Last update:
Thu Nov 2 08:11:42 MDT 2023
Anonymous Front Matter . . . . . . . . . . . . . . ??
Aaron Abrams and
Skip Garibaldi Finding Good Bets in the Lottery, and
Why You Shouldn't Take Them . . . . . . 3--26
Deborah E. Berg and
Serguei Norine and
Francis Edward Su and
Robin Thomas and
Paul Wollan Voting in Agreeable Societies . . . . . 27--39
Christopher S. Hardin Agreement in Circular Societies . . . . 40--49
Barry Lewis Revisiting the Pascal Matrix . . . . . . 50--66
Mircea I. C\^\irnu Newton's Identities and the Laplace
Transform . . . . . . . . . . . . . . . 67--71
Kurt Girstmair Farey Sums and Dedekind Sums . . . . . . 72--78
Friedrich Pillichshammer Euler's Constant and Averages of
Fractional Parts . . . . . . . . . . . . 78--83
Richard Bagby A Simple Proof that $ \Gamma '(1) = -
\gamma $ . . . . . . . . . . . . . . . . 83--85
Gerald A. Edgar and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 86--93
Jeffrey Nunemacher and
Amir Alexander Book Review: \booktitleThe Shape of
Content: Creative Writing in Mathematics
and Science, by Chandler Davis; Marjorie
Wikler Senechal; Jan Zwicky . . . . . . 94--96
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Frank A. Farris The Gini Index and Measures of
Inequality . . . . . . . . . . . . . . . 851--864
Gary Gordon and
Elizabeth McMahon Moving Faces to Other Places: Facet
Derangements . . . . . . . . . . . . . . 865--880
Oleg A. Ivanov On the Number of Regions into Which $n$
Straight Lines Divide the Plane . . . . 881--888
Joel C. Langer and
David A. Singer When Is a Curve an Octahedron? . . . . . 889--902
Monique Laurent and
Alexander Schrijver On Leonid Gurvits's Proof for Permanents 903--911
Jonathan Sondow and
Huang Yi New Wallis- and Catalan-Type Infinite
Products for $ \pi $, $e$ and $ \sqrt {2
+ \sqrt {2}}$ . . . . . . . . . . . . . 912--917
Nadish de Silva A Concise, Elementary Proof of
Arzel\`a's Bounded Convergence Theorem 918--920
Mihály Bessenyei Functional Equations and Finite Groups
of Substitutions . . . . . . . . . . . . 921--927
Shibo Liu On the Regularity of Operators Near a
Regular Operator . . . . . . . . . . . . 927--928
Gerald A. Edger and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 929--936
Jeffrey Nunemacher and
Ethan Akin Book Review: \booktitle[untitled] . . . 937--940
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Natalie Priebe Frank and
Sean M. Hart A Dynamical System Using the Voronoï
Tessellation . . . . . . . . . . . . . . 99--112
David Sherman Variations on Kuratowski's $ 14$-Set
Theorem . . . . . . . . . . . . . . . . 113--123
Tamás Keleti and
Elliot Paquette The Trouble with von Koch Curves Built
from $n$ gons . . . . . . . . . . . . . 124--137
Lutz Dümbgen and
Sara A. van de Geer and
Mark C. Veraar and
Jon A. Wellner Nemirovski's Inequalities Revisited . . 138--160
John E. Wetzel and
Ed Scheinerman An Ancient Elliptic Locus . . . . . . . 161--167
Lara K. Pudwell and
Eric S. Rowland Counting Interesting Elections . . . . . 167--174
Sam B. Nadler, Jr. A Proof of Darboux's Theorem . . . . . . 174--175
Emmanuel Lesigne On the Behavior at Infinity of an
Integrable Function . . . . . . . . . . 175--181
Gerald A. Edgar and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 182--189
Jeffrey Nunemacher and
Daniel S. Silver Book Review: \booktitle[untitled] . . . 190--192
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Barbara Faires Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2010 to Kenneth A. Ross for
Distinguished Service to Mathematics . . 195--197
Marvin Jay Greenberg Old and New Results in the Foundations
of Elementary Plane Euclidean and
Non-Euclidean Geometries . . . . . . . . 198--219
David A. Levin and
Yuval Peres Pólya's Theorem on Random Walks via
Pólya's Urn . . . . . . . . . . . . . . . 220--231
Alexander Borisov and
Mark Dickinson and
Stuart Hastings A Congruence Problem for Polyhedra . . . 232--249
Jan Hilmar and
Chris Smyth Euclid Meets Bézout: Intersecting
Algebraic Plane Curves with the
Euclidean Algorithm . . . . . . . . . . 250--260
Jun Tanaka and
Peter F. McLoughlin A Realization of Measurable Sets as
Limit Points . . . . . . . . . . . . . . 261--266
Dan McQuillan and
R. Bruce Richter A Parity Theorem for Drawings of
Complete and Complete Bipartite Graphs 267--273
Sanjay K. Khattri Three Proofs of the Inequality $ e <
{\left ({1 + \frac {1}{n}} \right)^{n +
0.5}} $ . . . . . . . . . . . . . . . . 273--277
Gerald A. Edgar and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 278--285
Anil Nerode Book Review: \booktitle[untitled] . . . 286--288
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Adrian Rice ``To a Factor pr\`es'': Cayley's Partial
Anticipation of the Weierstrass $ \wp
$-Function . . . . . . . . . . . . . . . 291--302
Geoffrey Pearce Transitive Decompositions of Graphs and
Their Links with Geometry and Origami 303--310
Warren P. Johnson Trigonometric Identities \`a la Hermite 311--327
David Burton and
John Coleman Quasi-Cauchy Sequences . . . . . . . . . 328--333
Grahame Bennett $p$-Free $ \ell^p$ Inequalities . . . . 334--351
Timothy Marshall A Short Proof of $ \zeta (2) = \pi^2 / 6
$ . . . . . . . . . . . . . . . . . . . 352--353
So Eun Park The Group of Symmetries of the Tower of
Hanoi Graph . . . . . . . . . . . . . . 353--360
Li Zhou and
Lubomir Markov Recurrent Proofs of the Irrationality of
Certain Trigonometric Values . . . . . . 360--362
M. John Curran Groups of Cube-Free Odd Order . . . . . 363--365
Mark Kozek An Asymptotic Formula for Goldbach's
Conjecture with Monic Polynomials in $
\mathbb {Z}[x] $ . . . . . . . . . . . . 365--369
Gerald A. Edgar and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 370--377
Jeffrey Nunemacher and
Sanford L. Segal Book Review: \booktitle[untitled] . . . 378--380
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Matthew Richey The Evolution of Markov Chain Monte
Carlo Methods . . . . . . . . . . . . . 383--413
A. B. Kharazishvili and
T. Sh. Tetunashvili On Some Coverings of the Euclidean Plane
with Pairwise Congruent Circles . . . . 414--423
Sherman Stein Transversals in Rectangular Arrays . . . 424--433
Cristinel Mortici Product Approximations via Asymptotic
Integration . . . . . . . . . . . . . . 434--441
Francisco J. Freniche On Riemann's Rearrangement Theorem for
the Alternating Harmonic Series . . . . 442--448
Richard Steiner Modular Divisor Functions and Quadratic
Reciprocity . . . . . . . . . . . . . . 448--451
Peter R. Mercer Another Application of Siebeck's Theorem 452--454
Alan C. Lazer and
Mark Leckband The Fundamental Theorem of Algebra via
the Fourier Inversion Formula . . . . . 455--457
Gerald A. Edgar and
Dough Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 458--465
Jeffrey Nunemacher and
Carol S. Schumacher Book Review: \booktitle[untitled] . . . 466--468
Daniel J. Velleman Editor's Endnotes . . . . . . . . . . . 469--470
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James T. Smith Definitions and Nondefinability in
Geometry . . . . . . . . . . . . . . . . 475--489
Hartmut Logemann and
Eugene P. Ryan Volterra Functional Differential
Equations: Existence, Uniqueness, and
Continuation of Solutions . . . . . . . 490--511
Stan Gudder Finite Quantum Measure Spaces . . . . . 512--527
David Borwein and
Jonathan M. Borwein and
Isaac E. Leonard $ L_p $ Norms and the Sinc Function . . 528--539
John H. Elton Indefinite Quadratic Forms and the
Invariance of the Interval in Special
Relativity . . . . . . . . . . . . . . . 540--547
Brian S. Thomson Monotone Convergence Theorem for the
Riemann Integral . . . . . . . . . . . . 547--550
Marco Manetti A Proof of a Version of a Theorem of
Hartogs . . . . . . . . . . . . . . . . 550--552
Timothy W. Jones Discovering and Proving that $ \pi $ Is
Irrational . . . . . . . . . . . . . . . 553--557
Gerald A. Edgar and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 558--565
Charles R. Hampton and
Jeffrey Nunemacher Book Review: \booktitle[untitled] . . . 566--568
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William Cavendish and
John H. Conway Symmetrically Bordered Surfaces . . . . 571--580
Sam Northshield Stern's Diatomic Sequence $ 0, 1, 1, 2,
