662
David Fowler Dedekind's theorem: $ \sqrt 2 \times \sqrt 3 = \sqrt 6 $ . . . . . . . . . . 725--733 Ronald J. Knill A modified Babylonian algorithm . . . . 734--737 E. A. Marchisotto Lines without order . . . . . . . . . . 738--745 Solomon W. Golomb An identity for $ \binom {2n}n $ . . . . 746--748 D. G. Mead Newton's identities . . . . . . . . . . 749--751 John A. Ewell On sums of triangular numbers and sums of squares . . . . . . . . . . . . . . . 752--757 Marco Vianello and Renato Zanovello On the superlinear convergence of the secant method . . . . . . . . . . . . . 758--761 T. N. Subramaniam and Donald E. G. Malm How to integrate rational functions . . 762--772
Cathleen S. Morawetz Giants . . . . . . . . . . . . . . . . . 819--828 R. B. Eggleton and C. B. Lacampagne and J. L. Selfridge Euclidean quadratic fields . . . . . . . 829--837 K. H. Kim and F. W. Roush and M. D. Intriligator Overview of mathematical social sciences 838--844 Mark F. Schilling Sequential partitioning . . . . . . . . 846--855 Jun Wang Goldbach's problem in the ring $ M_n({\bf Z}) $ . . . . . . . . . . . . . 856--857 J.-Cl. Evard and F. Jafari A complex Rolle's theorem . . . . . . . 858--861 Kenneth A. Brakke The opaque cube problem . . . . . . . . 866--871
Louis M. Rotando and Edward O. Thorp The Kelly criterion and the stock market 922--931 Paul R. Chernoff A simple proof of Tychonoff's theorem via nets . . . . . . . . . . . . . . . . 932--934 David C. Fisher and Jennifer Ryan Optimal strategies for a generalized ``scissors, paper, and stone'' game . . 935--942 Scott T. Chapman A simple example of nonunique factorization in integral domains . . . 943--945 John Beebee Bernoulli numbers and exact covering systems . . . . . . . . . . . . . . . . 946--948 Károly Bezdek Hadwiger's covering conjecture and its relatives . . . . . . . . . . . . . . . 954--956
Donald E. Knuth Problem 10280, a random binary operation 76 Donald E. Knuth Problem 10298, a divisibility property of Stirling numbers . . . . . . . . . . 400
G. Baley Price The seventy-fifth anniversary celebration . . . . . . . . . . . . . . 4--15 Leonard Gillman An axiomatic approach to the integral 16--25 István Szalkai and Dan Velleman Versatile coins . . . . . . . . . . . . 26--33 R. J. Duffin On seeing progressions of constant cross ratio . . . . . . . . . . . . . . . . . 38--47 Anonymous 100 years of Monthly editors . . . . . . 48--49 David Hobby and D. M. Silberger Quotients of primes . . . . . . . . . . 50--52 George C. Donovan and Arnold R. Miller and Timothy J. Moreland Pathological functions for Newton's method . . . . . . . . . . . . . . . . . 53--58 André Avez A short proof of a theorem of Erd\Hos and Mordell . . . . . . . . . . . . . . 60--62 Evan G. Houston A linear algebra approach to cyclic extensions in Galois theory . . . . . . 64--66 Dean Alvis Solution to Elementary problem E3415, a hypergenerating function . . . . . . . . 84--85
Ramanathan Gnanadesikan and Henry J. Landau Yueh-Gin Gung and Dr. Charles Y. Hu award for distinguished service to Henry O. Pollak . . . . . . . . . . . . . . . 115--116 John D. Maxwell John Marvin Colaw: and the American Mathematical Monthly . . . . . . . . . . 117--118 Tristan Needham Newton and the transmutation of force 119--137 Christoph Baxa A note on Diophantine representations 138--143 Terence R. Shore and Douglas B. Tyler Recurrence of simple random walk in the plane . . . . . . . . . . . . . . . . . 144--149 Branko Grünbaum and G. C. Shephard Pick's theorem . . . . . . . . . . . . . 150--161 Ulrich Abel and Hartmut Siebert Sequences with large numbers of prime values . . . . . . . . . . . . . . . . . 167--169 Horst Martini Regular simplices in spaces of constant curvature . . . . . . . . . . . . . . . 169--171 John K. Williams A simple example of little big set . . . 172--174
Edgar R. Lorch Szeged in 1934 . . . . . . . . . . . . . 219--230 Stanley Burris and Simon Lee Tarski's high school identities . . . . 231--236 Steven N. MacEachern and L. Mark Berliner Aperiodic chaotic orbits . . . . . . . . 237--241 William J. Gilbert Bricklaying and the Hermite normal form 242--245 Neil Falkner A characterization of inner product spaces . . . . . . . . . . . . . . . . . 246--249 Gilbert Strang Polar area is the average of strip areas 250--254 Alan Durfee and Nathan Kronenfeld and Heidi Munson and Jeff Roy and Ina Westby Counting critical points of real polynomials in two variables . . . . . . 255--271 Peter Walker Separation of the zeros of polynomials 272--273 George E. Andrews and Shalosh B. Ekhad and Doron Zeilberger A short proof of Jacobi's formula for the number of representations of an integer as a sum of four squares . . . . 274--276 Krzysztof Oleszkiewicz An elementary proof of Hilbert's inequality . . . . . . . . . . . . . . . 276--280 Camille Debi\`eve A note on Fubini's theorem . . . . . . . 281--281 Albert Nijenhuis Solution to Elementary problem E3267, a solitaire game . . . . . . . . . . . . . 292--294
Joseph H. Silverman Taxicabs and sums of two cubes . . . . . 331--340 Raymond Ayoub What is a Napierian logarithm . . . . . 351--364 J. W. Bruce A really trivial proof of the Lucas-Lehmer test . . . . . . . . . . . 370--371 Gregory S. Call and Daniel J. Velleman Pascal's matrices . . . . . . . . . . . 372--376 Thomas A. Fournelle Symmetries of the cube and outer automorphisms of $ S_6 $ . . . . . . . . 377--380 Timothy A. Murdoch Isogonal configurations . . . . . . . . 381--384
J. Helen Gardner and Robin J. Wilson Thomas Archer Hirst---mathematician xtravagant. I. A Yorkshire surveyor . . 435--441 William F. Reynolds Hyperbolic geometry on a hyperboloid . . 442--455 Michael Rubinstein A simple heuristic proof of Hardy and Littlewood's conjecture B . . . . . . . 456--460 H. Turner Laquer The Pompeiu problem . . . . . . . . . . 461--467 Duane W. DeTemple A quicker convergence to Euler's constant . . . . . . . . . . . . . . . . 468--470 William Watkins and Joel Zeitlin The minimal polynomial of $ \cos (2 \pi / n) $ . . . . . . . . . . . . . . . . . 471--474 B. Richmond and T. Richmond The equal area zones property . . . . . 475--477 Mark Copper Graph theory and the game of sprouts . . 478--482 Borislav Bojanov Elementary proof of the Remez inequality 483--485 T. S. Nanjundiah A note on an identity of Ramanujan . . . 485--487 Doron Zeilberger On an identity of Daubechies . . . . . . 487--487 Catherine C. McGeoch Data compression . . . . . . . . . . . . 493--497
J. Helen Gardner and Robin J. Wilson Thomas Archer Hirst---mathematician xtravagant. II. Student days in Germany 531--538 Robert S. Strichartz How to make wavelets . . . . . . . . . . 539--556 William C. Waterhouse A matrix maximum . . . . . . . . . . . . 557--562 S. P. Hastings and J. B. McLeod Chaotic motion of a pendulum with oscillatory forcing . . . . . . . . . . 563--572 David A. Wagstaff and Theodore A. Norman and Douglas M. Campbell An application for the curiosity $ (\log_x N)' $ . . . . . . . . . . . . . 573--574 Miriam Schapiro Grosof and Geraldine Taiani Vandermonde strikes again . . . . . . . 575--577 Fred Galvin Embedding countable groups in $2$-generator groups . . . . . . . . . . 578--580 Joseph A. Gallian and Michael Reid Abelian forcing sets . . . . . . . . . . 580--582
J. Helen Gardner and Robin J. Wilson Thomas Archer Hirst---mathematician xtravagant. III. Göttingen and Berlin . . 619--625 W. A. Beyer and Blair Swartz Bisectors of triangles and tetrahedra 626--640 D. G. Mead and S. K. Stein More on rectangles tiled by rectangles 641--643 Bruce C. Berndt and S. Bhargava Ramanujan --- for lowbrows . . . . . . . 644--656 D. Y. Savio and E. R. Suryanarayan Chebychev polynomials and regular polygons . . . . . . . . . . . . . . . . 657--661 Ren Ding and Krzysztof Ko\lodziejczyk and Grattan Murphy and John Reay A fast Pick-type approximation for areas of $H$-polygons . . . . . . . . . . . . 669--673
J. Helen Gardner and Robin J. Wilson Thomas Archer Hirst---mathematician xtravagant. IV. Queenwood, France and Italy . . . . . . . . . . . . . . . . . 723--731 David Mornhinweg and Daniel B. Shapiro and K. G. Valente The principal axis theorem over arbitrary fields . . . . . . . . . . . . 749--754 Tristan Needham A visual explanation of Jensen's inequality . . . . . . . . . . . . . . . 768--771 Catherine Hassell and Elmer Rees The index of a constrained critical point . . . . . . . . . . . . . . . . . 772--778 Norbert Hegyvári On some irrational decimal fractions . . 779--780 Louis Brickman The symmetry principle for Möbius transformations . . . . . . . . . . . . 781--782 T. von Petersdorff A short proof for Romberg integration 783--785 Ollie Nanyes An elementary proof that the Borromean rings are nonsplittable . . . . . . . . 786--789
J. Helen Gardner and Robin J. Wilson Thomas Archer Hirst---mathematician xtravagant. V. London in the 1860s . . . 827--834 Iris Lee Anshel and Michael Anshel From the Post-Markov theorem through decision problems to public-key cryptography . . . . . . . . . . . . . . 835--844 Gilbert Strang The fundamental theorem of linear algebra . . . . . . . . . . . . . . . . 848--855 Albrecht Dold A simple proof of the Jordan-Alexander complement theorem . . . . . . . . . . . 856--857 Hansklaus Rummler Squaring the circle with holes . . . . . 858--860 Paul Monsky Simplifying the proof of Dirichlet's theorem . . . . . . . . . . . . . . . . 861--862 Hiroshi Maehara Why is $ {\bf P}^2 $ not embeddable in $ {\bf R}^3 $ . . . . . . . . . . . . . . 862--864 Bruce Anderson Polynomial root dragging . . . . . . . . 864--866
J. Helen Gardner and Robin J. Wilson Thomas Archer Hirst---mathematician xtravagant. VI. Years of decline . . . . 907--915 Hans Melissen Densest packings of congruent circles in an equilateral triangle . . . . . . . . 916--925 Jan van Yzeren A simple proof of Pascal's hexagon theorem . . . . . . . . . . . . . . . . 930--931 Andrew T. Hyman The mathematical relationship between Kepler's laws and Newton's laws . . . . 932--936 R\uazvan Gelca A short proof of a result on polynomials 936--937 Robert A. Proctor Two amusing Dynkin diagram graph classifications . . . . . . . . . . . . 937--941 Paul Halmos Postcards from Max . . . . . . . . . . . 942--944
Donald E. Knuth Solution to problem E3062, A versatile identity . . . . . . . . . . . . . . . . 376--377
Donald E. Knuth Problem 103xx, a knight's surprise . . . (to appear) Donald E. Knuth Solution to Advanced problem 6649, a generalized gamma function with independent branches . . . . . . . . . . (to appear) Donald E. Knuth Solution to Advanced problem 6649, a generalized gamma function with independent branches . . . . . . . . . . 77--78