1, 3, 2, 3, 1, 4, \ldots {} $ . . . . . 581--598
Peter J. Olver Dispersive Quantization . . . . . . . . 599--610
Thomas Stoll A Fancy Way to Obtain the Binary Digits
of $ 759250125 \sqrt {2} $ . . . . . . . 611--617
T. Amdeberhan and
O. Espinosa and
V. H. Moll and
A. Straub Wallis--Ramanujan--Schur--Feynman . . . 618--632
Mike Krebs and
Thomas Wright On Cantor's First Uncountability Proof,
Pick's Theorem, and the Irrationality of
the Golden Ratio . . . . . . . . . . . . 633--637
Filip Najman The Diophantine Equation $ x^4 \pm y^4 =
i z^2 $ in Gaussian Integers . . . . . . 637--641
Christopher Frayer and
James A. Swenson Polynomial Root Motion . . . . . . . . . 641--646
Aviezri S. Fraenkel From Enmity to Amity . . . . . . . . . . 646--648
Gerald A. Edgar and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 649--656
Jeffrey Nunemacher and
Peter Sin Book Review: \booktitle[untitled] . . . 657--660
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Gerald B. Folland A Tale of Topology . . . . . . . . . . . 663--672
Jack S. Calcut Grade School Triangles . . . . . . . . . 673--685
Mark A. Conger and
Jason Howald A Better Way to Deal the Cards . . . . . 686--700
Tom M. Apostol and
Mamikon A. Mnatsakanian Tanvolutes: Generalized Involutes . . . 701--713
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Seventieth William Lowell Putnam
Mathematical Competition . . . . . . . . 714--721
Alin Bostan and
Philippe Dumas Wronskians and Linear Independence . . . 722--727
Abbas M. Alhakim A Simple Combinatorial Algorithm for de
Bruijn Sequences . . . . . . . . . . . . 728--732
Albert Nijenhuis Short Gamma Products with Simple Values 733--737
Miyeon Kwon Dimension, Linear Functionals, and Norms
in a Vector Space . . . . . . . . . . . 738--740
Anonymous Problems and Solutions . . . . . . . . . 741--748
Marion Deutsche Cohen Book Review: \booktitle[untitled] . . . 749--753
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Francis Edward Su Teaching Research: Encouraging
Discoveries . . . . . . . . . . . . . . 759--769
Harold P. Boas Julius and Julia: Mastering the Art of
the Schwarz Lemma . . . . . . . . . . . 770--785
Taras Banakh and
Oleg Verbitsky and
Yaroslav Vorobets Fermat's Spiral and the Line Between Yin
and Yang . . . . . . . . . . . . . . . . 786--800
Karel Hrbacek and
Olivier Lessmann and
Richard O'Donovan Analysis with Ultrasmall Numbers . . . . 801--816
Hendrik Lenstra Irreducible Cubics Modulo Five . . . . . 817--821
Mateusz Micha\lek A Short Proof of Combinatorial
Nullstellensatz . . . . . . . . . . . . 821--823
Sam H. Creswell A Continuous Bijection from $ \ell^2 $
onto a Subset of $ \ell^2 $ Whose
Inverse Is Everywhere Discontinuous . . 823--828
Nicolae Anghel On a Question of Connes and Zagier
Regarding Parallelograms Inscribed in a
Pair of Confocal Ellipses . . . . . . . 828--831
Stephen M. Walk A Streamlined Proof of an Essential
Calculus Fact . . . . . . . . . . . . . 832--833
Gerald A. Edger and
Doug Hensley and
Douglas B. West Problems and Solutions . . . . . . . . . 834--843
Jeffrey Nunemacher and
Rebecca F. Goldin Book Review: \booktitle[untitled] . . . 844--847
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Anonymous Front Matter . . . . . . . . . . . . . . 1--2
David A. Cox Why Eisenstein Proved the Eisenstein
Criterion and Why Schönemann Discovered
It First . . . . . . . . . . . . . . . . 3--21
Jennifer M. Johnson and
János Kollár How Small Can a Polynomial Be Near
Infinity? . . . . . . . . . . . . . . . 22--40
Nikolai V. Ivanov Arnol'd, the Jacobi Identity, and
Orthocenters . . . . . . . . . . . . . . 41--65
Nicholas Pippenger Two Extensions of Results of Archimedes 66--71
Paul Pollack On Polynomial Rings with a Goldbach
Property . . . . . . . . . . . . . . . . 71--77
Alfonso Villani Measurable Functions with a Given Set of
Integrability Exponents . . . . . . . . 77--82
Alexis Akira Toda Operator Reverse Monotonicity of the
Inverse . . . . . . . . . . . . . . . . 82--83
Anonymous Problems and Solutions . . . . . . . . . 84--91
Virginia McShane Warfield Book Review: \booktitle[untitled] . . . 92--95
Anonymous Back Matter . . . . . . . . . . . . . . 96--96
Anonymous Front Matter . . . . . . . . . . . . . . 861--862
Henryk Gerlach and
Heiko von der Mosel On Sphere-Filling Ropes . . . . . . . . 863--876
Géza Kós On the Grasshopper Problem with Signed
Jumps . . . . . . . . . . . . . . . . . 877--886
Giovanni Falcone and
Marco Pavone Kirkman's Tetrahedron and the Fifteen
Schoolgirl Problem . . . . . . . . . . . 887--900
Paul Baginski and
Scott T. Chapman Factorizations of Algebraic Integers,
Block Monoids, and Additive Number
Theory . . . . . . . . . . . . . . . . . 901--920
Hayri Ardal and
Tom Brown and
Veselin Jungi\'c Chaotic Orderings of the Rationals and
Reals . . . . . . . . . . . . . . . . . 921--925
Raphaël Cerf and
Pierre Petit A Short Proof of Cramér's Theorem in $
\mathbb {R} $ . . . . . . . . . . . . . 925--931
Bahman Kalantari A Geometric Modulus Principle for
Polynomials . . . . . . . . . . . . . . 931--935
Anonymous Problems and Solutions . . . . . . . . . 936--945
Andrew Odlyzko Book Review: \booktitle[untitled] . . . 946--951
Daniel J. Velleman Book Review: \booktitleEndnotes . . . . 952--953
Anonymous Index to Volume 118 . . . . . . . . . . 954--964
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David M. Bressoud Historical Reflections on Teaching the
Fundamental Theorem of Integral Calculus 99--115
Ravi Vakil The Mathematics of Doodling . . . . . . 116--129
Ian Short Ford Circles, Continued Fractions, and
Rational Approximation . . . . . . . . . 130--135
Markus Müller and
Dierk Schleicher How to Add a Noninteger Number of Terms:
From Axioms to New Identities . . . . . 136--152
Lenny Jones When Does Appending the Same Digit
Repeatedly on the Right of a Positive
Integer Generate a Sequence of Composite
Integers? . . . . . . . . . . . . . . . 153--160
Paul Pollack On Dickson's Theorem Concerning Odd
Perfect Numbers . . . . . . . . . . . . 161--164
Eyal Ackerman and
Rom Pinchasi and
Ludmila Scharf and
Marc Scherfenberg Every Simple Arrangement of n Lines
Contains an Inducing Simple $n$-gon . . 164--167
José L. Gámez-Merino and
Gustavo A. Muñoz-Fernández and
Juan B. Seoane-Sepúlveda A Characterization of Continuity
Revisited . . . . . . . . . . . . . . . 167--170
Sam Northshield A Short Proof and Generalization of
Lagrange's Theorem on Continued
Fractions . . . . . . . . . . . . . . . 171--175
Guisong Chang and
Chen Xu Generalization and Probabilistic Proof
of a Combinatorial Identity . . . . . . 175--177
Anonymous Problems and Solutions . . . . . . . . . 178--185
Jeffrey Nunemacher Book Review: \booktitle[untitled] . . . 186--189
Anonymous Back Matter . . . . . . . . . . . . . . 190--192
Anonymous Front Matter . . . . . . . . . . . . . . 193--194
Barbara Faires Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2011 to Joseph A. Gallian for
Distinguished Service to Mathematics . . 195--197
Fernando Q. Gouvêa Was Cantor Surprised? . . . . . . . . . 198--209
Steven H. Weintraub On Legendre's Work on the Law of
Quadratic Reciprocity . . . . . . . . . 210--216
Alexander Ryba and
Joseph Stern Equimodular Polynomials and the
Tritangency Theorems of Euler,
Feuerbach, and Guinand . . . . . . . . . 217--228
Keith Burns and
Boris Hasselblatt The Sharkovsky Theorem: a Natural Direct
Proof . . . . . . . . . . . . . . . . . 229--244
John H. Hubbard and
Benjamin E. Lundell A First Look at Differential Algebra . . 245--261
Grant Keady Lines of Best Fit for the Zeros and for
the Critical Points of a Polynomial . . 262--264
Sascha Kurz and
Rom Pinchasi Regular Matchstick Graphs . . . . . . . 264--267
Edward Chlebus A Recursive Scheme for Improving the
Original Rate of Convergence to the
Euler--Mascheroni Constant . . . . . . . 268--274
Anonymous Problems and Solutions . . . . . . . . . 275--282
Christopher C. Leary Book Review: \booktitle[untitled] . . . 283--286
Anonymous Back Matter . . . . . . . . . . . . . . 287--288
Anonymous Front Matter . . . . . . . . . . . . . . 289--290
Peter Sarnak Integral Apollonian Packings . . . . . . 291--306
Thomas C. Hull Solving Cubics With Creases: The Work of
Beloch and Lill . . . . . . . . . . . . 307--315
Heng Huat Chan and
Ling Long and
YiFan Yang A Cubic Analogue of the Jacobsthal
Identity . . . . . . . . . . . . . . . . 316--326
H. M. Hilden and
J. M. Montesinos and
D. M. Tejada and
M. M. Toro Artifacts for Stamping Symmetric Designs 327--343
Jaume Paradís and
Pelegrí Viader and
Lluís Bibiloni A New Singular Function . . . . . . . . 344--354
Roger Cooke A Remark on Euclid's Theorem on the
Infinitude of the Primes . . . . . . . . 355--358
James Rickards When Is a Polynomial a Composition of
Other Polynomials? . . . . . . . . . . . 358--363
Pieter Moree A Top Hat for Moser's Four Mathemagical
Rabbits . . . . . . . . . . . . . . . . 364--370
Anonymous Problems and Solutions . . . . . . . . . 371--378
Susan Jane Colley Book Review: \booktitle[untitled] . . . 379--382
Anonymous Back Matter . . . . . . . . . . . . . . 383--384
Anonymous Front Matter . . . . . . . . . . . . . . 385--386
David S. Watkins Francis's Algorithm . . . . . . . . . . 387--403
R. Michael Range Where Are Limits Needed in Calculus? . . 404--417
Vincent Vatter Maximal Independent Sets and Separating
Covers . . . . . . . . . . . . . . . . . 418--423
M. Skopenkov Packing a Cake into a Box . . . . . . . 424--433
Alan Tucker What Every Mathematician Should Know
about Standards-Based Tests . . . . . . 434--447
Geoffrey R. Robinson Cauchy's Theorem and Sylow's Theorem
from the Cyclic Case . . . . . . . . . . 448--449
Alan D. Sokal A Really Simple Elementary Proof of the
Uniform Boundedness Theorem . . . . . . 450--452
Marian Deaconescu and
Gary L. Walls On the Group of Automorphisms of a Group 452--455
Bogdan Nica The Unreasonable Slightness of $ E_2 $
over Imaginary Quadratic Rings . . . . . 455--462
Anonymous Problems and Solutions . . . . . . . . . 463--470
Peggy Aldrich Kidwell Book Review: \booktitle[untitled] . . . 471--474
Anonymous Back Matter . . . . . . . . . . . . . . 475--476
Anonymous Front Matter . . . . . . . . . . . . . . 477--478
Fred Kuczmarski Roads and Wheels, Roulettes and Pedals 479--496
Martin Griffiths The Golden String, Zeckendorf
Representations, and the Sum of a Series 497--507
Rafe Jones Achievement Sets of Sequences . . . . . 508--521
Pamela Gorkin and
Elizabeth Skubak Polynomials, Ellipses, and Matrices: Two
Questions, One Answer . . . . . . . . . 522--533
Ronald F. Wotzlaw and
Günter M. Ziegler A Lost Counterexample and a Problem on
Illuminated Polytopes . . . . . . . . . 534--543
János Pach and
Ethan Sterling Conway's Conjecture for Monotone
Thrackles . . . . . . . . . . . . . . . 544--548
Kieren MacMillan and
Jonathan Sondow Proofs of Power Sum and Binomial
Coefficient Congruences via Pascal's
Identity . . . . . . . . . . . . . . . . 549--551
Caleb Emmons Meromorphic Continuation of Dirichlet
Series via Derivations . . . . . . . . . 551--556
Anonymous Problems and Solutions . . . . . . . . . 557--564
Robin Hartshorne Book Review: \booktitle[untitled] . . . 565--568
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 569--570
Kenneth A. Ross Benford's Law, a Growth Industry . . . . 571--583
Graham Everest and
Thomas Ward A Repulsion Motif in Diophantine
Equations . . . . . . . . . . . . . . . 584--598
Alberto Torchinsky The Fourier Transform and the Wave
Equation . . . . . . . . . . . . . . . . 599--609
W. Aitken and
F. Lemmermeyer Counterexamples to the Hasse Principle 610--628
Peyman Eslami and
Pawel Góra On Eventually Expanding Maps of the
Interval . . . . . . . . . . . . . . . . 629--635
Hichem Ben-El-Mechaiekh and
Robert W. Dimand A Simpler Proof of the von Neumann
Minimax Theorem . . . . . . . . . . . . 636--641
Luigi Pace Probabilistically Proving that $ \zeta
(2) = \pi^2 / 6 $ . . . . . . . . . . . 641--643
M. Ram Murty and
V. Kumar Murty On a Problem of Ruderman . . . . . . . . 644--650
Alan F. Beardon Cyclic Absolute Differences of Integers 650--652
Anonymous Problems and Solutions . . . . . . . . . 653--660
Peter Winkler Book Review: \booktitle[untitled] . . . 661--664
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Anonymous Front Matter . . . . . . . . . . . . . . 665--666
Murad \HOzaydìn and
Charlotte Simmons The Birthday Trick with Lies . . . . . . 667--679
Russell A. Gordon Semiperimeter and Pythagorean Triples 680--692
A. B. Kharazishvili Measurability Properties of Vitali Sets 693--703
Stephan Ramon Garcia and
Vincent Selhorst-Jones and
Daniel E. Poore and
Noah Simon Quotient Sets and Diophantine Equations 704--711
P. J. Giblin and
J. P. Warder Reconstruction from Medial
Representations . . . . . . . . . . . . 712--725
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson and
Mark Krusemeyer The Seventy-First William Lowell Putnam
Mathematical Competition . . . . . . . . 726--733
R. K. Oliver On the Parity of a Permutation . . . . . 734--735
Wouter Kager The Hitting Time Theorem Revisited . . . 735--737
R. Thangadurai and
A. Vatwani The Least Prime Congruent to One Modulo
$n$ . . . . . . . . . . . . . . . . . . 737--742
Penghao Cao and
Liping Yuan A Blichfeldt-type Theorem for $H$-points 743--746
Anonymous Problems and Solutions . . . . . . . . . 747--754
Richard Askey Book Review: \booktitle[untitled] . . . 755--762
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Anonymous Front Matter . . . . . . . . . . . . . . 765--766
Bruce C. Berndt The Chief Accountant and Mathematical
Friend of Ramanujan --- S. Narayana
Aiyar . . . . . . . . . . . . . . . . . 767--776
P. Haxell On Forming Committees . . . . . . . . . 777--788
Tom M. Apostol and
Mamikon A. Mnatsakanian Complete Dissections: Converting Regions
and Their Boundaries . . . . . . . . . . 789--798
Giacomo Drago and
Pier Domenico Lamberti and
Paolo Toni A ``Bouquet'' of Discontinuous Functions
for Beginners in Mathematical Analysis 799--811
John B. Cosgrave and
Karl Dilcher An Introduction to Gauss Factorials . . 812--829
S. P. Glasby Enumerating the Rationals from Left to
Right . . . . . . . . . . . . . . . . . 830--835
Semyon N. Litvinov On the Banach--Steinhaus Theorem for
Topological Groups . . . . . . . . . . . 836--838
Michael D. Hirschhorn Ramanujan's ``Most Beautiful Identity'' 839--845
Anonymous Problems and Solutions . . . . . . . . . 846--853
Matthew Richey Book Review: \booktitle[untitled] . . . 854--858
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2
Scott Chapman A Letter from the Editor . . . . . . . . 3--3
Daniel Brinkman and
Peter J. Olver Invariant Histograms . . . . . . . . . . 4--24
Thomas Bauer and
Mirel Caib\uar and
Gary Kennedy Zariski Decomposition: a New (Old)
Chapter of Linear Algebra . . . . . . . 25--41
Dan Kalman and
Mark McKinzie Another Way to Sum a Series: Generating
Functions, Euler, and the Dilog Function 42--51
Costas J. Efthimiou A Class of Periodic Continued Radicals 52--58
Parames Laosinchai and
Bhinyo Panijpan A Geometric Interpretation of Pascal's
Formula for Sums of Powers of Integers 58--64
Pete L. Clark Covering Numbers in Linear Algebra . . . 65--67
Anonymous Problems and Solutions . . . . . . . . . 68--75
Alan Durfee Book Review: \booktitle[untitled] . . . 76--82
Anonymous Back Matter . . . . . . . . . . . . . . 83--84
Anonymous Front Matter . . . . . . . . . . . . . . 85--86
Boris S. Mordukhovich and
Nguyen Mau Nam and
Juan Salinas, Jr. Solving a Generalized Heron Problem by
Means of Convex Analysis . . . . . . . . 87--99
Sam Vandervelde Jacobi Sum Matrices . . . . . . . . . . 100--114
Donald J. Bindner and
Martin Erickson Alcuin's Sequence . . . . . . . . . . . 115--121
Burkard Polster and
Marty Ross and
David Treeby A Case of Continuous Hangover . . . . . 122--139
David A. Herron Riemann Maps and Diameter Distance . . . 140--147
Cristinel Mortici A Power Series Approach to Some
Inequalities . . . . . . . . . . . . . . 147--151
Julian Rosen and
Zachary Scherr and
Benjamin Weiss and
Michael E. Zieve Chebyshev Mappings of Finite Fields . . 151--155
Igor Pak and
Rom Pinchasi Collapsing Walls Theorem . . . . . . . . 156--160
Anonymous Problems and Solutions . . . . . . . . . 161--168
José Ferreirós Book Review: \booktitle[untitled] . . . 169--176
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 177--178