David A. Cox Introduction to Fermat's last theorem 3--14 John Stillwell Galois theory for beginners . . . . . . 22--27 E. Bruce Pitman Into the hourglass: reflections on the forces acting on a granular material . . 28--35 John Dewey Jones Orderly currencies . . . . . . . . . . . 36--38 Robert F. Brown and Robert E. Greene An interior fixed point property of the disc . . . . . . . . . . . . . . . . . . 39--47 J. Michael Steele Le Cam's inequality and Poisson approximations . . . . . . . . . . . . . 48--54 Dorina Mitrea and Marius Mitrea A generalization of a theorem of Euler 55--58 Petru Mironescu and Lauren\ctiu Panaitopol The existence of a triangle with prescribed angle bisector lengths . . . 58--60 A. Shenitzer and J. Stepr\=ans The evolution of integration . . . . . . 66--72
David W. Ballew Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to J. Sutherland Frame . . . . . . . . . . . . 107--108 Branko Grünbaum and G. C. Shephard A new look at Euler's theorem for polyhedra . . . . . . . . . . . . . . . 109--128 Philip J. Davis Otto Neugebauer: reminiscences and appreciation . . . . . . . . . . . . . . 129--131 Richard Kavinoky Correction to: ``From Newton to Einstein'' [Amer. Math. Monthly \bf 99 (1992), no. 6, 507--521, MR 93c:01001] by B. Temple and C. A. Tracy . . . . . . 131--131 Elias Wegert and Lloyd N. Trefethen From the Buffon needle problem to the Kreiss matrix theorem . . . . . . . . . 132--139 William C. Waterhouse A counterexample for Germain . . . . . . 140--150 H. B. Griffiths and A. E. Hirst Cubic equations, or Where did the examination question come from? . . . . 151--161 Hellmuth Stachel On the identity of polyhedra . . . . . . 162--165 David C. Ullrich More on the Pompeiu problem . . . . . . 165--168 Richard K. Guy Every number is expressible as the sum of how many polygonal numbers . . . . . 169--172
Fernando Q. Gouvêa A marvelous proof . . . . . . . . . . . 203--222 David Aldous Triangulating the circle, at random . . 223--233 Michael A. B. Deakin Hypatia and her mathematics . . . . . . 234--243 Richard Barshinger Calculus II and Euler also (with a nod to series integral remainder bounds) . . 244--249 Marc Frantz A focusing property of the ellipse . . . 250--258 Roberto Peirone Reflections can be trapped . . . . . . . 259--260 Katherine Heinrich and Peter Horák Euler's theorem . . . . . . . . . . . . 260--261 Joan Feigenbaum and Nick Reingold Universal traversal sequences . . . . . 262--265 John Stillwell What are algebraic integers and what are they for . . . . . . . . . . . . . . . . 266--270
Edward A. Bender and Oren Patashnik and Howard Rumsey, Jr. Pizza slicing, phi's, and the Riemann hypothesis . . . . . . . . . . . . . . . 307--317 Ralph Walde and Paula Russo Rational periodic points of the quadratic function $ Q_c(x) = x^2 + c $ 318--331 Ernesto Acosta G. and Cesar Delgado G. Fréchet vs. Carathéodory . . . . . . . . . 332--338 A. C. Thompson Odd magic powers . . . . . . . . . . . . 339--342 Frank Morgan Mathematicians, including undergraduates, look at soap bubbles . . 343--351 Fred Galvin A proof of Dilworth's chain decomposition theorem . . . . . . . . . 352--353 Michel Vellekoop and Raoul Berglund On intervals, transitivity = chaos . . . 353--355 Kiran Kedlaya Proof of a mixed arithmetic-mean, geometric-mean inequality . . . . . . . 355--357
Thomas Banchoff and Peter Giblin On the geometry of piecewise circular curves . . . . . . . . . . . . . . . . . 403--416 Elliot Linzer The two envelope paradox . . . . . . . . 417--419 Stephen B. Maurer Comment: ``Orderly currencies'' [Amer. Math. Monthly \bf 101 (1994), no. 1, 36--38] by J. D. Jones . . . . . . . . . 419--419 Alain Robert Fourier series of polygons . . . . . . . 420--428 Richard P. Savage, Jr. The paradox of nontransitive dice . . . 429--436 Laurent Beeckmans Squares expressible as sum of consecutive squares . . . . . . . . . . 437--442 Stephen M. Turner Square roots mod $p$ . . . . . . . . . . 443--449 Jing Cheng Tong Kummer's test gives characterizations for convergence or divergence of all positive series . . . . . . . . . . . . 450--452 Chi-Kwong Li and Wasin So Isometries of $ l_p$-norm . . . . . . . 452--453 Bo Ying Wang and Fu Zhen Zhang A trace inequality for unitary matrices 453--455 Loukas Grafakos An elementary proof of the square summability of the discrete Hilbert transform . . . . . . . . . . . . . . . 456--458 Abe Shenitzer How hyperbolic geometry became respectable . . . . . . . . . . . . . . 464--470
Joe Buhler and David Eisenbud and Ron Graham and Colin Wright Juggling drops and descents . . . . . . 507--519 Gary Gordon Workable gears, Archimedian solids and planar bipartite graphs . . . . . . . . 527--534 Reese T. Prosser On the Kummer solutions of the hypergeometric equation . . . . . . . . 535--543 John W. Emert and Kay I. Meeks and Roger B. Nelson Reflections on a Mira . . . . . . . . . 544--549 Ed Waymire Buffon noodles . . . . . . . . . . . . . 550--559 Victor Bronstein and Aviezri S. Fraenkel On a curious property of counting sequences . . . . . . . . . . . . . . . 560--563 Carsten Knudsen Chaos without nonperiodicity . . . . . . 563--565 Josip Pe\vcari\'c A reverse Stolarsky's inequality . . . . 565--567 A. McD. Mercer A note on some irrational decimal fractions . . . . . . . . . . . . . . . 567--568 David Callan A possible permanent formula . . . . . . 571--573
Jonathan L. King Three problems in search of a measure 609--628 Igor Rivin and Ilan Vardi and Paul Zimmermann The $n$-queens problem . . . . . . . . . 629--639 Roger L. Kraft What's the difference between Cantor sets . . . . . . . . . . . . . . . . . . 640--650 Jean-Paul Allouche and Dan Astoorian and Jim Randall and Jeffrey Shallit Morphisms, squarefree strings, and the Tower of Hanoi puzzle . . . . . . . . . 651--658 A. A. Ageev Sierpi\'nski's theorem is deducible from Euler and Dirichlet . . . . . . . . . . 659--660 F. Matú\vs On nonnegativity of symmetric polynomials . . . . . . . . . . . . . . 661--664 N. Graham and R. C. Entringer and L. A. Székely New tricks for old trees: maps and the pigeonhole principle . . . . . . . . . . 664--667 Jeffrey Ondich Do you know the way to vertex $A$ . . . 668--673 Erwin Kreyszig On the calculus of variations and its major influences on the mathematics of the first half of our century. I . . . . 674--678
Maria S. Terrell and Robert E. Terrell Behind the scenes of a random dot stereogram . . . . . . . . . . . . . . . 715--724 Goro Shimura Fractional and trigonometric expressions for matrices . . . . . . . . . . . . . . 744--758 Barbara L. Osofsky Noether Lasker primary decomposition revisited . . . . . . . . . . . . . . . 759--768 S. Stein and S. Szabó Elementary infinite sources of non-unique factorization rings . . . . . 769--770 Antal E. Fekete Apropos ``Two notes on notation'' [Amer. Math. Monthly \bf 99 (1992), no. 5, 403--422, MR 93f:05001] by D. E. Knuth 771--778 Lyle Ramshaw Erratum: ``On the geometry of piecewise circular curves'' [Amer. Math. Monthly \bf 101 (1994), no. 5, 403--416, MR 95k:51030a] by T. Banchoff and P. Giblin 778--778 Leonard Gillman Congruence of triangles . . . . . . . . 782--783 Norbert Hungerbühler A short elementary proof of the Mohr-Mascheroni theorem . . . . . . . . 784--787 Folke Eriksson Which triangles are plane sections of regular tetrahedra . . . . . . . . . . . 788--789 Edward C. Waymire Addendum: ``Buffon noodles'' . . . . . . 791--791
Robert Gray Georg Cantor and transcendental numbers 819--832 Milton Sobel and Krzysztof Frankowski The 500th anniversary of the sharing problem (the oldest problem in the theory of probability) . . . . . . . . . 833--847 Hugh Thurston What is wrong with the definition of $ d y / d x $ . . . . . . . . . . . . . . . 855--857 Louis Gordon A stochastic approach to the gamma function . . . . . . . . . . . . . . . . 858--865 Jacob E. Goodman and Richard Pollack and Rephael Wenger and Tudor Zamfirescu Arrangements and topological planes . . 866--878 Jeff Boyle An application of Fourier series to the most significant digit problem . . . . . 879--886 Andrew Dittmer Cross product identities in arbitrary dimension . . . . . . . . . . . . . . . 887--891 D. H. Armitage A non-constant continuous function on the plane whose integral on every line is zero . . . . . . . . . . . . . . . . 892--894 Doron Zeilberger Chu's 1303 identity implies Bombieri's 1990 norm-inequality (via an identity of Beauzamy and Dégot) . . . . . . . . . . . 894--896 Catherine C. McGeoch How to stay competitive . . . . . . . . 897--901 Erwin Kreyszig On the calculus of variations and its major influences on the mathematics of the first half of our century. II . . . 902--908
Edward R. Scheinerman and Herbert S. Wilf The rectilinear crossing number of a complete graph and Sylvester's ``four point problem'' of geometric probability 939--943 Ora E. Percus and Jerome K. Percus String matching for the novice . . . . . 944--947 Don Rawlings Bernoulli trials and number theory . . . 948--952 William H. Paulsen What is the shape of a mylar balloon . . 953--958 Peter Hilton and Jean Pedersen Euler's theorem for polyhedra: a topologist and geometer respond. Comment to: ``A new look at Euler's theorem for polyhedra'' [Amer. Math. Monthly \bf 101 (1994), no. 2, 109--128, MR 95c:52032] by B. Grünbaum and G. C. Shephard. With a response by Grünbaum and Shephard . . . . 959--962 I. Kleiner and N. Movshovitz-Hadar The role of paradoxes in the evolution of mathematics . . . . . . . . . . . . . 963--974 Richard A. Brualdi and Stephen Mellendorf Regions in the complex plane containing the eigenvalues of a matrix . . . . . . 975--985 Blair K. Spearman and Kenneth S. Williams Characterization of solvable quintics $ x^5 + a x + b $ . . . . . . . . . . . . 986--992 John B. Cosgrave A Halmos problem and a related problem 993--996 Kurt Girstmair A ``popular'' class number formula . . . 997--1001 Emre Alkan Variations on Wolstenholme's theorem . . 1001--1004 Leonard Gillman The second-partials test for local extrema of $ f(x, y) $ . . . . . . . . . 1004--1006