Ann E. Watkins Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2012 to John Ewing for
Distinguished Service to Mathematics . . 179--182
Jessica Sidman An Introduction to Algebraic Geometry:
Polygons, Parameterizations, and
Equations . . . . . . . . . . . . . . . 183--198
Daniel Daners The Mercator and Stereographic
Projections, and Many in Between . . . . 199--210
Yves Nievergelt Real and Generic Data without
Unconstrained Best-Fitting Verhulst
Curves and Sufficient Conditions for
Median Mitscherlich and Verhulst Curves
to Exist . . . . . . . . . . . . . . . . 211--234
William C. Waterhouse Square Root as a Homomorphism . . . . . 235--239
Michael P. Cohen Sample Means of Independent Standard
Cauchy Random Variables Are Standard
Cauchy: a New Approach . . . . . . . . . 240--244
Daniel Reem Character Analysis Using Fourier Series 245--246
Anonymous Problems and Solutions . . . . . . . . . 247--254
Gerald L. Alexanderson Book Review: \booktitleLoving and Hating
Mathematics: Challenging the Myths of
Mathematical Life, by Reuben Hersh and
Vera John-Steiner. Princeton University
Press, Princeton, NJ, 2011, xii + 416
pp. ISBN 978-0-691-14247-0, \$29.95} . . 255--259
Anonymous Back Matter . . . . . . . . . . . . . . 260--260
Anonymous Front Matter . . . . . . . . . . . . . . 261--262
Rachel Wells Hall and
Dmitri Tymoczko Submajorization and the Geometry of
Unordered Collections . . . . . . . . . 263--283
Stephen McAdam Unknowable Matters: How Nature's Speed
Limit on Communication Relates to
Quantum Physics . . . . . . . . . . . . 284--299
Barry Cox and
Stan Wagon Drilling for Polygons . . . . . . . . . 300--312
Kenneth Hicks and
Xiang-dong Hou and
Gary L. Mullen Sums of Reciprocals of Polynomials over
Finite Fields . . . . . . . . . . . . . 313--317
Evgeny Lakshtanov and
Vera Roshchina On Finiteness in the Card Game of War 318--323
Djurdje Cvijovi\'c and
Hari M. Srivastava Limit Representations of Riemann's Zeta
Function . . . . . . . . . . . . . . . . 324--330
Christian Elsholtz Prime Divisors of Thin Sequences . . . . 331--333
I. E. Leonard and
A. C. F. Liu A Familiar Recurrence Occurs Again . . . 333--336
Robbert Fokkink Tossing Coins to Guess a Secret Number 337--339
Lizhou Chen A Generalization of the Cayley--Hamilton
Theorem . . . . . . . . . . . . . . . . 340--342
R. McCutcheon Monochromatic Permutation Quadruples ---
a Schur Thing in $ S_n $ . . . . . . . . 342--343
Anonymous Problems and Solutions . . . . . . . . . 344--351
Bonnie Shulman Book Review: \booktitlePopulation Games
and Evolutionary Dynamics, by William H.
Sandholm. MIT Press, Cambridge, MA,
2011, xxv + 589 pp., ISBN
978-0-262-19587-4, \$65} . . . . . . . . 352--356
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 357--358
Tony Gilbert Lost Mail: The Missing Envelope in the
Problem of the Minimal Surface of
Revolution . . . . . . . . . . . . . . . 359--372
Frits Beukers and
Florian Luca and
Frans Oort Power Values of Divisor Sums . . . . . . 373--380
Hassan Boualem and
Robert Brouzet On What Is the Almost-Near Principle . . 381--397
Serge Tabachnikov The (Un)equal Tangents Problem . . . . . 398--405
Lance Bryant and
James Hamblin and
Lenny Jones A Variation on the Money-Changing
Problem . . . . . . . . . . . . . . . . 406--414
David Callan Flexagons Lead to a Catalan Number
Identity . . . . . . . . . . . . . . . . 415--419
R. D. Arthan Aronszajn's Criterion for Euclidean
Space . . . . . . . . . . . . . . . . . 419--422
Joseph E. Borzellino and
Morgan Sherman When Is a Trigonometric Polynomial Not a
Trigonometric Polynomial? . . . . . . . 422--425
Anonymous Problems and Solutions . . . . . . . . . 426--433
James A. Walsh Book Review: \booktitleRandomness and
Recurrence in Dynamical Systems, by
Rodney Nillsen. The Carus Mathematical
Monographs Number 31, Mathematical
Association of America, Washington, DC,
2010, xviii + 357 pp., ISBN
978-0-88385-043-5, \$52.95} . . . . . . 434--438
Anonymous Back Matter . . . . . . . . . . . . . . 439--440
Anonymous Front Matter . . . . . . . . . . . . . . 441--442
Dimitris Koukoulopoulos and
Johann Thiel Arrangements of Stars on the American
Flag . . . . . . . . . . . . . . . . . . 443--450
Fred Kuczmarski Rolling Sinusoidal Spirals . . . . . . . 451--467
Robert Mandl and
Thomas Pühringer and
Maximilian Thaler Analytic Approach to Galileo's Theorem
on the Descent Time Along Two-Chord
Paths in a Circle . . . . . . . . . . . 468--476
Paul Binding and
Hans Volkmer A Prüfer Angle Approach to the Periodic
Sturm--Liouville Problem . . . . . . . . 477--484
Raymond Mortini and
Rudolf Rupp Mappings into the Euclidean Sphere . . . 485--494
Branko Grünbaum Is Napoleon's Theorem Really Napoleon's
Theorem? . . . . . . . . . . . . . . . . 495--501
Michael J. Dorfling and
Johan H. Meyer On Polynomials and Divisibility . . . . 502--506
Pedro Roitman Gaussian Curvature, Mirrors, and Maps 506--509
Alan J. Aw The Turán Number and Probabilistic
Combinatorics . . . . . . . . . . . . . 510--513
Walter Wyss Perfect Parallelograms . . . . . . . . . 513--515
Timothy C. Wallstrom The Equalization Probability of the Pólya
Urn . . . . . . . . . . . . . . . . . . 516--518
Lars Holst A Proof of Euler's Infinite Product for
the Sine . . . . . . . . . . . . . . . . 518--521
Anonymous Problems and Solutions . . . . . . . . . 522--529
Jennifer J. Quinn Book Review: \booktitleCombinatorics the
Rota Way, by Joseph P. S. Kung,
Gian-Carlo Rota, and Catherine H. Yan.
Cambridge University Press, New York,
2009, xii + 396 pp., ISBN
978-0-521-73794-4, \$40.99} . . . . . . 530--532
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 533--534
David Borwein and
Jonathan M. Borwein and
Armin Straub A Sinc that Sank . . . . . . . . . . . . 535--549
Lionel Levine and
Katherine E. Stange How to Make the Most of a Shared Meal:
Plan the Last Bite First . . . . . . . . 550--565
Kai F. Kristensen A Nearest Integer Solution to the
Longest Run of Randomly Generated Words 566--572
F. Lemmermeyer Parametrization of Algebraic Curves from
a Number Theorist's Point of View . . . 573--583
Peter Borwein and
Joe Hobart The Extraordinary Power of Division in
Straight Line Programs . . . . . . . . . 584--592
Alin Bostan and
Thierry Combot A Binomial-like Matrix Equation . . . . 593--597
Ezra Brown and
Marc Chamberland Generalizing Gauss's Gem . . . . . . . . 597--601
Greg Kuperberg Norms as a Function of p Are Linearly
Independent in Finite Dimensions . . . . 601--603
Cédric De Groote and
Mitia Duerinckx Functions with Constant Mean on Similar
Countable Subsets of $ \mathbb {R}^2 $ 603--605
Tomasz Tkocz An Upper Bound for Spherical Caps . . . 606--607
Anonymous Problems and Solutions . . . . . . . . . 608--615
Marion Cohen Book Review: \booktitleChange Is
Possible: Stories of Women and
Minorities in Mathematics, by Patricia
Clark Kenschaft. American Mathematical
Society, Providence, RI, 2005, ix + 211
pp., ISBN 0-8218-3748-6, \$32.00} . . . 616--620
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 621--622
Leonard F. Klosinski and
Gerald L. Alexanderson and
Mark Krusemeyer The Seventy-Second William Lowell Putnam
Mathematical Competition . . . . . . . . 623--635
Yuval Ginosar and
Ilan Yona A Model for Pairs of Beatty Sequences 636--645
David H. Bailey and
Jonathan M. Borwein Ancient Indian Square Roots: An Exercise
in Forensic Paleo-Mathematics . . . . . 646--657
Bruce Ebanks Looking for a Few Good Means . . . . . . 658--669
Paul Pollack Finiteness Theorems for Perfect Numbers
and Their Kin . . . . . . . . . . . . . 670--681
Akira Sakurai Vector Analysis Proof of Erd\Hos'
Inequality for Triangles . . . . . . . . 682--684
Boris M. Makarov Calculation of the Volume of
Multidimensional Cones and Balls Using
Cavalieri's Principle . . . . . . . . . 685--689
David Angell Evaluation of Certain Legendre Symbols 690--693
Jonathan Groves An Elementary Counterexample in the
Compact-Open Topology . . . . . . . . . 693--694
Robert Dawson Arithmetic Polygons . . . . . . . . . . 695--698
Anonymous Problems and Solutions . . . . . . . . . 699--706
Mark Schwartz Book Review: \booktitleGeometry for
College Students, by I. Martin Isaacs.
American Mathematical Society, The Sally
Series, Pure and Applied Undergraduate
Texts No. 8, Providence, RI, 2001. vii +
222 pp., ISBN 978-0-8218-4794-7. \$62
(\$49.60 to AMS members) . . . . . . . . 707--711
Anonymous Back Matter . . . . . . . . . . . . . . 712--712
Anonymous Front Matter . . . . . . . . . . . . . . 713--714
Michael Eisermann The Fundamental Theorem of Algebra Made
Effective: An Elementary Real-Algebraic
Proof via Sturm Chains . . . . . . . . . 715--752
Oswaldo Rio Branco de Oliveira The Fundamental Theorem of Algebra: From
the Four Basic Operations . . . . . . . 753--758
John Lorch Magic Squares and Sudoku . . . . . . . . 759--770
Panagiota N. Panagopoulou and
Paul G. Spirakis Playing a Game to Bound the Chromatic
Number . . . . . . . . . . . . . . . . . 771--778
David Brink The Spiral of Theodorus and Sums of
Zeta-values at the Half-integers . . . . 779--786
B. Shapiro and
M. Shapiro A Few Riddles Behind Rolle's Theorem . . 787--793
Boris Alexeev and
Jacob Tsimerman Note on a War-like Card Game . . . . . . 793--795
Florian Breuer Newton Identities for Weierstrass
Products . . . . . . . . . . . . . . . . 796--799
Anonymous Problems and Solutions . . . . . . . . . 800--807
Stan Wagon Book Review: \booktitleIn Pursuit of the
Traveling Salesman, by William J. Cook.
Princeton University Press, Princeton,
NJ, 2012 xiii + 228 pp., ISBN
978-0-691-15270-7, \$27.95} . . . . . . 808--811
Anonymous Back Matter . . . . . . . . . . . . . . 812--812
Anonymous Front Matter . . . . . . . . . . . . . . 813--814
Tanya Khovanova and
Alexey Radul Killer Problems . . . . . . . . . . . . 815--823
Robert T. Jantzen and
Klaus Volpert On the Mathematics of Income Inequality:
Splitting the Gini Index in Two . . . . 824--837
Carla D. Martin and
Mason A. Porter The Extraordinary SVD . . . . . . . . . 838--851
William F. Trench An Elementary View of Weyl's Theory of
Equal Distribution . . . . . . . . . . . 852--861
Yong-Gao Chen and
Min Tang On the Elementary Symmetric Functions of
$1$, $ 1 / 2$, \ldots, $ 1 / n$ . . . . 862--867
Rolfdieter Frank and
Harald Riede Hyperplane Sections of the
$n$-Dimensional Cube . . . . . . . . . . 868--872
Jacob A. Siehler Tiling Hamiltonian Cycles on the $
24$-Cell . . . . . . . . . . . . . . . . 872--875
Witold Sadowski A Toy Forecast Model . . . . . . . . . . 876--879
Anonymous Problems and Solutions . . . . . . . . . 880--887
Gerald L. Alexanderson Book Review: \booktitleTranscending
Tradition: Jewish Mathematicians in
German-Speaking Academic Culture, by
Birgit Bergmann, Moritz Epple, and Ruti
Ungar, editors. Springer Verlag, Berlin
and Heidelberg, 2012, xi + 289 pp., ISBN
978-3-642-22463-8, \$49.95} . . . . . . 888--891
Anonymous Editor's Endnotes . . . . . . . . . . . 892--894
Anonymous Title Index, Author Index, Problems
Proposed, Problems Solved, Solutions,
Referees . . . . . . . . . . . . . . . . 895--905
Anonymous Back Matter . . . . . . . . . . . . . . 906--908
Anonymous Front Matter . . . . . . . . . . . . . . 1--2
Nicholas R. Baeth and
Roger Wiegand Factorization Theory and Decompositions
of Modules . . . . . . . . . . . . . . . 3--34
Steven J. Brams and
Michael A. Jones and
Christian Klamler $N$-Person Cake-Cutting: There May Be No
Perfect Division . . . . . . . . . . . . 35--47
M. Ram Murty and
Anastasia Zaytseva Transcendence of Generalized Euler
Constants . . . . . . . . . . . . . . . 48--54
Jean-Baptiste Hiriart-Urruty and
Patrice Lass\`ere When Is $ L^r(R) $ Contained in $ L^p(R)
+ L^q(R) $? . . . . . . . . . . . . . . 55--61
Vinicius Nicolae Petre Anghel A Use of Symmetry: Generalization of an
Integral Identity Found by M. L. Glasser 62--69
Yi Jun Chen A Proof that Zeilberger Missed: a New
Proof of an Identity by Chaundy and
Bullard Based on the Wilf--Zeilberger
Method . . . . . . . . . . . . . . . . . 69--70
L. P. Withers, Jr. Visual Angular Momentum: Mamikon Meets
Kepler . . . . . . . . . . . . . . . . . 71--73
Wlodzimierz Bak A Simple Characterization of
Differentiation . . . . . . . . . . . . 74--75
Anonymous Problems and Solutions . . . . . . . . . 76--83
Fernando Q. Gouvêa Book Review: \booktitleElliptic Curves,
Modular Forms, and Their L-functions
(Student Mathematical Library IAS/Park
City Subseries, vol, by Álvaro
Lozano-Robledo. 58), American
Mathematical Society, Providence, RI,
2011, 195 pp., ISBN 978-0-8218-5242-2,
\$29.60} . . . . . . . . . . . . . . . . 84--94
Anonymous Back Matter . . . . . . . . . . . . . . 95--96
Anonymous Front Matter . . . . . . . . . . . . . . 97--98
Holger Teismann Toward a More Complete List of
Completeness Axioms . . . . . . . . . . 99--114
Freeman J. Dyson and
Norman E. Frankel and
M. Lawrence Glasser Lehmer's Interesting Series . . . . . . 116--130
Dexter Kozen and
Alexandra Silva On Moessner's Theorem . . . . . . . . . 131--139
Susan H. Marshall and
Alexander R. Perlis Heronian Tetrahedra Are Lattice
Tetrahedra . . . . . . . . . . . . . . . 140--149
Jeremy Alm and
Michael Gramelspacher and
Theodore Rice Rubik's on the Torus . . . . . . . . . . 150--160
David C. Ullrich A Simple Elementary Proof of Hilbert's
Inequality . . . . . . . . . . . . . . . 161--164
Aaron Melman The Twin of a Theorem by Cauchy . . . . 164--168
Marco Dalai How Would Riemann Evaluate $ \zeta (2 n)
$? . . . . . . . . . . . . . . . . . . . 169--171
Vladimir Dragovi\'c Polynomial Dynamics and a Proof of the
Fermat Little Theorem . . . . . . . . . 171--173
Anonymous Problems and Solutions . . . . . . . . . 174--181
Michael Nathanson Book Review: \booktitleElements of
Information Theory, by Thomas M. Cover
and Joy A. Thomas. John Wiley and Sons,
Inc., Hoboken, NJ, 2006, xxiv + 748 pp.,
ISBN 0-471-24195-4, \$111.00} . . . . . 182--187
Anonymous Back Matter . . . . . . . . . . . . . . 188--188
Anonymous Front Matter . . . . . . . . . . . . . . 189--190
Dierk Schleicher and
Serge Tabachnikov Letter from the Guest Editors . . . . . 191--191
John H. Conway On Unsettleable Arithmetical Problems 192--198
Robert Foote and
Mark Levi and
Serge Tabachnikov Tractrices, Bicycle Tire Tracks, Hatchet
Planimeters, and a 100-year-old
Conjecture . . . . . . . . . . . . . . . 199--216
Dmitry Fuchs Evolutes and Involutes of Spatial Curves 217--231
Étienne Ghys Intersecting Curves (Variation on an
Observation of Maxim Kontsevich) . . . . 232--242
Aimeric Malter and
Dierk Schleicher and
Don Zagier New Looks at Old Number Theory . . . . . 243--264
Tadashi Tokieda Roll Models . . . . . . . . . . . . . . 265--282
Rade T. Zivaljevi\'c Book Review: \booktitleMathematical
Omnibus: Thirty Lectures on Classic
Mathematics, by Dmitry Fuchs and Serge
Tabachnikov. American Mathematical
Society, Providence, RI, 2007, xv + 463
pp., ISBN-13: 978-0-8218-4316-1, \$61} 283--286
Pieter Moree Book Review: \booktitleAn Invitation to
Mathematics: From Competitions to
Research, [edited] by Dierk Schleicher
and Malte Lackmann, editors.
Springer-Verlag, Heidelberg, 2011, xiv +
220 pp. ISBN-13: 978-3-642-19532-7,
\$34.95} . . . . . . . . . . . . . . . . 286--288
Christoph Pöppe Book Review: \booktitleDimensions, by
Jos Leys, Étienne Ghys, and Aurélien
Alvarez. A mathematical video.