Michael Orkin and Richard Kakigi What is the worth of free casino credit 3--8 Steven J. Brams and Alan D. Taylor An envy-free cake division protocol . . 9--18 Michael E. Hoffman Derivative polynomials for tangent and secant . . . . . . . . . . . . . . . . . 23--30 Thomas M. Liggett and Peter Petersen The law of large numbers and $ \sqrt {2} $ . . . . . . . . . . . . . . . . . . . 31--35 R. H. Redfield Exponentiation in rings . . . . . . . . 36--40 Blake E. Peterson and James H. Jordan Integer hexahedra equivalent to perfect boxes . . . . . . . . . . . . . . . . . 41--45 Richard J. Bagby Calculating normal probabilities . . . . 46--48 Paul Shutler Constrained critical points . . . . . . 49--52 S. Tabachnikov A cone eversion . . . . . . . . . . . . 52--56 Ran Libeskind-Hadas Approximation algorithms: good solutions to hard problems . . . . . . . . . . . . 57--61 Stefan Mykytiuk and Abe Shenitzer Four significant axiomatic systems and some of the issues associated with them 62--67
Deborah Tepper Haimo Experimentation and conjecture are not enough . . . . . . . . . . . . . . . . . 102--112 Fan Chung and Ron Graham and John Morrison and Andrew Odlyzko Pebbling a chessboard . . . . . . . . . 113--123 S. J. Chapman Drums that sound the same . . . . . . . 124--138 Sheldon Axler Down with determinants . . . . . . . . . 139--154 Peter Andrews Where not to find the critical points of a polynomial---variation on a Putnam theme . . . . . . . . . . . . . . . . . 155--158 Peter D. Lax A short path to the shortest path . . . 158--159 Dmitry Khavinson A note on entire solutions of the eiconal [eikonal] equation . . . . . . . 159--161 David B. Surowski The uniqueness aspect of the fundamental theorem of finite abelian groups . . . . 162--163
Stanley Rabinowitz and Stan Wagon A spigot algorithm for the digits of $ \pi $ . . . . . . . . . . . . . . . . . 195--203 Philip J. Davis The rise, fall, and possible transfiguration of triangle geometry: a mini-history . . . . . . . . . . . . . . 204--214 David Auckly and John Cleveland Totally real origami and impossible paper folding . . . . . . . . . . . . . 215--226 Massimo Furi and Mario Martelli A multidimensional version of Rolle's theorem . . . . . . . . . . . . . . . . 243--249 Noga Alon and Melvyn B. Nathanson and Imre Ruzsa Adding distinct congruence classes modulo a prime . . . . . . . . . . . . . 250--255 Lech Maligranda A simple proof of the Hölder and the Minkowski inequality . . . . . . . . . . 256--259 Irving Kaplansky Never too late. Addendum to: ``Determinants whose elements are $0$ and $1$'' [Amer. Math. Monthly 53 (1946), 427--434, MR 8, 128] by J. Williamson . . . . . . . . . . . . . . . 259--259 I. G. Bashmakova and A. N. Rudakov The evolution of algebra 1800--1870 . . 266--270
Alan Hausrath and Bradley Jackson and John Mitchem and Edward Schmeichel Gale's round-trip jeep problem . . . . . 299--309 Steven H. Weintraub Count-wheels: a mathematical problem arising in horology . . . . . . . . . . 310--316 Donald R. Chalice How to teach a class by the modified Moore method . . . . . . . . . . . . . . 317--321 Theodore P. Hill The significant-digit phenomenon . . . . 322--327 LaDawn Haws and Terry Kiser Exploring the brachistochrone problem 328--336 William Derrick and Jack Eidswick Continued fractions, Chebychev polynomials, and chaos . . . . . . . . . 337--344 Zheng Bing Wang and Robert Fokkink and Wan Fokkink A relation between partitions and the number of divisors . . . . . . . . . . . 345--346 Paolo Starni Answers to two questions concerning quotients of primes . . . . . . . . . . 347--349 James W. M. Ford Avoiding the exchange lemma . . . . . . 350--351 Stephen Silverman Intervals contained in arithmetic combinations of sets . . . . . . . . . . 351--353 D. Flath and A. Zulauf Does the Möbius function determine multiplicative arithmetic . . . . . . . 354--356
I. Grattan-Guinness Why did George Green write his essay of 1828 on electricity and magnetism . . . 387--396 Susan Bassein Order and chaos on your desk . . . . . . 409--416 T. R. Scavo and J. B. Thoo On the geometry of Halley's method . . . 417--426 A. R. Meijer The binary expansion of $ 1 / p $ . . . 427--430 Ricardo Diaz and Sinai Robins Pick's formula via the Weierstrass $ \wp $-function . . . . . . . . . . . . . . . 431--437 George Mackiw Permutations as products of transpositions . . . . . . . . . . . . . 438--440 Bjorn Poonen Congruences relating the order of a group to the number of conjugacy classes 440--442 Peter Andersson The color invariant for knots and links 442--448 Hermann Weyl Topology and abstract algebra as two roads of mathematical comprehension. I. Translated from the German by Abe Shenitzer . . . . . . . . . . . . . . . 453--460
S. L. Zabell Alan Turing and the central limit theorem . . . . . . . . . . . . . . . . 483--494 Michael I. Rosen Niels Hendrik Abel and equations of the fifth degree . . . . . . . . . . . . . . 495--505 John Oprea Geometry and the Foucault pendulum . . . 515--522 David P. Robbins Areas of polygons inscribed in a circle 523--530 Paul D. Scofield Curves of constant precession . . . . . 531--537 Jeffery C. Allen Matrix expansion by orthogonal Kronecker products . . . . . . . . . . . . . . . . 538--540 Walter Rudin Injective polynomial maps are automorphisms . . . . . . . . . . . . . 540--543 Robin J. Chapman An elementary proof of the simplicity of the Mathieu groups $ M_{11} $ and $ M_{23} $ . . . . . . . . . . . . . . . . 544--545
Heikki Hämäläinen and Iiro Honkala and Simon Litsyn and Patric Östergård Football pools --- a game for mathematicians . . . . . . . . . . . . . 579--588 Reuben Hersh Fresh breezes in the philosophy of mathematics . . . . . . . . . . . . . . 589--594 Nigel Boston and Marshall L. Greenwood Quadratics representing primes . . . . . 595--599 Leslie Lamport How to write a proof . . . . . . . . . . 600--608 Kenneth B. Stolarsky Searching for common generalizations: the case of hyperbolic functions . . . . 609--619 P. Sabinin and M. G. Stone Transforming $n$-gons by folding the plane . . . . . . . . . . . . . . . . . 620--627 David A. Singer Isometries of the plane . . . . . . . . 628--631 V. A. Geyler One more construction which is impossible . . . . . . . . . . . . . . . 632--634 Takashi Matsuda An inductive proof of a mixed arithmetic-geometric mean inequality . . 634--637 T. S. Michael The ranks of tournament matrices . . . . 637--639 David L. Ranum On some applications of Fibonacci numbers . . . . . . . . . . . . . . . . 640--645 Hermann Weyl Topology and abstract algebra as two roads of mathematical comprehension. II. Translated from the German by Abe Shenitzer . . . . . . . . . . . . . . . 646--651
G. Myerson and A. J. van der Poorten Some problems concerning recurrence sequences . . . . . . . . . . . . . . . 698--705 Dana Mackenzie A hyperbolic plane coloring and the simple group of order $ 168 $ . . . . . 706--715 Kent E. Morrison Cosine products, Fourier transforms, and random sums . . . . . . . . . . . . . . 716--724 Geza Schay How to add fast --- on average . . . . . 725--730 H. R. Morton Fibonacci-like sequences and greatest common divisors . . . . . . . . . . . . 731--734 I. M. Isaacs and Thilo Zieschang Generating symmetric groups . . . . . . 734--739 Lutz G. Lucht On the arithmetic-geometric mean inequality . . . . . . . . . . . . . . . 739--740
Richard K. Guy My favorite elliptic curve: a tale of two types of triangles . . . . . . . . . 771--781 Keith M. Kendig Stalking the wild ellipse . . . . . . . 782--787 Annalisa Crannell The role of transitivity in Devaney's definition of chaos . . . . . . . . . . 788--797 David G. Poole The stochastic group . . . . . . . . . . 798--801 J. W. Sander A story of binomial coefficients and primes . . . . . . . . . . . . . . . . . 802--807 Martin Aigner Turán's graph theorem . . . . . . . . . . 808--816 Hans Samelson More on Kummer's test . . . . . . . . . 817--818 G. M. Tuynman The derivation of the exponential map of matrices . . . . . . . . . . . . . . . . 818--820 Vlastimil Pták The Kantorovich inequality . . . . . . . 820--821 Robert Kalaba and Rong Xu On the generalized inverse form of the equations of constrained motion . . . . 821--825 John Stillwell Elliptic curves . . . . . . . . . . . . 831--837
George W. Tokarsky Polygonal rooms not illuminable from every point . . . . . . . . . . . . . . 867--879 Gunnar Blom and Lars Holst and Dennis Sandell Three SING-SING problems . . . . . . . . 880--887 John E. Morrill A Nobel Prize in mathematics . . . . . . 888--891 Richard Blecksmith and Purushottam W. Laud Some exact number theory computations via probability mechanisms . . . . . . . 893--903 Ilse C. F. Ipsen and Carl D. Meyer The angle between complementary subspaces . . . . . . . . . . . . . . . 904--911 Serge Tabachnikov The four-vertex theorem revisited --- two variations on the old theme . . . . 912--916 R. B. Burckel Entire functions which vanish at infinity . . . . . . . . . . . . . . . . 916--918 D. Zagier A converse to Cauchy's inequality . . . 919--920 Richard K. Guy and Richard J. Nowakowski Monthly unsolved problems, 1969--1995 921--926
David Fowler The binomial coefficient function . . . 1--17 Jim Henle Classical mathematics. Baroque mathematics. Romantic mathematics? Mathematics jazz! Also atonal, New Age, minimalist, and punk mathematics . . . . 18--29 Bruce Solomon Tantrices of spherical curves . . . . . 30--39 D. Borwein and J. M. Borwein and P. B. Borwein and R. Girgensohn Giuga's conjecture on primality . . . . 40--50 William M. Faucette A geometric interpretation of the solution of the general quartic polynomial . . . . . . . . . . . . . . . 51--57 Bruno Codenotti and Luciano Margara Transitive cellular automata are sensitive . . . . . . . . . . . . . . . 58--62 Ray Redheffer Use of a differential inequality in combinatorics . . . . . . . . . . . . . 62--64 V. M. Tikhomirov The evolution of methods of convex optimization . . . . . . . . . . . . . . 65--71
H. O. Pollak Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Andrew Gleason . . . . . . . . . . . . . 105--106 James T. Sandefur Using self-similarity to find length, area, and dimension . . . . . . . . . . 107--120 Peter Hilton and Jean Pedersen The Euler characteristic and Pólya's dream . . . . . . . . . . . . . . . . . 121--131 Benno Artmann A Roman icosahedron discovered . . . . . 132--133 Manuel Barros and Oscar J. Garay Free elastic parallels in a surface of revolution . . . . . . . . . . . . . . . 149--156 Israel Gohberg and Seymour Goldberg A simple proof of the Jordan decomposition theorem for matrices . . . 157--159 A. Caruth A concise proof of Hilbert's basis theorem . . . . . . . . . . . . . . . . 160--161 Jesús Ferrer Rolle's theorem fails in $ l_2 $ . . . . 161--165 Gheorghe P\uaun and Arto Salomaa Self-reading sequences . . . . . . . . . 166--168