\urlwww.dimensions-math.org, 117
minutes, no cost . . . . . . . . . . . . 288--290
Anonymous Back Matter . . . . . . . . . . . . . . 291--292
Anonymous Front Matter . . . . . . . . . . . . . . 293--294
Ann E. Watkins Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2013 to William A. Hawkins for
Distinguished Service to Mathematics . . 295--297
Tom M. Apostol and
Mamikon A. Mnatsakanian New Balancing Principles Applied to
Circumsolids of Revolution, and to
$n$-Dimensional Spheres, Cylindroids,
and Cylindrical Wedges . . . . . . . . . 298--321
Matthew Jenssen and
Daniel Montealegre and
Vadim Ponomarenko Irreducible Factorization Lengths and
the Elasticity Problem within $ \mathbb
{N} $ . . . . . . . . . . . . . . . . . 322--328
Kenneth S. Williams The Parents of Jacobi's Four Squares
Theorem Are Unique . . . . . . . . . . . 329--345
Kathryn L. Nyman and
Francis Edward Su A Borsuk--Ulam Equivalent that Directly
Implies Sperner's Lemma . . . . . . . . 346--354
Habib Bin Muzaffar A New Proof of a Classical Formula . . . 355--358
Steve Alpern and
Robbert Fokkink Illuminating a Network from Its Nodes 358--359
Orr Moshe Shalit A Sneaky Proof of the Maximum Modulus
Principle . . . . . . . . . . . . . . . 359--362
Olivier Bernardi A Short Proof of Rayleigh's Theorem with
Extensions . . . . . . . . . . . . . . . 362--364
Anonymous Problems and Solutions . . . . . . . . . 365--372
Marie Snipes Book Review: \booktitleLinear and
Nonlinear Programming, 3rd ed, by David
G. Luenberger and Yinyu Ye., Springer,
New York, 2008, xiv + 546 pp., ISBN
0-387-74502-5, \$109} . . . . . . . . . 373--379
Anonymous Back Matter . . . . . . . . . . . . . . 380--380
Anonymous Front Matter . . . . . . . . . . . . . . 381--382
Scott Chapman A Letter from the Editor . . . . . . . . 383--383
Ehud Kalai Foreword: The High Priest of Game Theory 384--385
D. Gale and
L. S. Shapley College Admissions and the Stability of
Marriage . . . . . . . . . . . . . . . . 386--391
James Propp Real Analysis in Reverse . . . . . . . . 392--408
Melvyn B. Nathanson On the Fractional Parts of Roots of
Positive Real Numbers . . . . . . . . . 409--429
Stephen M. Buckley and
Desmond MacHale Variations on a Theme: Rings Satisfying
$ x^3 = x $ Are Commutative . . . . . . 430--440
Joshua Cooper and
Aaron Dutle Greedy Galois Games . . . . . . . . . . 441--451
Rachid Marsli and
Frank J. Hall Geometric Multiplicities and Gersgorin
Discs . . . . . . . . . . . . . . . . . 452--455
Jim X. Xiang A Note on the Cauchy--Schwarz Inequality 456--459
Costas J. Efthimiou A Class of Continued Radicals . . . . . 459--461
D. Aharonov and
U. Elias A Binomial Identity via Differential
Equations . . . . . . . . . . . . . . . 462--466
F. Galaz-Fontes Another Proof for Non-Supercyclicity in
Finite Dimensional Complex Banach Spaces 466--468
Anonymous Problems and Solutions . . . . . . . . . 469--476
Kevin Woods Book Review: \booktitleSymmetry: A
Mathematical Exploration, by Kristopher
Tapp. Springer, New York, 2012, xiv +
215pp., ISBN 978-1-4614-0298-5, \$49.95} 477--481
Anonymous Editor's Endnotes . . . . . . . . . . . 482--483
Anonymous Back Matter . . . . . . . . . . . . . . 484--484
Anonymous Front Matter . . . . . . . . . . . . . . 485--486
Andrew D. Hwang Paper Surface Geometry . . . . . . . . . 487--499
Joanna M. Papakonstantinou and
Richard A. Tapia Origin and Evolution of the Secant
Method in One Dimension . . . . . . . . 500--518
Nathan Bliss and
Ben Fulan and
Stephen Lovett and
Jeff Sommars Strong Divisibility, Cyclotomic
Polynomials, and Iterated Polynomials 519--536
Steven H. Weintraub Several Proofs of the Irreducibility of
the Cyclotomic Polynomials . . . . . . . 537--545
Kurt Girstmair The Equation $ x^2 + \bar {m} y^2 = \bar
{k} $ in $ \mathbb {Z} / p \mathbb {Z} $ 546--552
Claire-Soizic Henry Coxeter Friezes and Triangulations of
Polygons . . . . . . . . . . . . . . . . 553--558
Jonathon Peterson A Probabilistic Proof of a Binomial
Identity . . . . . . . . . . . . . . . . 558--562
S. A. Rankin The Euclidean Algorithm and the Linear
Diophantine Equation $ a x + b y = {\rm
gcd}(a, b) $ . . . . . . . . . . . . . . 562--564
Tadashi Tokieda A Buoyancy-Driven Perpetual Motion
Machine . . . . . . . . . . . . . . . . 564--566
Manas R. Sahoo Example of a Monotonic, Everywhere
Differentiable Function on $ \mathbb {R}
$ Whose Derivative Is not Continuous . . 566--568
Anonymous Problems and Solutions . . . . . . . . . 569--576
David Bressoud Book Review: \booktitleCalculus, by
Michael Spivak; \booktitleCalculus
Deconstructed: A Second Course in
First-Year Calculus. MAA Textbooks,
Mathematical Association of America,
Washington, DC, 2009, xvi + 491 pp.,
ISBN 978-0-88385-756-4, \$ 59.95. by
Zbigniew Nitecki;
\booktitle{Approximately Calculus}.
American Mathematical Society,
Providence, RI, 2006, xvii + 292 pp.,
ISBN 978-0-8218-3750-4, \$50.00. by
Shahriar Sharhriari; \booktitleGuide to
Cauchy's Calculus: A Translation and
Analysis of Calcul Infinitésimal.
Fairview Academic Press, Walnut Creek,
CA, 2012, viii + 616 pp., ISBN
978-0-9838837-0-8, \$139.00. by Dennis
M. Cates; \booktitle{The Calculus
Integral}. ClassicalRealAnalysis.com,
Charleston, SC, 2010, x + 291, ISBN
978-1442180956, \$14.95. by Brian S.
Thomson. 4th edition. Publish or Perish,
Houston, TX, 2008, xiv + 680 pp., ISBN
978-0-914098-91-1, \$85.00} . . . . . . 577--580
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 581--582
David J. Aldous Using Prediction Market Data to
Illustrate Undergraduate Probability . . 583--593
Stephen D. Casey and
Brian M. Sadler Pi, the Primes, Periodicities, and
Probability . . . . . . . . . . . . . . 594--608
Peter Kuchment and
Sergey Lvin Identities for $ \sin x $ that Came from
Medical Imaging . . . . . . . . . . . . 609--621
Steve Butler and
Ron Graham Subdivision Using Angle Bisectors Is
Dense in the Space of Triangles . . . . 622--630
Mikhail G. Katz and
Eric Leichtnam Commuting and Noncommuting
Infinitesimals . . . . . . . . . . . . . 631--641
Daniele Ritelli Another Proof of $ {\zeta (2) = \frac
{\pi^2}{6}} $ Using Double Integrals . . 642--645
Matthias Arnold and
Werner Glaß Simple Approximation Formulas for the
Birthday Problem . . . . . . . . . . . . 645--648
Anthony J. Bevelacqua Another Irreducibility Criterion . . . . 648--650
Jaban Meher and
M. Ram Murty Ramanujan's Proof of Bertrand's
Postulate . . . . . . . . . . . . . . . 650--653
T. Samuel A Simple Proof of Vitali's Theorem for
Signed Measures . . . . . . . . . . . . 654--659
Anonymous Problems and Solutions . . . . . . . . . 660--669
Joseph Malkevitch Book Review: \booktitleThe Mathematical
Coloring Book, by Alexander Soifer.
Springer, New York, xxx + 607 pp., ISBN
978-0-387-74640-1, \$69.95} . . . . . . 670--674
Samuel G. Moreno and
Esther M. García-Caballero Book Review: \booktitleOn the
Irrationality of $ \surd 2 $ Once Again 674--674
Anonymous Back Matter . . . . . . . . . . . . . . 675--676
Anonymous Front Matter . . . . . . . . . . . . . . 677--678
Leonard F. Klosinski and
Gerald L. Alexanderson and
Mark Krusemeyer The Seventy-Third William Lowell Putnam
Mathematical Competition . . . . . . . . 679--688
Alan Tucker The History of the Undergraduate Program
in Mathematics in the United States . . 689--705
Brant Jones and
Laura Taalman and
Anthony Tongen Solitaire Mancala Games and the Chinese
Remainder Theorem . . . . . . . . . . . 706--724
Paul Monsky Frobenius' Result on Simple Groups of
Order $ \frac {p^3 - p^2}{2} $ . . . . . 725--732
Bhaskar Bagchi and
Basudeb Datta Higher-Dimensional Analogues of the Map
Coloring Problem . . . . . . . . . . . . 733--737
Dorin Ervin Dutkay and
Constantin P. Niculescu and
Florin Popovici Stirling's Formula and Its Extension for
the Gamma Function . . . . . . . . . . . 737--740
Jean Van Schaftingen A Direct Proof of the Existence of
Eigenvalues and Eigenvectors by
Weierstrass's Theorem . . . . . . . . . 741--746
A. G. Ramm A Variational Principle and Its
Application to Estimating the Electrical
Capacitance of a Perfect Conductor . . . 747--751
Zsolt Lengvárszky Proving the Pythagorean Theorem via
Infinite Dissections . . . . . . . . . . 751--753
Anonymous Problems and Solutions . . . . . . . . . 754--761
Takis Konstantopoulos Book Review: \booktitleAn Introduction
to Measure Theory, by Terence Tao.