A. F. Beardon Sums of powers of integers . . . . . . . 201--213 Reinhold Remmert Wielandt's theorem about the $ \Gamma $-function . . . . . . . . . . . . . . . 214--220 Louis Zulli Charting the $3$-sphere --- an exposition for undergraduates . . . . . 221--229 Doron Zeilberger The method of undetermined generalization and specialization. Illustrated with Fred Galvin's amazing proof of the Dinitz conjecture . . . . . 233--239 Thomas Hull A note on ``impossible'' paper folding 240--241 Gary Lawlor A new minimization proof for the brachistochrone . . . . . . . . . . . . 242--249 Richard Mansfield Strategies for the Shannon switching game . . . . . . . . . . . . . . . . . . 250--252 Gerald J. Porter $k$-volume in $ {\bf R}^n$ and the generalized Pythagorean theorem . . . . 252--256 Abe Shenitzer A few expository mini-essays . . . . . . 257--263
Richard Askey and Deborah Tepper Haimo Similarities between Fourier and power series . . . . . . . . . . . . . . . . . 297--304 Richard H. Warren Disks on a chessboard . . . . . . . . . 305--307 Bennett Eisenberg and Rosemary Sullivan Random triangles in $n$ dimensions . . . 308--318 Adrian Oldknow The Euler-Gergonne-Soddy triangle of a triangle . . . . . . . . . . . . . . . . 319--329 Robert E. Hartwig Roth's removal rule and the rational canonical form . . . . . . . . . . . . . 332--335 Manfred Krause A simple proof of the Gale-Ryser theorem 335--337 Yves Martinez-Maure A note on the tennis ball theorem . . . 338--340
Frank Morgan What is a surface . . . . . . . . . . . 369--376 Ron Perline Non-Euclidean flashlights . . . . . . . 377--385 Saber Elaydi On a converse of Sharkovsky's theorem 386--392 Kimmo Eriksson Splitting a polygon into two congruent pieces . . . . . . . . . . . . . . . . . 393--400 John Hannah A geometric approach to determinants . . 401--409 Darrell Desbrow On zero derivatives . . . . . . . . . . 410--411 Peter Duren and Walter Hengartner and Richard S. Laugesen The argument principle for harmonic functions . . . . . . . . . . . . . . . 411--415 Richard B. Darst and Gerald D. Taylor Differentiating powers of an old friend 415--416 Israel Kleiner The genesis of the abstract ring concept 417--424
Daniel Henry Gottlieb All the way with Gauss--Bonnet and the sociology of mathematics . . . . . . . . 457--469 Roger A. Horn and Ingram Olkin When does $ A^*A = B^*B $ and why does one want to know . . . . . . . . . . . . 470--482 Susan Bassein A sampler of randomness . . . . . . . . 483--490 Don Fallis Mathematical proof and the reliability of DNA evidence . . . . . . . . . . . . 491--497 Charles H. Jepsen Equidissections of trapezoids . . . . . 498--500 Paul Monsky Calculating a trapezoidal spectrum . . . 500--501 Doron Zeilberger Reverend Charles to the aid of Major Percy and Fields medalist Enrico . . . . 501--502 József Bukor and János T. Tóth On accumulation points of ratio sets of positive integers . . . . . . . . . . . 502--504
Paulo Ribenboim Catalan's conjecture . . . . . . . . . . 529--538 Roger S. Pinkham Mathematics and modern technology . . . 539--545 C. W. Groetsch Tartaglia's Inverse Problem in a Resistive Medium . . . . . . . . . . . . 546--551 Donald P. Minassian The current state of actuarial science 552--561 T. Y. Lam and K. H. Leung On the cyclotomic polynomial $ \Phi_{pq}(X) $ . . . . . . . . . . . . . 562--564 Edward B. Burger and Thomas Struppeck Does $ \sum^\infty_{n = 0}{1} / {n!} $ really converge? Infinite series and $p$-adic analysis or ``You can sum some of the series some of the time and some of the series none of the time$ \ldots $ but can you sum some of the series all of the time?'' . . . . . . . . . . . . . 565--577 Charles R. Johnson and Erik A. Schreiner The relationship between $ A B $ and $ B A $ . . . . . . . . . . . . . . . . . . 578--582 Hajrudin Fejzi\'c On thin sets of circles . . . . . . . . 582--585 Horst Alzer A proof of the arithmetic mean-geometric mean inequality . . . . . . . . . . . . 585--585 Joseph L. Doob The development of rigor in mathematical probability (1900--1950) [in \it Development of mathematics 1900--1950 (Luxembourg, 1992), 157--170, Birkhäuser, Basel, 1994, MR 95i:60001] . . . . . . . 586--595
Robert G. Bartle Return to the Riemann integral . . . . . 625--632 Richard D. Neidinger and R. John Annen, III The road to chaos is filled with polynomial curves . . . . . . . . . . . 640--653 Stephen Bedding and Keith Briggs Iteration of quaternion functions . . . 654--664 Patrick Ahern and Walter Rudin Geometric properties of the gamma function . . . . . . . . . . . . . . . . 678--681 Sadahiro Saeki A proof of the existence of infinite product probability measures . . . . . . 682--683 Leo S. Gurin A problem . . . . . . . . . . . . . . . 683--686
Paul T. Bateman and Harold G. Diamond A hundred years of prime numbers . . . . 729--741 Thomas Burger and Peter Gritzmann and Victor Klee Polytope projection and projection polytopes . . . . . . . . . . . . . . . 742--755 Aleksandar Juri\vsi\'c The Mercedes knot problem . . . . . . . 756--770 Arthur T. White Fabian Stedman: the first group theorist 771--778 Herbert I. Brown and James W. Burgmeier and David S. Dummit Functions whose successive tangent lines enclose proportional areas . . . . . . . 779--787 M. H. Eggar On the discriminant criterion and a generalization . . . . . . . . . . . . . 788--792 Ernst Snapper Expressing primes as quadratic forms of integers . . . . . . . . . . . . . . . . 793--794 Richard J. Bagby Volumes of cones . . . . . . . . . . . . 794--796 Edward Bertram and Marcel Herzog On regular bases of finite groups . . . 796--799 Freeman Dyson The scientist as rebel . . . . . . . . . 800--805
Shawnee L. McMurran and James J. Tattersall The mathematical collaboration of M. L. Cartwright and J. E. Littlewood . . . . 833--845 Roman Kossak What are infinitesimals and why they cannot be seen . . . . . . . . . . . . . 846--853 John Brillhart and Patrick Morton A case study in mathematical research: the Golay--Rudin--Shapiro sequence . . . 854--869 Edward Aboufadel A mathematician catches a baseball . . . 870--878 Victoria Powers Hilbert's 17th problem and the champagne problem . . . . . . . . . . . . . . . . 879--887 W. McCune and A. D. Sands Computer and human reasoning: single implicative axioms for groups and for abelian groups . . . . . . . . . . . . . 888--892 Roger Webster An elementary proof of Horn's theorem 892--894 James Angelos and George Grossman and Yury Ionin and Edwin Kaufman and Terry Lenker and Leela Rakesh Packability of five spheres on a sphere implies packability of six . . . . . . . 894--896
Bruce Pourciau Reading the master: Newton and the birth of celestial mechanics . . . . . . . . . 1--19 Jack W. Rogers, Jr. Applications of linear algebra in calculus . . . . . . . . . . . . . . . . 20--26 A. Vince Periodicity, quasiperiodicity, and Bieberbach's theorem on crystallographic groups . . . . . . . . . . . . . . . . . 27--35 John A. Baker Integration over spheres and the divergence theorem for balls . . . . . . 36--47 R. B. Burckel Three secrets about harmonic functions 52--56 Vilmos Komornik A short proof of the Erd\Hos--Mordell theorem . . . . . . . . . . . . . . . . 57--60 Don Buckholtz Inverting the difference of Hilbert space projections . . . . . . . . . . . 60--61 I. G. Bashmakova and E. I. Slavutin Glimpses of algebraic geometry. Introduction to: \booktitleA History of Diophantine analysis (Russian) [``Nauka'', Moscow, 1984; MR 85m:01004]. Translated by Abe Shenitzer . . . . . . 62--67
Carole B. Lacampagne Yueh-Gin Gung and Dr. Charles Y. Hu award for distinguished service to Deborah Tepper Haimo . . . . . . . . . . 97--98 Bryan L. Shader and Chanyoung Lee Shader Scheduling conflict-free parties for a dating service . . . . . . . . . . . . . 99--106 Ralph H. Buchholz and Randall L. Rathbun An infinite set of Heron triangles with two rational medians . . . . . . . . . . 107--115 T. K. Lam Connected Sprouts . . . . . . . . . . . 116--119 Ronald E. Prather Regular expressions for program computations . . . . . . . . . . . . . . 120--130 R. Bruce Richter and Carsten Thomassen Relations between crossing numbers of complete and complete bipartite graphs 131--137 John M. Holte Carries, combinatorics, and an amazing matrix . . . . . . . . . . . . . . . . . 138--149 Walter Nef A new look at Euler's theorem for polyhedra: a comment . . . . . . . . . . 150--151 Tadashi F. Tokieda The hopping hoop . . . . . . . . . . . . 152--154 John Greene Principal ideal domains are almost Euclidean . . . . . . . . . . . . . . . 154--156 Shmuel Onn A colorful determinantal identity, a conjecture of Rota, and Latin squares 156--159 W. K. Nicholson Very semisimple modules . . . . . . . . 159--162
Jim Pitman Some probabilistic aspects of set partitions . . . . . . . . . . . . . . . 201--209 Karen Hunger Parshall and Eugene Seneta Building an international reputation: the case of J. J. Sylvester (1814--1897) 210--222 Geoffrey R. Goodson The inverse-similarity problem for real orthogonal matrices . . . . . . . . . . 223--230 Thomas W. Tucker Rethinking rigor in calculus: the role of the mean value theorem . . . . . . . 231--240 Howard Swann Commentary on rethinking rigor in calculus: the role of the mean value theorem . . . . . . . . . . . . . . . . 241--245 Edward B. Burger and Frank Morgan Fermat's Last Theorem, the Four Color Conjecture, and Bill Clinton for April Fools' Day . . . . . . . . . . . . . . . 246--255 D. J. Newman Euler's $ \phi $ function on arithmetic progressions . . . . . . . . . . . . . . 256--257 Steve Fisk A note on Weyl's inequality . . . . . . 257--258 Ming-chang Kang Minimal polynomials over cyclotomic fields . . . . . . . . . . . . . . . . . 258--260 Wilhelm Magnus The significance of mathematics: the mathematicians' share in the general human condition . . . . . . . . . . . . 261--269
Eric H. Mason and Stephen M. Gagola, Jr. and John Todd and Theodore J. Rivlin and David Callan Polynomialrecurrencology: 10300 . . . . 272--273
A. J. Berrick and M. E. Keating Rectangular invertible matrices . . . . 297--302 Maarten C. Boerlijst and Martin A. Nowak and Karl Sigmund Equal pay for all prisoners . . . . . . 303--305 Jim Sauerberg and Linghsueh Shu The long and the short on counting sequences . . . . . . . . . . . . . . . 306--317 Daniel J. Velleman Characterizing continuity . . . . . . . 318--322 A. M. Bruckstein and C. L. Mallows and I. A. Wagner Probabilistic pursuits on the grid . . . 323--343 Richard P. Stanley Hipparchus, Plutarch, Schröder, and Hough 344--350 Gert Almkvist Many correct digits of $ \pi $, revisited . . . . . . . . . . . . . . . 351--353 Martin L. Jones A note on a cake cutting algorithm of Banach and Knaster . . . . . . . . . . . 353--355 Hassan Sedaghat The impossibility of unstable, globally attracting fixed points for continuous mappings of the line . . . . . . . . . . 356--358