American Mathematical Society,
Providence RI, 2011, xvi + 206 pp., ISBN
978-0-8218-6919-2, \$53.00} . . . . . . 762--768
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 769--770
Jacques Lévy Véhel and
Franklin Mendivil Christiane's Hair . . . . . . . . . . . 771--786
Daniel J. Velleman and
Gregory S. Warrington What to Expect in a Game of Memory . . . 787--805
Antonín Slavík Mixing Problems with Many Tanks . . . . 806--821
Jonathan Bayless and
Dominic Klyve Reciprocal Sums as a Knowledge Metric:
Theory, Computation, and Perfect Numbers 822--831
Jorge Luis Cimadevilla Villacorta Certain Inequalities Associated with the
Divisor Function . . . . . . . . . . . . 832--837
Charles S. Kahane On the Nonexistence of Certain Limits
for the Complex Exponential . . . . . . 837--840
Árpád Bényi and
Branko \'Curgus A Generalization of Routh's Triangle
Theorem . . . . . . . . . . . . . . . . 841--846
David Pan A Maximum Principle for High-Order
Derivatives . . . . . . . . . . . . . . 846--848
Gerhard J. Woeginger Nothing New about Equiangular Polygons 849--850
Stephan Ramon Garcia Quotients of Gaussian Primes . . . . . . 851--853
Anonymous Problems and Solutions . . . . . . . . . 854--861
Betty Mayfield Book Review: \booktitleCalculus:
Modeling and Application, second
edition, by David A. Smith and Lawrence
C. Moore. Mathematical Association of
America, Washington, D.C., 2010.
http://maa.pinnaclecart.com. Price:
\$35.00. ISBN 978-1-6144-610-1} . . . . 862--864
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 865--866
David Pengelley Quick, Does $ 23 / 67 $ Equal $ 33 / 97
$ ? A Mathematician's Secret from Euclid
to Today . . . . . . . . . . . . . . . . 867--876
Alexander P. Campbell and
Daniel Daners Linear Algebra via Complex Analysis . . 877--892
Olle Häggström and
Johan Wästlund Rigorous Computer Analysis of the
Chow--Robbins Game . . . . . . . . . . . 893--900
Will Traves From Pascal's Theorem to
$d$-Constructible Curves . . . . . . . . 901--915
Roger E. Howe The Cuoco Configuration . . . . . . . . 916--923
Ulrich Abel A Generalization of the Leibniz Rule . . 924--928
Jonathan Sondow The Parbelos, a Parabolic Analog of the
Arbelos . . . . . . . . . . . . . . . . 929--935
G. J. O. Jameson Inequalities for Gamma Function Ratios 936--940
Anonymous Problems and Solutions . . . . . . . . . 941--948
James M. Henle and
Michael G. Henle Book Review: \booktitleReal Analysis
Through Modern Infinitesimals, Cambridge
University Press, 2011, xix + 565 pp, by
Nader Vakil., ISBN 978-1-107-00202-9,
\$127.00} . . . . . . . . . . . . . . . 949--953
Anonymous Editor's Endnotes . . . . . . . . . . . 954--956
Anonymous Title Index, Author Index, Problems
Proposed, Problems Solved, Solutions,
Referees . . . . . . . . . . . . . . . . 957--967
Anonymous Back Matter . . . . . . . . . . . . . . 968--968
Anonymous Front Matter . . . . . . . . . . . . . . 1--2
Scott T. Chapman A Letter from the Editor: What's In a
Color? . . . . . . . . . . . . . . . . . 3--4
Melvyn B. Nathanson Additive Systems and a Theorem of de
Bruijn . . . . . . . . . . . . . . . . . 5--17
Mario Ponce and
Patricio Santibáñez On Equidistant Sets and Generalized
Conics: The Old and the New . . . . . . 18--32
Anthony Mendes and
Kent E. Morrison Guessing Games . . . . . . . . . . . . . 33--44
Chris D. Lynd Using Difference Equations to Generalize
Results for Periodic Nested Radicals . . 45--59
J. A. Conejero and
P. Jiménez-Rodríguez and
G. A. Muñoz-Fernández and
J. B. Seoane-Sepúlveda When the Identity Theorem ``Seems'' to
Fail . . . . . . . . . . . . . . . . . . 60--68
Ádám Besenyei Peano's Unnoticed Proof of Borel's
Theorem . . . . . . . . . . . . . . . . 69--72
Steven H. Weintraub Values of Polynomials over Integral
Domains . . . . . . . . . . . . . . . . 73--74
Bao Qin Li A Direct Proof and a Transcendental
Version of the Fundamental Theorem of
Algebra via Cauchy's Theorem . . . . . . 75--77
Samuel Clowes Huneke An Inductive Proof of Hex Uniqueness . . 78--80
Karim Boulabiar Real-Valued Ring Homomorphisms on $
C(\Omega) $ . . . . . . . . . . . . . . 81--82
Anonymous Problems and Solutions . . . . . . . . . 83--90
Kenneth A. Ross Book Review: \booktitleIn the Dark on
the Sunny Side: a Memoir of an
Out-of-Sight Mathematician, Mathematical
Association of America, Washington, DC,
2012, 206 pp, by Larry Baggett., ISBN
978-0-88385-581-2, \$50} . . . . . . . . 91--92
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 93--94
Eric C. Chi and
Kenneth Lange A Look at the Generalized Heron Problem
through the Lens of
Majorization-Minimization . . . . . . . 95--108
Vincent Coll and
Mike Harrison Two Generalizations of a Property of the
Catenary . . . . . . . . . . . . . . . . 109--119
Pantelis A. Damianou A Beautiful Sine Formula . . . . . . . . 120--135
Ron Evans and
Lihua Huang and
Tuan Nguyen Keeler's Theorem and Products of
Distinct Transpositions . . . . . . . . 136--144
Jaime Gaspar Non-recursive Polynomial Formula for the
Sum of the Powers of the Integers . . . 144--144
David Grant The Quadratic Gauss Sum Redux . . . . . 145--149
Miles Dillon Edwards A Possibly New Proof of the Law of Cos 149--149
Yuly Billig and
John D. Dixon An Eigenvalue Theorem for Systems of
Polynomial Equations . . . . . . . . . . 150--153
Hongwei Lou A Short Proof of Stirling's Formula . . 154--157
Richard Ehrenborg Hamiltonian Cycles on Archimedean Solids
Are Twisting Free . . . . . . . . . . . 158--161
Chua Cheong Siong A Simple Proof of Ljunggren's Binomial
Congruence . . . . . . . . . . . . . . . 162--164
Daniel J. Velleman Monthly Gems . . . . . . . . . . . . . . 164--164
Peter J. McGrath Another Proof of Clairaut's Theorem . . 165--166
Hossein Hosseini Giv Proving the Banach--Alaoglu Theorem via
the Existence of the Stone-\vCech
Compactification . . . . . . . . . . . . 167--169
Anonymous Problems and Solutions . . . . . . . . . 170--177
Harold P. Boas Book Review: \booktitleInvitation to
Classical Analysis, American
Mathematical Society, Providence, RI,
2012, xiii + 392 pp, by Peter Duren.,
ISBN 978-0-8218-6932-1, \$74.00} . . . . 178--182
Peter D. Lax Book Review: \booktitleNumbers and
Functions: From a Classical Experimental
Mathematicians Point of View, American
Mathematical Society, Providence, RI,
2012, 504 pp, by Victor H. Moll., ISBN
978-0-8218-8795-0, \$58} . . . . . . . . 183--183
Anonymous Back Matter . . . . . . . . . . . . . . 184--184
Anonymous Front Matter . . . . . . . . . . . . . . 185--186
Kenneth A. Ross and
Ann E. Watkins Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2014 to Joan Leitzel for
Distinguished Service to Mathematics . . 187--190
David H. Bailey and
Jonathan Borwein Pi Day Is Upon Us Again and We Still Do
Not Know if Pi Is Normal . . . . . . . . 191--206
Stephan Berendonk The Length of Spirographic Curves . . . 207--212
Alec S. Cooper and
Oleg Pikhurko and
John R. Schmitt and
Gregory S. Warrington Martin Gardner's Minimum
No-$3$-in-a-Line Problem . . . . . . . . 213--221
Aleksander Maliszewski and
Marcin Szyszkowski Level Sets on Disks . . . . . . . . . . 222--228
Junesang Choi and
Hari M. Srivastava Series Involving the Zeta Functions and
a Family of Generalized Goldbach--Euler
Series . . . . . . . . . . . . . . . . . 229--236
B. Sury A Polynomial Parent to a
Fibonacci--Lucas Relation . . . . . . . 236--236
Trevor Hyde A Wallis Product on Clovers . . . . . . 237--243
Mircea Merca On Some Power Sums of Sine or Cosine . . 244--248
William Johnston The Weighted Hermite Polynomials Form a
Basis for $ L_2 (\mathbb {R}) $ . . . . 249--253
Gerd Herzog A Proof of Lie's Product Formula . . . . 254--257
Kenneth Lange Hadamard's Determinant Inequality . . . 258--259