Hardy Grant Reviews: \em Vita Mathematica: Historical Research and Integration with Teaching, edited by Ronald Calinger . . ?? Andre Toom Reviews: \em Mathematical Circles (Russian Experience), by Dmitri Fomin, Sergey Genkin, and Ilia Itenberg . . . . ?? Judith V. Grabiner Was Newton's calculus a dead end? The continental influence of Maclaurin's treatise of fluxions . . . . . . . . . . 393--410 Pat Touhey Yet another definition of chaos . . . . 411--414 Scott A. McCullough and Leiba Rodman Hereditary classes of operators and matrices . . . . . . . . . . . . . . . . 415--430 Clark Kimberling Major centers of triangles . . . . . . . 431--438 M. Laczkovich On Lambert's proof of the irrationality of $ \pi $ . . . . . . . . . . . . . . . 439--443 Winfried Kohnen A simple congruence modulo $p$ . . . . . 444--445 Marcelo Polezzi A geometrical method for finding an explicit formula for the greatest common divisor . . . . . . . . . . . . . . . . 445--446 Detlef Laugwitz The Evolution of \ldots: On the historical development of infinitesimal mathematics . . . . . . . . . . . . . . 447--455
Sheldon Axler Reviews: \em The Life of Stefan Banach, by Roman Kaluza . . . . . . . . . . . . ?? J. Kevin Colligan Reviews: \em 101 Careers in Mathematics, edited by Andrew Sterrett . . . . . . . ?? J. Dénes Unsolved Problems: When Is There a Latin Power Set? . . . . . . . . . . . . . . . ?? Melanie A. King Lecturing at the `Bored' . . . . . . . . ?? Rajendra Bhatia and Peter \vSemrl Approximate isometries on Euclidean spaces . . . . . . . . . . . . . . . . . 497--504 István Nemes and Marko Petkov\vsek and Herbert S. Wilf and Doron Zeilberger How to do Monthly problems with your computer . . . . . . . . . . . . . . . . 505--519 Lawrence W. Baggett and Herbert A. Medina and Kathy D. Merrill Simultaneously symmetric functions . . . 520--528 R. A. Mollin Prime-producing quadratics . . . . . . . 529--544 Wladyslaw Kulpa The Poincaré-Miranda theorem . . . . . . 545--550 M. Bayat A generalization of Wolstenholme's theorem . . . . . . . . . . . . . . . . 557--560 Bao-lin Zhang A note on the mean value theorem for integrals . . . . . . . . . . . . . . . 561--562
J. N. Anthony Danby Reviews: \em The Sheer Joy of Celestial Mechanics, by Nathaniel Grossman . . . . ?? Jennifer R. Galovich Reviews: \em Strength in Numbers: Discovering the Joy and Power of Mathematics in Everyday Life, by Sherman K. Stein . . . . . . . . . . . . . . . . ?? Kent G. Merryfield and Ngo Viet and Saleem Wats Notes: The Wallet Paradox . . . . . . . ?? S. C. Coutinho The many avatars of a simple algebra . . 593--604 Tiberiu Trif Multiple integrals of symmetric functions . . . . . . . . . . . . . . . 605--608 John Chollet Some inequalities for principal submatrices . . . . . . . . . . . . . . 609--617 Eugene Gutkin Two applications of calculus to triangular billiards . . . . . . . . . . 618--622 Steven H. Weintraub Early transcendentals . . . . . . . . . 623--631 Keith Devlin The logical structure of computer-aided mathematical reasoning . . . . . . . . . 632--646 Henryk Gzyl and José Luis Palacios Notes: The Weierstrass approximation theorem and large deviations . . . . . . 651--653 Detlef Laugwitz The Evolution of \ldots: On the historical development of infinitesimal mathematics. II. The conceptual thinking of Cauchy. Translated from the German by Abe Shenitzer with the editorial assistance of Hardy Grant . . . . . . . 654--663
Norbert Peyerimhoff Areas and Intersections in Convex Domains . . . . . . . . . . . . . . . . 697--704 D. Zagier Newman's Short Proof of the Prime Number Theorem . . . . . . . . . . . . . . . . 705--708 David Callan An Exploratory Approach to Kaplansky's Lemma Leads to a Generalized Resultant 709--712 Bettina Richmond and Thomas Richmond Metric Spaces in Which All Triangles Are Degenerate . . . . . . . . . . . . . . . 713--719 Albert Fathi Partitions of Unity for Countable Covers 720--723 Jeff Knisley Calculus: a Modern Perspective . . . . . 724 Paul Zorn and Arnold Ostebee Pro Choice . . . . . . . . . . . . . . . 728 James J. Kaput Rethinking Calculus: Learning and Thinking . . . . . . . . . . . . . . . . 731 Richard Askey What Do We Do About Calculus? First, Do No Harm . . . . . . . . . . . . . . . . 738 Gerald L. Alexanderson and Leonard F. Klosinski and Loren C. Larson The Fifty-Seventh William Lowell Putnam Mathematical Competition . . . . . . . . 744 Joseph Kupka Notes: a Quadratic Trio . . . . . . . . 755--757 Apoloniusz Tyszka Notes: a Discrete Form of the Beckman-Quarles Theorem . . . . . . . . 757--761 J. Daniel Christensen and Mark Tilford Unsolved Problems: David Gale's Subset Take-Away Game . . . . . . . . . . . . . 762 Ronald E. Mickens Reviews: \em An Introduction to Difference Equations, by Saber Elyadi 777 Wayne Roberts Reviews: \em Calculus Lite, by Frank Morgan . . . . . . . . . . . . . . . . . 780
George W. Cobb and David S. Moore Mathematics, Statistics, and Teaching 801 Marco Abate When is a Linear Operator Diagonalizable? . . . . . . . . . . . . 824--830 Eric Bach Energy Arguments in the Theory of Algorithms . . . . . . . . . . . . . . . 831--837 Thomas Forster Quine's $ {\rm NF} $---60 years on . . . 838--845 Micha\l Misiurewicz Remarks on Sharkovsky's Theorem . . . . 846--847 Andrew Granville Correction to: ``Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle'' [Amer. Math. Monthly \bf 99 (1992), no. 4, 318--331; MR 93a:05008] . . . . . . . . . . . . . . . 848--851 Victor Adamchik and Stan Wagon A Simple Formula for $ \pi $ . . . . . . 852--855 Francis Edward Su Borsuk--Ulam Implies Brouwer: a Direct Construction . . . . . . . . . . . . . . 855--859 Zdzis\law Pogoda and Leszek M. Soko\lowski The Evolution of\ldots: Does mathematics distinguish certain dimensions of spaces? Translated by Abe Shenitzer . . 860--869 William D. Dunbar Reviews: \em Knots and Surfaces: A Guide to Discovering Mathematics, by David W. Farmer and Theodore Stanford & \em Knots and Surfaces, by N. D. Gilbert and T. Porter . . . . . . . . . . . . . . . . . 882 Andrew Bremner Reviews: \em The Book of Numbers, by John Horton Conway and Richard K. Guy 884
Bruce C. Berndt and Heng Huat Chan and Liang-Cheng Zhang Ramanujan's Association with Radicals in India . . . . . . . . . . . . . . . . . 905--911 Ken Ono Ramanujan, Taxicabs, Birthdates, ZIP Codes, and Twists . . . . . . . . . . . 912--917 George E. Andrews Simplicity and Surprise in Ramanujan's ``Lost'' Notebook . . . . . . . . . . . 918--925 Lou Shapiro and D. G. Rogers and Wen-Jin Woan The Catalan Numbers, the Lebesgue Integral, and $ 4^n - 2 $ . . . . . . . 926--931 R. Bruce Richter and William P. Wardlaw Good Matrices: Matrices that Preserve Ideals . . . . . . . . . . . . . . . . . 932--938 Peter A. Braza and Jingcheng Tong A Converse of the Mean Value Theorem . . 939--942 Andrew Granville and Takashi Agoh and Paul Erd\Hos Primes at a (Somewhat Lengthy) Glance 943--945 H. Wu The Mathematics Education Reform: Why You Should be Concerned and What You Can Do . . . . . . . . . . . . . . . . . . . 946 Jeremy Kilpatrick Confronting Reform . . . . . . . . . . . 955 John L. Drost A Shorter Proof of the Ramanujan Congruence Modulo 5 . . . . . . . . . . 963--964 Scott Ahlgren and Lars English and Ron Winters An Amusing Representation of $ x / (\sin x) $ . . . . . . . . . . . . . . . . . . 964--966 Richard J. Nowakowski and Richard K. Guy Monthly Unsolved Problems, 1969--1997 967 Saunders Mac Lane \em Conceptual Mathematics: A First Introduction to Categories, by F. William Lawvere and Steven Schanuel . . 985 Ezra Brown \em Early Astronomy, by Hugh Thurston 988
Jerry L. Kazdan Solving Equations, an Elegant Legacy . . 1--21 Donald W. Robinson Separation of Subspaces by Volume . . . 22--27 Kai Lai Chung Probability and Doob . . . . . . . . . . 28--35 George E. Andrews The Geometric Series in Calculus . . . . 36--40 Timothy Y. Chow The Surprise Examination or Unexpected Hanging Paradox . . . . . . . . . . . . 41--51 Michael David Hirschhorn Notes: Two or Three Identities of Ramanujan . . . . . . . . . . . . . . . 52--55 Michael E. Hoffman The Bull and the Silo: An Application of Curvature . . . . . . . . . . . . . . . 55--58 N. Luzin The Evolution of \ldots Function: Part I 59--67 John Troutman Reviews: \em Analysis by its History, by E. Hairer and G. Wanner . . . . . . . . 79 Anthony Ralston Reviews: \em Principles and Practices of Mathematics, by COMAP . . . . . . . . . 81 Andre Toom Reviews: \em A Mathematical Mosaic: Patterns & Problem Solving, by Ravi Vakil 86
Linda R. Sons Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Alice Turner Schafer . . . . . . . . . . . . . 105 Russell A. Gordon The Use of Tagged Partitions in Elementary Real Analysis . . . . . . . . 107--117 Susan Bassein The Dynamics of a Family of One-Dimensional Maps . . . . . . . . . . 118--130 Hunter S. Snevily and Douglas B. West The Bricklayer Problem and the Strong Cycle Lemma . . . . . . . . . . . . . . 131--143 Craig M. Johnson A Computer Search for Free Actions on Surfaces . . . . . . . . . . . . . . . . 144--153 John C. McConnell Division Algebras --- Beyond the Quaternions . . . . . . . . . . . . . . 154--162 Brian Gerard and Lawrence Roberts Graphical Discovery of a New Identity for Jacobi Polynomials . . . . . . . . . 163--166 Philippe Revoy The Generalized Level of a Non Prime Finite Field is Two . . . . . . . . . . 167--168 Wolfgang Kühn and Zuzana Kühn Cutting High-Dimensional Cakes . . . . . 168--169 Joan Hutchinson and Stan Wagon Kempe Revisited . . . . . . . . . . . . 170--174 Jean Pedersen and Gerald L. Alexanderson Reviews: \em ``Invertible'' Polyhedron Models, distributed by Snyder Engineering . . . . . . . . . . . . . . 186 William Goldman Reviews: \em Topology and Geometry, by Glen E. Bredon . . . . . . . . . . . . . 192
Béla Bollobás To Prove and Conjecture: Paul Erd\Hos and His Mathematics . . . . . . . . . . 209--237 Ran Libeskind-Hadas Sorting in Parallel . . . . . . . . . . 238--245 Murray Schechter Integration Over a Polyhedron: An Application of the Fourier-Motzkin Elimination Method . . . . . . . . . . . 246--251 Kenneth A. Ross Doing and Proving: The Place of Algorithms and Proofs in School Mathematics . . . . . . . . . . . . . . 252--255 David Beckwith Legendre Polynomials and Polygon Dissections? . . . . . . . . . . . . . . 256--257 Takayuki Furuta and Masahiro Yanagida Generalized Means and Convexity of Inversion for Positive Operators . . . . 258--259 Mohammad Saleh and Hasan Yousef The Number of Ring Homomorphisms from $ {Z}_{m_1} \times \cdots \times {Z}_{m_r} i n t o {Z}_{k_1} \times \cdots \times {Z}_{k_s} $ . . . . . . . . . . . . . . 259--260 M. Mirzakhani A Simple Proof of a Theorem of Schur . . 260--262 N. Luzin The Evolution of \ldots Function: Part II . . . . . . . . . . . . . . . . . . . 263--270 Anonymous Problems and Solutions . . . . . . . . . 271--283 Roger Cooke \em Évariste Galois 1811--1832, by Laura Toti Rigatelli. Translated from the Italian by John Denton. Birkhäuser, 1996, 168pp., \$29.50 . . . . . . . . . . . . 284--288 Jet Wimp Reviews: \em The Fast Fourier Transform Workshop, by Richard and Sandra McPeak 289--292 Daniel H. Ullman Reviews: \em Which Way Did the Bicycle Go?, by Joseph D. E. Konhauser, Dan Velleman, and Stan Wagon and \em Problems and Solutions from the Mathematical Visitor, edited by Stanley Rabinowitz . . . . . . . . . . . . . . . 292--296 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 297--301
Ilan Vardi Archimedes' Cattle Problem . . . . . . . 305--319 C. W. Groetsch Lanczos' Generalized Derivative . . . . 320--326 Ellen Gethner and Stan Wagon and Brian Wick A Stroll Through the Gaussian Primes . . 327--337 Herman Erlichson Galileo's Work on Swiftest Descent from a Circle and How He Almost Proved the Circle Itself Was the Minimum Time Path 338--347 Michael Sheard Induction the Hard Way . . . . . . . . . 348--353 C. Douglas Howard Good Paths Don't Double Back . . . . . . 354--357 Xianfu Wang A Note on the Clarke Subdifferential . . 357--359 Michael Reid The Number of Conjugacy Classes . . . . 359--361 Branko Grünbaum Which Coronas Are Simple? . . . . . . . 362--365 Anonymous Problems and Solutions . . . . . . . . . 366--376 David A. Sánchez Ordinary Differential Equations Texts 377--383 Owen Thomas \em The Schools We Need, by E. D. Hirsch, Jr. . . . . . . . . . . . . . . 384--386 Victor J. Katz \em Force and Geometry in Newton's Principia, by François De Gandt, translated by Curtis Wilson . . . . . . 386--392 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 393--397
James Case The Modeling and Analysis of Financial Time Series . . . . . . . . . . . . . . 401--411 Franklin Lowenthal and Arnold Langsen and Clark T. Benson Merton's Partial Differential Equation and Fixed Point Theory . . . . . . . . . 412--420 Wilbur R. Knorr ``Rational Diameters'' and the Discovery of Incommensurability . . . . . . . . . 421--429 Michel Balinski and Guillaume Ratier Graphs and Marriages . . . . . . . . . . 430--445 Laurent Habsieger and Maxim Kazarian and Sergei Lando On the Second Number of Plutarch . . . . 446--446 Bruce Anderson and Jeffrey Jackson and Meera Sitharam Descartes' Rule of Signs Revisited . . . 447--451 Ralph Faudree A Conjecture of Erd\Hos . . . . . . . . 451--453 R. D. Driver Toricelli's Law --- An Ideal Example of an Elementary ODE . . . . . . . . . . . 453--455 Zdzis\law Pogoda and Leszek M. Soko\lowski Does Mathematics Distinguish Certain Dimensions of Spaces? Part II . . . . . 456--463 Anonymous Problems and Solutions . . . . . . . . . 464--476 Daniel Schwalbe and Hal R. Varian Computational Economics and Finance: Modeling and Analysis with Mathematica 477--481 Peter Hilton and T. W. Korner The Pleasures of Counting . . . . . . . 481--485 Leonard Gillman and Richard Courant and Herbert Robbins and Ian Stewart What is Mathematics? . . . . . . . . . . 485--488 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 489--493 Roger A. Horn Editor's Endnotes . . . . . . . . . . . 494--494
Guershon Harel Two Dual Assertions: The First on Learning and the Second on Teaching (Or Vice Versa) . . . . . . . . . . . . . . 497 Alan Gluchoff and Frederick Hartmann Univalent polynomials and non-negative trigonometric sums . . . . . . . . . . . 508--522 Peter M. Neumann Reflections on reflection in a spherical mirror . . . . . . . . . . . . . . . . . 523--528 Richard Blecksmith and Michael McCallum and J. L. Selfridge $3$-smooth representations of integers 529--543 C. W. Groetsch Aristotle's fall . . . . . . . . . . . . 544--547 B. Banaschewski On proving the existence of complete ordered fields . . . . . . . . . . . . . 548--551 Charles Kicey and Sudhir Goel A Series for $ \ln k $ . . . . . . . . . 552--554 Gerd Herzog $ C^1 $-solutions of $ x = f(x') $ are convex or concave . . . . . . . . . . . 554--555 Douglas E. Lampert and Peter J. Slater Parallel knockouts in the complete graph 556--558 Frank A. Farris \em Visual Complex Analysis, by Tristan Needham . . . . . . . . . . . . . . . . 570 Robert Messer \em Linear Algebra Problem Book, by Paul R. Halmos . . . . . . . . . . . . . . . 577 David Singmaster \em After Math. Puzzles and Brainteasers, by Ed Barbeau; \em The Chicken from Minsk, by Yuri B. Chernyak and Robert M. Rose; \em New Mathematical Diversions, revised edition, by Martin Gardner . . . . . . . . . . . . . . . . 579
Robert A. Bosch and Jason A. Smith Separating hyperplanes and the authorship of the disputed Federalist papers . . . . . . . . . . . . . . . . . 601--608 Marc Frantz Two functions whose powers make fractals 609--617 M. H. Eggar Pinhole cameras, perspective, and projective geometry . . . . . . . . . . 618--630 Kosta Do\vsen Functions redefined . . . . . . . . . . 631--635 Vilmos Komornik and Paola Loreti Unique developments in non-integer bases 636--639 R. W. Hamming Mathematics on a distant planet . . . . 640--650 T. Y. Lam A theorem of Burnside on matrix rings 651--653 Peter Dierolf and Volker Schmidt A proof of the change of variable formula for $d$-dimensional integrals 654--656 Hong Bing Yu On the Diophantine Equation $ (x + 1)^y - x^z = 1 $ . . . . . . . . . . . . . . 656--657 Ira M. Gessel Wolstenholme revisited . . . . . . . . . 657--658 F. A. Medvedev Nonstandard analysis and the history of classical analysis . . . . . . . . . . . 659--664 Steven G. Krantz \em Introduction to Calculus and Classical Analysis, by Omar Hijab; \em Introduction to Mathematical Structures and Proofs, by Larry J. Gerstein . . . . 677 Joby Milo Anthony \em Mathematical Reflections: In a Room with Many Mirrors, by Peter Hilton, Derek Holton, and Jean Pedersen . . . . 682 Robert L. Devaney \em Interactive Differential Equations, by Beverly West, Steven Strogatz, Jean Marie McDill, and John Cantwell; software designer Hubert Hohn . . . . . 687
Tadashi F. Tokieda Mechanical Ideas in Geometry . . . . . . 697--703 R. Cheng and A. Dasgupta and B. R. Ebanks and L. F. Kinch and L. M. Larson and R. B. McFadden When Does $ f - 1 = 1 / f $ ? . . . . . 704--717 Roger L. Kraft A Golden Cantor Set . . . . . . . . . . 718--725 Darrell Desbrow On evaluating $ \int^{+ \infty }_{- \infty }e^{ax(x - 2b)}d x $ by contour integration round a parallelogram . . . 726--731 C. Groß and T.-K. Strempel On Generalizations of Conics and on a Generalization of the Fermat--Torricelli Problem . . . . . . . . . . . . . . . . 732--743 Leonard F. Klosinski and Gerald L. Alexanderson and Loren C. Larson The Fifty-Eighth William Lowell Putnam Mathematical Competition . . . . . . . . 744 T. W. Körner Butterfly Hunting and the Symmetry of Mixed Partial Derivatives . . . . . . . 756--758 Stephen M. Gagola, Jr. A Note on the Non-existence of Regular Bases for Finite Groups . . . . . . . . 759--761 Joseph Amal Nathan The Irrationality of $ e^x $ for Nonzero Rational $x$ . . . . . . . . . . . . . . 762--763 Giles Warrack A Note on Variable Replacement Rates in Urn Models . . . . . . . . . . . . . . . 764--765 Richard K. Guy and John L. Selfridge Factoring Factorial $n$ . . . . . . . . 766 Gerald B. Folland \em Handbook of Writing for the Mathematical Sciences, by Nicholas J. Higham; \em A Primer of Mathematical Writing, by Steven G. Krantz . . . . . . 779 Robert V. Hogg \em Leading Personalities in Statistical Sciences, edited by Norman L. Johnson and Samuel Kotz . . . . . . . . . . . . 782
Alfred B. Manaster Some Characteristics of Eighth Grade Mathematics Classes in the TIMSS Videotape Study . . . . . . . . . . . . 793 Lily Yau and Adi Ben-Israel The Newton and Halley Methods for Complex Roots . . . . . . . . . . . . . 806--818 Kiran S. Kedlaya and Lenhard L. Ng The Rook on the Half-Chessboard, or How Not to Diagonalize a Matrix . . . . . . 819--824 Jack Cassidy The Last Round of Betting in Poker . . . 825--831 Yoav Benyamini Applications of the Universal Surjectivity of the Cantor Set . . . . . 832--839 Apostolos Thoma The Group $ {Z}_2 \times {Z}_n $ and Regular Polygonal Paths . . . . . . . . 840--841 Busiso P. Chisala A Quick Cayley--Hamilton . . . . . . . . 842--844 J. Marshall Ash The Probability of a Tie in an $n$-Game Match . . . . . . . . . . . . . . . . . 844--846 J. M. Borwein and Xianfu Wang The Converse of the Mean Value Theorem May Fail Generically . . . . . . . . . . 847--848 John A. Ewell A Trio of Triangular Number Theorems . . 848--849 John Stillwell Exceptional Objects . . . . . . . . . . 850--858 Dan Schnabel \em Goodbye, Descartes, by Keith Devlin 870 Jeffrey Nunemacher \em Fourier Analysis and Boundary Value Problems, by Enrique A. González-Velasco 874 William F. Lucas \em Fair Division: From Cake-Cutting to Dispute Resolution, by Steven J. Brams and Alan D. Taylor . . . . . . . . . . . 877
Ilse C. F. Ipsen and Carl D. Meyer The Idea Behind Krylov Methods . . . . . 889--899 Kiran S. Kedlaya Product-Free Subsets of Groups . . . . . 900--906 Bernd Sturmfels Polynomial Equations and Convex Polytopes . . . . . . . . . . . . . . . 907--922 Aviezri S. Fraenkel Multivision: An Intractable Impartial Game With a Linear Winning Strategy . . 923--928 Brian J. McCartin Seven Deadly Sins of Numerical Computation . . . . . . . . . . . . . . 929--941 S. C. Woon Generating Integrals and an Elementary Proof of the Finite Harmonic Series Theorem by Fractional Calculus . . . . . 942--945 Raymond M. Redheffer Monotonicity of the Maxima . . . . . . . 945--948 Vilmos Komornik A Simple Proof of Farkas' Lemma . . . . 949--950 Richard K. Guy Nothing's New in Number Theory? . . . . 951--954 Lenore Blum \em Julia, A Life in Mathematics, by Constance Reid . . . . . . . . . . . . . 964 Daniel P. Maki \em Would-be Worlds, by John L. Casti 972 Reuben Hersh \em The Number Sense: How the Mind Creates Mathematics, by Stanislas Dehaene . . . . . . . . . . . . . . . . 975
P. J. McKenna Large torsional oscillations in suspension bridges revisited: fixing an old approximation . . . . . . . . . . . 1--18 Geoffrey R. Goodson Inverse conjugacies and reversing symmetry groups . . . . . . . . . . . . 19--26 Dmitry Fuchs and Serge Tabachnikov More on paperfolding . . . . . . . . . . 27--35 L. R. Bragg Trigonometric integrals and Hadamard products . . . . . . . . . . . . . . . . 36--42 Richard Blecksmith and Paul Erd\Hos and J. L. Selfridge Cluster primes . . . . . . . . . . . . . 43--48 John A. Zuehlke Fermat's last theorem for Gaussian integer exponents . . . . . . . . . . . 49--49 M. J. Jamieson On rational function approximations to square roots . . . . . . . . . . . . . . 50--52 A. J. van der Poorten and P. G. Walsh A note on Jacobi symbols and continued fractions . . . . . . . . . . . . . . . 52--56 I. G. Bashmakova and G. S. Smirnova The birth of literal algebra. Translated from the Russian and edited by Abe Shenitzer . . . . . . . . . . . . . . . 57--66
Kenneth A. Ross Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Leonard Gillman . . . . . . . . . . . . 97--98 Solomon Feferman Does mathematics need new axioms . . . . 99--111 Gerald S. Goodman Statistical independence and normal numbers: an aftermath to Mark Kac's Carus Monograph . . . . . . . . . . . . 112--126 Lyle N. Long and Howard Weiss The velocity dependence of aerodynamic drag: a primer for mathematicians . . . 127--135 D. M. Cannell George Green: an enigmatic mathematician 136--151 Arthur T. Benjamin and Kan Yasuda Magic ``squares'' indeed . . . . . . . . 152--156 Zoltán Sasvári An elementary proof of Binet's formula for the gamma function . . . . . . . . . 156--158 Richard G. Swan A simple proof of Rankin's campanological theorem . . . . . . . . . 159--161
Junpei Sekino $n$-ellipses and the minimum distance sum problem . . . . . . . . . . . . . . 193--202 Arcadii Z. Grinshpan The Bieberbach conjecture and Milin's functionals . . . . . . . . . . . . . . 203--214 Dimitris A. Sardelis and Theodoros M. Valahas Decision making: a golden rule . . . . . 215--226 Vilmos Totik A tale of two integrals . . . . . . . . 227--240 Jaume Paradís and Pelegrí Viader and Lluís Bibiloni A mathematical excursion: from the three-door problem to a Cantor-type set 241--251
Robert L. Devaney The Mandelbrot set, the Farey tree, and the Fibonacci sequence . . . . . . . . . 289--302 Fred Richman Existence proofs . . . . . . . . . . . . 303--308 Paul Corazza Introduction to metric-preserving functions . . . . . . . . . . . . . . . 309--323 Bernard D. Flury and Robert Irving and M. N. Goria Magic dice . . . . . . . . . . . . . . . 324--337 Andrew Granville and Friedrich Roesler The set of differences of a given set 338--344 S. Anoulova and J. Bennies and J. Lenhard and D. Metzler and Y. Sung and A. Weber Six ways of looking at Burtin's lemma 345--351 Hiroshi Maehara Lexell's Theorem via an Inscribed Angle Theorem . . . . . . . . . . . . . . . . 352--353 Khristo Boyadzhiev A Characteristic Property of Differentiation . . . . . . . . . . . . 353--355 Kiran S. Kedlaya A Weighted Mixed-Mean Inequality . . . . 355--358 Ian Caines and Carrie Gates and Richard K. Guy and Richard J. Nowakowski Periods in Taking and Splitting Games 359--361 Vasile Mihai Problem 10725 . . . . . . . . . . . . . 362--362 Donald E. Knuth Problem 10726 . . . . . . . . . . . . . 362--362 Jean Anglesio Problem 10727 . . . . . . . . . . . . . 362--362 Titu Andreescu Problem 10728 . . . . . . . . . . . . . 362--362 David P. Bellamy and Felix Lazebnik Problem 10729 . . . . . . . . . . . . . 362--362 Walther Janous Problem 10730 . . . . . . . . . . . . . 363--363 M. J. Pelling Problem 10731 . . . . . . . . . . . . . 363--363 Daniel Goffinet and Kiran S. Kedlaya and Kenneth Schilling and Arlo W. Schurle and Fredric D. Ancel and Phil Bowers and John Bryant Connected Sets of Periodic Functions: 10434 . . . . . . . . . . . . . . . . . 363--364 Marius Cavachi and Sam Northshield and Simeon T. Stefanov and Victor Klee The Plane Covered by Disks: 10440 . . . 364--365 Joaquin Gomez Rey and Jose Heber Nieto Random Perfect Matchings: 10587 . . . . 365--365 Marcin Mazur Characterizations of the Medial Triangle: 10588 . . . . . . . . . . . . 365--366 Paul Bateman and David Bradley and David Callan and Richard Stong Binary Expansions and $k$ th Powers: 10596 . . . . . . . . . . . . . . . . . 366--367 Joseph Rosenblatt and Thomas Hermann and John H. Lindsey, II A Supremum of Sine Differences: 10604 368--368 Jovan Vukmirovic and Kenneth Schilling A Convergent Series: 10657 . . . . . . . 368--368 Tony Rothman Book Review: \booktitleThe French Mathematician, by Tom Petsinis . . . . . 369--373 Bonnie Gold Book Review: \booktitleSocial Constructivism as a Philosophy of Mathematics, by Paul Ernest; What is Mathematics, Really? by Reuben Hersh . . 373--380 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 381--384 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Front Matter . . . . . . . . . . . . . . ??
George K. Francis and Jeffrey R. Weeks Conway's ZIP Proof . . . . . . . . . . . 393--399 Roger L. Kraft Chaos, Cantor Sets, and Hyperbolicity for the Logistic Maps . . . . . . . . . 400--408 Tom M. Apostol An Elementary View of Euler's Summation Formula . . . . . . . . . . . . . . . . 409--418 David B. Leep and Gerry Myerson Marriage, Magic, and Solitaire . . . . . 419--429 Hugh Howards and Michael Hutchings and Frank Morgan The Isoperimetric Problem on Surfaces 430--439 Timothy . Chow What is a Closed-Form Number? . . . . . 440--448 Greg Martin The Smallest Solution of $ \phi (30 n + 1) $ Is \ldots . . . . . . . . . . . . . 449--451 Frank K. Kenter A Matrix Representation for Euler's Constant, $ \gamma $ . . . . . . . . . . 452--454 H. Fejzic and D. Rinne More on a Mean Value Theorem Converse 454--455 L. J. Lange An Elegant Continued Fraction for $ \pi $ . . . . . . . . . . . . . . . . . . . 456--458 Matthias Beck The Reciprocity Law for Dedekind Sums via the Constant Ehrhart Coefficient . . 459--462 Detlef Laugwitz Riemann's Dissertation and Its Effect on the Evolution of Mathematics . . . . . . 463--469 M. N. Deshpande Problems: 10732 . . . . . . . . . . . . 470--470 Sung Soo Kim Problems: 10733 . . . . . . . . . . . . 470--470 Floor van Lamoen Problems: 10734 . . . . . . . . . . . . 470--470 Gustavus J. Simmons Problems: 10735 . . . . . . . . . . . . 470--470 Mizan R. Khan Problems: 10736 . . . . . . . . . . . . 470--470 Hassan Ali Shah Ali Problems: 10737 . . . . . . . . . . . . 471--471 Radu Theodorescu Problems: 10738 . . . . . . . . . . . . 471--471 Fu-Chuen Chang and Paul Deiermann and Walter Van Assche and Franz Peherstorfer and Johannes Kepler Moments of Roots of Chebyshev Polynomials: 10448 . . . . . . . . . . . 471--472 Tim Keller and Gchq Problem Solving Group Indecomposable Numbers: 10589 . . . . . 473--473 Donald E. Knuth and Gchq Problem Solving Group Negatively Correlated Vectors of Signs: 10593 . . . . . . . . . . . . . . . . . 473--474 David Cox and Gchq Problem Solving Group $n$-Tuples Whose Elements Divide Their Sum: 10597 . . . . . . . . . . . . . . . 474--475 Olaf Krafft and Martin Schaefer and Nora Thornber and The National Security Agency Problems Group and Ulrich Abel Binomial Ratios: 10625 . . . . . . . . . 475--476 Mihaly Bencze and Gchq Problems Group A Triangle Inequality: 10644 . . . . . . 476--476 N. P. Bhatia Limit of a Recurrence: 10648 . . . . . . 476--477 Colin L. Mallows and Kenneth Schilling Random Polynomials with Real Roots: 10660 . . . . . . . . . . . . . . . . . 477--477 Dan Schnabel Book Review: \booktitleLife's Other Secret, by Ian Stewart; \booktitleThe Magical Maze, by Ian Stewart . . . . . . 478--481 Cynthia Woodburn Book Review: \booktitleAn Introductory Course in Commutative Algebra. by A. W. Chatters, C. R. Hajarnavis; \booktitleIntroduction to Algebra, by Peter J. Cameron . . . . . . . . . . . . 481--483 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 484--487 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Front Matter . . . . . . . . . . . . . . ??
Peter D. Lax Change of Variables in Multiple Integrals . . . . . . . . . . . . . . . 497--501 Louis J. Billera and Kenneth S. Brown and Persi Diaconis Random Walks and Plane Arrangements in Three Dimensions . . . . . . . . . . . . 502--524 Mizan R. Khan A Counting Formula for Primitive Tetrahedra in $ Z^3 $ . . . . . . . . . 525--533 Adrian Rice What Makes a Great Mathematics Teacher? The Case of Augustus De Morgan . . . . . 534--552 Frank Gerth III The TEAM Approach to Investing . . . . . 553--558 William J. Schwind and Jun Ji and Daniel E. Koditschek A Physically Motivated Further Note on the Mean Value Theorem for Integrals . . 559--564 James P. Butler Hopping Hoops Don't Hop . . . . . . . . 565--568 Peter Mathe Approximation of Holder Continuous Functions by Bernstein Polynomials . . . 568--574 Miguel de Guzman An Extension of the Wallace--Simson Theorem: Projecting in Arbitrary Directions . . . . . . . . . . . . . . . 574--580 Michael D. Hirschhorn Another Short Proof of Ramanujan's $ \bmod 5 $ Partition Congruence, and More 580--583 Hunter S. Snevily The Cayley Addition Table of $ Z_n $ . . 584--585 Oscar Ciaurri Problems: 10739 . . . . . . . . . . . . 586--586 Charles Vanden Eynden Problems: 10740 . . . . . . . . . . . . 586--586 Tim Keller Problems: 10741 . . . . . . . . . . . . 586--586 Emre Alkan Problems: 10742 . . . . . . . . . . . . 586--586 C\ualin Popescu Problems: 10743 . . . . . . . . . . . . 586--586 Peter Lindqvist Problems: 10744 . . . . . . . . . . . . 587--587 M. J. Pelling Problems: 10745 . . . . . . . . . . . . 587--587 Jordan Tabov and Murray S. Klamkin Using the Walls to Find the Center: 10386 . . . . . . . . . . . . . . . . . 587--587 Seung-Jin Bang and Jeremy E. Dawson and A. N. 't Woord and O. P. Lossers and Victor Hernandez A Reciprocal Summation Identity: 10490 588--590 Yury J. Ionin and Robin R. Lewis A Limit of Periods: 10603 . . . . . . . 590--590 Thomas Zaslavsky and Stephen M. Gagola, Jr. Avoiding the Identity: 10606 . . . . . . 590--591 Brian Conolly and Allen Stenger and Thomas Hermann Some Sums Require Care: 10638 . . . . . 591--592 Ricardo Diaz Book Review: \booktitleAn Imaginary Tale: The Story of $ \sqrt {-1} $, by Paul J. Nahin . . . . . . . . . . . . . 593--594 John Beebee and Karen Willmore Book Review: \booktitleLeaning towards Infinity, by Sue Woolfe . . . . . . . . 594--596 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 597--600 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Front Matter . . . . . . . . . . . . . . ??
Timothy Pritchett The Hopping Hoop Revisited . . . . . . . 609--617 Della Dumbaugh Fenster Why Dickson Left Quadratic Reciprocity out of His History of the Theory of Numbers . . . . . . . . . . . . . . . . 618--627 Mark Bridger and Gabriel Stolzenberg Uniform Calculus and the Law of Bounded Change . . . . . . . . . . . . . . . . . 628--635 Gary Gordon The Answer is $ 2^n. n! $ What's the Question? . . . . . . . . . . . . . . . 636--645 William F. Trench Conditional Convergence of Infinite Products . . . . . . . . . . . . . . . . 646--651 F. W. Clarke and W. N. Everitt and L. L. Littlejohn and S. J. R. Vorster H. J. S. Smith and the Fermat Two Squares Theorem . . . . . . . . . . . . 652--665 Melvyn B. Nathanson Number Theory and Semigroups of Intermediate Growth . . . . . . . . . . 666--669 Randall McCutcheon The Gottschalk--Hedlund Theorem . . . . 670--672 Tadashi F. Tokieda A Mean Value Theorem . . . . . . . . . . 673--674 B. Sury On an Example of Jacobson . . . . . . . 675--676 Israel Kleiner Field Theory: From Equations to Axiomatization . . . . . . . . . . . . . 677--684 C\ualin Popescu Problems: 10743 . . . . . . . . . . . . 685--685 Stepan Tersian Problems: 10746 . . . . . . . . . . . . 685--685 Athanasios Kalakos Problems: 10747 . . . . . . . . . . . . 685--685 Itshak Borosh and Douglas A. Hensley and Joel Zinn Problems: 10748 . . . . . . . . . . . . 685--685 Alain Grigis Problems: 10749 . . . . . . . . . . . . 685--685 Leonard Smiley Problems: 10750 . . . . . . . . . . . . 686--686 Emeric Deutsch Problems: 10751 . . . . . . . . . . . . 686--686 Gh. Costovici Problems: 10752 . . . . . . . . . . . . 686--686 Joseph H. Silverman and David Bradley and Donald A. Darling A Zeta Function over a Recurrent Sequence: 10486 . . . . . . . . . . . . 686--688 Fred Galvin and Frank Jelen and Eberhard Triesch A Matrix of Inequalities: 10599 . . . . 688--688 Wen-Xiu Ma and Robin J. Chapman and Joseph J. Rushanan A Complex Determinant: 10601 . . . . . . 688--689 Donald E. Knuth and David Callan On a Convolution of Eulerian Numbers: 10609 . . . . . . . . . . . . . . . . . 690--691 Richard Hall and National Security Agency Problems Group and Gchq Problems Group A Variation on Additive Bases: 10610 . . 691--692 Joaquin Gomez Rey and Anchorage Math Solutions Group and Gchq Problems Group An Identity Involving Rooted Trees: 10615 . . . . . . . . . . . . . . . . . 692--693 James G. Merickel and John P. Robertson Divisors of Sums of Divisors: 10617 . . 693--693 Albert A. Mullin Book Review: \booktitleMy Brain is Open: The Mathematical Journeys of Paul Erd\Hos, by Bruce Schechter; \booktitleThe Man Who Loved Only Numbers: The Story of Paul Erd\Hos and the Search for Mathematical Truth, by Paul Hoffman . . . . . . . . . . . . . . 694--696 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 697--700 Anonymous Lester R. Ford Awards for 1998 . . . . . 701--702 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Front Matter . . . . . . . . . . . . . . ??
William J. Terrell Some Fundamental Control Theory I: Controllability, Observability, and Duality . . . . . . . . . . . . . . . . 705--719 Bruce Pourciau The Education of a Pure Mathematician 720--732 Daniel J. Velleman Multivariable Calculus and the Plus Topology . . . . . . . . . . . . . . . . 733--740 John H. Hubbard The Forced Damped Pendulum: Chaos, Complication and Control . . . . . . . . 741--758 Abraham A. Ungar The Hyperbolic Pythagorean Theorem in the Poincaré Disc Model of Hyperbolic Geometry . . . . . . . . . . . . . . . . 759--763 Jitan Lu Is the Composite Function Integrable? 763--766 Jianhong Shen On the Generalized ''Lanczos' Generalized Derivative'' . . . . . . . . 766--768 Walter Rudin A Stability Theorem . . . . . . . . . . 768--770 Roger C. Alperin Rationals and the Modular Group . . . . 771--773 Thomas J. Osler The Union of Vieta's and Wallis's Products for Pi . . . . . . . . . . . . 774--776 Louis Shapiro Problems: 10753 . . . . . . . . . . . . 777--777 Paul Bracken Problems: 10754 . . . . . . . . . . . . 777--777 Jiro Fukuta Problems: 10755 . . . . . . . . . . . . 777--777 Douglas Iannucci Problems: 10756 . . . . . . . . . . . . 778--778 Mark Kidwell Problems: 10757 . . . . . . . . . . . . 778--778 Mark Sapir Problems: 10758 . . . . . . . . . . . . 778--778 C\ualin Popescu Problems: 10759 . . . . . . . . . . . . 778--778 Kiran S. Kedlaya and Alain Tissier Common Eigenvector of Commuting Matrices: 10633 . . . . . . . . . . . . 778--779 C. F. Parry and Robert L. Young Reflected Concurrent Lines: 10637 . . . 779--780 Hassan Ali Shah Ali and Patrick A. Staley A Constrained Maximization: 10646 . . . 780--781 Zoltan Sasvari and William F. Trench A Pólya--Szeg\Ho Exercise Revisited: 10650 . . . . . . . . . . . . . . . . . 781--782 W. K. Hayman and Tewodros Amdeberhan and Irl C. Bivens Harmonic Products of Harmonic Functions: 10651 . . . . . . . . . . . . . . . . . 782--782 David P. Bellamy and Felix Lazebnik and Jeffrey Lagarias and Stephen M. Gagola, Jr. Large Values of Tangent: 10656 . . . . . 782--784 Vasile A. Mihai and J. Schaer The Ellipse in a Paper Cup: 10664 . . . 784--784 John A. Koch Book Review: \booktitleThe Four-Color Theorem. by Rudolf Fritsch, Gerda Fritsch, J. Peschke . . . . . . . . . . 785--787 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 788--791 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Front Matter . . . . . . . . . . . . . . ??
Aaron F. Archer A Modern Treatment of the 15 Puzzle . . 793--799 James F. Hurley and Uwe Koehn and Susan L. Ganter Effects of Calculus Reform: Local and National . . . . . . . . . . . . . . . . 800--811 William J. Terrell Some Fundamental Control Theory II: Feedback Linearization of Single Input Nonlinear Systems . . . . . . . . . . . 812--828 John A. Baker The Dirichlet Problem for Ellipsoids . . 829--834 David A. Singer Curves Whose Curvature Depends on Distance from the Origin . . . . . . . . 835--841 Leonard F. Klosinski and Gerald L. Alexanderson and Loren C. Larson The Fifty-Ninth William Lowell Putnam Mathematical Competition . . . . . . . . 842--849 Carsten Thomassen On the Nelson Unit Distance Coloring Problem . . . . . . . . . . . . . . . . 850--853 David J. Grabiner Descartes' Rule of Signs: Another Construction . . . . . . . . . . . . . . 854--856 Jonathan P. McCammond Integrating Polynomials in Secant and Tangent . . . . . . . . . . . . . . . . 856--858 Israel Kleiner Field Theory: From Equations to Axiomatization . . . . . . . . . . . . . 859--863 Bruce Reznick Problems: 10760 . . . . . . . . . . . . 864--864 Fred Galvin Problems: 10761 . . . . . . . . . . . . 864--864 Leroy Quet Problems: 10762 . . . . . . . . . . . . 864--864 Jean Anglesio Problems: 10763 . . . . . . . . . . . . 864--864 Ray Redheffer Problems: 10764 . . . . . . . . . . . . 864--864 Peter J. Ferraro Problems: 10765 . . . . . . . . . . . . 864--864 Szilard Andras Problems: 10766 . . . . . . . . . . . . 865--865 S. Lakshminarayanan and S. L. Shah and K. Nandakumar and Gchq Problems Group Cramer's Rule for Non-Square Matrices: 10618 . . . . . . . . . . . . . . . . . 865--865 James Propp An Identity for Strongly Connected Digraphs: 10620 . . . . . . . . . . . . 865--867 M. N. Deshpande and Hansruedi Widmer and Zachary Franco Simultaneous Squares from Arithmetic Progressions: 10622 . . . . . . . . . . 867--868 Roy Barbara and Nasha Komanda and Robin J. Chapman The Divisibility Poset inside Itself: 10623 . . . . . . . . . . . . . . . . . 868--869 Florian Luca and Nasha Komanda An Equation Involving the Totient: 10626 869--870 Jiro Fukuta and Gchq Problems Group and C\ualin Popescu Three Congruent Circles between Two Triangles: 10659 . . . . . . . . . . . . 870--870 Harold G. Diamond and Nathaniel Grossman Logarithmic Convexity of Stirling's Ratio: 10680 . . . . . . . . . . . . . . 871--871 Joseph D. E. Konhauser and Stan Wagon and Con Amore Problems Group Quadrilateral Center of Gravity: 10662 871--871 James V. Rauff Book Review: \booktitleAfrican Fractals: Modern Computing and Indigenous Design. by Ron Eglash . . . . . . . . . . . . . 872--875 Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 876--879 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Front Matter . . . . . . . . . . . . . . ??
Jonathan M. Borwein and Robert M. Corless Emerging Tools for Experimental Mathematics . . . . . . . . . . . . . . 889--909 Thomas W. Tucker Reform, Tradition, and Synthesis . . . . 910--914 Steven G. Krantz You Don't Need a Weatherman to Know Which Way the Wind Blows . . . . . . . . 915--918 Helene Shapiro The Weyr Characteristic . . . . . . . . 919--929 Francis Edward Su Rental Harmony: Sperner's Lemma in Fair Division . . . . . . . . . . . . . . . . 930--942 Leonid G. Hanin Which Tanks Empty Faster? . . . . . . . 943--947 David Callan Two Uniformly Distributed Parameters Defining Catalan Numbers . . . . . . . . 948--949 Istvan Kovacs and Daniel S. Silver and Susan G. Williams Determinants of Commuting-Block Matrices 950--952 Paul iu Mixtilinear Incircles . . . . . . . . . 952--955 David N. Etter The Area of the Medial Parallelogram of a Tetrahedron . . . . . . . . . . . . . 956--958 Richard Nowakowski Unsolved Problems, 1969--1999 . . . . . 959--962 Bruce Dearden and Jerry Metzger Problems: 10767 . . . . . . . . . . . . 963--963 Sung Soo Kim Problems: 10768 . . . . . . . . . . . . 963--963 Christian Blatter Problems: 10769 . . . . . . . . . . . . 963--963 C\ualin Popescu Problems: 10770 . . . . . . . . . . . . 963--963 Mowaffaq Hajja and Peter Walker Problems: 10771 . . . . . . . . . . . . 963--963 William C. Waterhouse Problems: 10772 . . . . . . . . . . . . 963--963 Jean Anglesio Problems: 10773 . . . . . . . . . . . . 964--964 Greg Huber and Gchq Problems Group Tracking the Incenters: 10631 . . . . . 964--965 William F. Trench and Ronald A. Kopas An Appearance of the Beta Function: 10632 . . . . . . . . . . . . . . . . . 965--965 Nicholas R. Farnum and Alain Tissier Apery's Constant: 10635 . . . . . . . . 965--966 Abram Kagan and Larry Shepp and Kenneth Schilling Essentially Discontinuous Functions: 10668 . . . . . . . . . . . . . . . . . 966--967 Salomon Benchimol and Elliott Cohen and Con Amore Problems Group Two Recurrence Relations, One Easy, One Hard: 10670 . . . . . . . . . . . . . . 967--968 F. Rothe and Sung Soo Kim The Number of Zeros of a Maclaurin Polynomial: 10671 . . . . . . . . . . . 968--968 V. Anil Kumar and John H. Lindsey, II An AM--GM Variation: 10672 . . . . . . . 969--969 Harry Tamvakis and Gchq Problems Group Functions with a Polynomial Addition Formula: 10675 . . . . . . . . . . . . . 969--969 Horst Alzer and M. J. Pelling An Unsettled Inequality: 10337 . . . . . 970--970 Edward Aboufadel and Matthew Boelkins and Steven Schlicker Book Review: \booktitleWavelets: A Primer. by Christian Blatter, A. K. Peters; \booktitleWavelets in a Box, by Charles K. Chui, Andrew K. Chan, C. Steve Liu; \booktitleA Primer on Wavelets for Scientists and Engineers, by James S. Walker; \booktitleWavelet Analysis: The Scalable Structure of Information, by Howard L. Resnikoff, Raymond O. Wells, Jr. . . . . . . . . . 971--977 Daniel Henry Gottlieb Book Review: \booktitlePoincaré and the Three Body Problem. by June Barrow-Green 977--980 Anonymous Volume Information . . . . . . . . . . . 981--992 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Front Matter . . . . . . . . . . . . . . ??
David Bailey and Peter Borwein and Simon Plouffe On the rapid computation of various polylogarithmic constants . . . . . . . 903--913