S. Koçak and
M. Limoncu Mean of the Mean of the Mean \ldots . . 259--259
Justin Tatch Moore Justin Tatch Moore . . . . . . . . . . . 260--262
Marc Chamberland and
Doron Zeilberger A Short Proof of McDougall's Circle
Theorem . . . . . . . . . . . . . . . . 263--265
Anonymous Problems and Solutions . . . . . . . . . 266--273
Mark Kozek Book Review: \booktitleMathematics in
Popular Culture: Essays on Appearances
in Film, Fiction, Games, Television and
Other Media. Edited by Jessica K. Sklar
and Elizabeth S. Sklar; Foreword by
Keith Devlin. McFarland, Jefferson, NC,
2012, viii + 345 pp., ISBN
978-0-7864-4978-1, \$45} . . . . . . . . 274--278
Anonymous Back Matter . . . . . . . . . . . . . . 279--280
Anonymous Front Matter . . . . . . . . . . . . . . 281--282
Andrew J. Simoson Periodicity Domains and the Transit of
Venus . . . . . . . . . . . . . . . . . 283--298
Daniel J. Velleman A Drug-Induced Random Walk . . . . . . . 299--317
Alexei Yu. Uteshev Analytical Solution for the Generalized
Fermat--Torricelli Problem . . . . . . . 318--331
Samuel J. Ferguson A One-Sentence Line-of-Sight Proof of
the Extreme Value Theorem . . . . . . . 331--331
Martin Kovár and
Alena Chernikava On the Proof of the Existence of
Undominated Strategies in Normal Form
Games . . . . . . . . . . . . . . . . . 332--337
Chao-Ping Chen and
Junesang Choi An Asymptotic Formula for $ (1 + 1 /
x)^x $ Based on the Partition Function 338--343
Steffen Eger Stirling's Approximation for Central
Extended Binomial Coefficients . . . . . 344--349
Thorsten Neuschel A New Proof of Stirling's Formula . . . 350--352
Ralph M. Krause Zeta(2) Once Again . . . . . . . . . . . 353--354
Andrea M. Hyde and
Paul D. Lee and
Blair K. Spearman Polynomials $ (x^3 - n)(x^2 + 3) $
Solvable Modulo Any Integer . . . . . . 355--358
B. Sury Macaulay Expansion . . . . . . . . . . . 359--360
J. J. Koliha Evaluating Lebesgue Integrals
Efficiently with the FTC . . . . . . . . 361--364
Anonymous Problems and Solutions . . . . . . . . . 365--372
Jeffrey Nunemacher Book Review: \booktitleEncounters with
Chaos and Fractals, 2nd edition. By
Denny Gulick. Chapman and Hall/CRC
Press, Boca Raton, 2012, xvi + 371 pp.,
ISBN 978-1-58488-517-7, \$79.95} . . . . 373--376
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 377--378
Allison Henrich and
Louis H. Kauffman Unknotting Unknots . . . . . . . . . . . 379--390
Alan F. Beardon and
Ian Short A Geometric Representation of Continued
Fractions . . . . . . . . . . . . . . . 391--402
Tom Leinster Rethinking Set Theory . . . . . . . . . 403--415
Allan J. Kroopnick An Elementary Application of Brouwer's
Fixed Point Theorem to Transition
Matrices . . . . . . . . . . . . . . . . 415--415
Jon Grantham and
Witold Jarnicki and
John Rickert and
Stan Wagon Repeatedly Appending Any Digit to
Generate Composite Numbers . . . . . . . 416--421
Iddo Ben-Ari and
Diana Hay and
Alexander Roitershtein On Wallis-type Products and Pólya's Urn
Schemes . . . . . . . . . . . . . . . . 422--432
Paul Pollack and
Enrique Treviño The Primes that Euclid Forgot . . . . . 433--437
Emmanuel Tsukerman Solution of Sondow's Problem: A
Synthetic Proof of the Tangency Property
of the Parbelos . . . . . . . . . . . . 438--443
José Ángel Cid Araújo A Difference Equation Leading to the
Irrationality of $ \surd 2 $ . . . . . . 443--443
Nathan A. Carlson A Connection between Furstenberg's and
Euclid's Proofs of the Infinitude of
Primes . . . . . . . . . . . . . . . . . 444--444
Ming-Chia Li An Elementary Proof of a Generalization
of Banach's Mapping Theorem . . . . . . 445--446
M. L. Glasser A Technique in Contour Integration . . . 447--448
Kyle Luh and
Nicholas Pippenger Large-Deviation Bounds for Sampling
without Replacement . . . . . . . . . . 449--454
Anonymous Problems and Solutions . . . . . . . . . 455--462
Daniel Ullman Book Review: \booktitleMath on Trial:
How Mathematics Is Used and Abused in
the Courtroom, By Leila Schneps and
Coralie Colmez, Basic Books, New York,
2013, xi + 256 pp., ISBN
978-0-465-03292-1, \$26.99} . . . . . . 463--466
Anonymous Editor's Endnotes . . . . . . . . . . . 467--468
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 469--470
Alberto Facchini and
Giulia Simonetta Rational Numbers, Finite Cyclic Monoids,
Divisibility Rules, and Numbers of Type
$ 99 \cdots {} 900 \cdots {} 0 $ . . . . 471--485
David Borwein and
Jonathan M. Borwein and
Brailey Sims On the Solution of Linear Mean
Recurrences . . . . . . . . . . . . . . 486--498
Josef Rukavicka Rejection of Laplace's Demon . . . . . . 498--498
C. W. Groetsch and
S. A. Yost Vertical Projection in a Resisting
Medium: Reflections on Observations of
Mersenne . . . . . . . . . . . . . . . . 499--505
J. Scott Carter and
Daniel S. Silver and
Susan G. Williams Three Dimensions of Knot Coloring . . . 506--514
Harris Kwong An Alternate Proof of Sury's
Fibonacci--Lucas Relation . . . . . . . 514--514
Jose Pujol On Hamilton's Nearly-Forgotten Early
Work on the Relation between Rotations
and Quaternions and on the Composition
of Rotations . . . . . . . . . . . . . . 515--522
B. Sury A Heuristic Argument for Hua's Identity
Using Geometric Series . . . . . . . . . 522--522
Tommy Wright Lagrange's Identity and Congressional
Apportionment . . . . . . . . . . . . . 523--528
Chai Wah Wu Pigeonholes and Repunits . . . . . . . . 529--533
Kevin K. Ferland Record Crossword Puzzles . . . . . . . . 534--536
Michael Z. Spivey A Combinatorial Proof for the
Alternating Convolution of the Central
Binomial Coefficients . . . . . . . . . 537--540
Nikolai Nikolov and
Blagovest Sendov A Converse of the Gauss--Lucas Theorem 541--544
Yared Nigussie Finding Your Seat Versus Tossing a Coin 545--546
Erich Badertscher A Simple Direct Proof of Marden's
Theorem . . . . . . . . . . . . . . . . 547--548
Anonymous Problems and Solutions . . . . . . . . . 549--556
James A. Swenson Book Review: \booktitleWhich Numbers Are
Real?, By Michael Henle. Mathematical
Association of America, Washington, DC,
2012, x + 219 pp., ISBN
978-0-88385-777-9, \$53.00} . . . . . . 557--560
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 561--562
Erwan Brugallé and
Kristin Shaw A Bit of Tropical Geometry . . . . . . . 563--589
Marcelo Brafman Another Algebraic Pythagorean Proof . . 589--589
Bryan Brown and
Michael Dairyko and
Stephan Ramon Garcia and
Bob Lutz and
Michael Someck Four Quotient Set Gems . . . . . . . . . 590--598
Vinícius G. Pereira de Sá and
Celina M. H. de Figueiredo Blind-friendly von Neumann's Heads or
Tails . . . . . . . . . . . . . . . . . 600--609
Richard Katz and
Mike Krebs and
Anthony Shaheen Zero Sums on Unit Square Vertex Sets and
Plane Colorings . . . . . . . . . . . . 610--618
D. Zagier A Refinement of a Theorem of J. E.
Littlewood . . . . . . . . . . . . . . . 618--618
Rajendra Bhatia and
Rajesh Sharma Positive Linear Maps and Spreads of
Matrices . . . . . . . . . . . . . . . . 619--624
Wen D. Chang and
Russell A. Gordon Trisecting Angles in Pythagorean
Triangles . . . . . . . . . . . . . . . 625--631
Diego Marques Yet Another Direct Proof of the
Uncountability of the Transcendental
Numbers . . . . . . . . . . . . . . . . 631--631
Rom Pinchasi Points Covered an Odd Number of Times by
Translates . . . . . . . . . . . . . . . 632--636
Meinolf Geck On the Characterization of Galois
Extensions . . . . . . . . . . . . . . . 637--639
Samuel G. Moreno and
Esther M. García-Caballero Simpson's Rule and Sums of Powers . . . 639--639
F. Dreher and
T. Samuel Continuous Images of Cantor's Ternary
Set . . . . . . . . . . . . . . . . . . 640--643
Robert A. Beezer Extended Echelon Form and Four Subspaces 644--647
Anonymous Problems and Solutions . . . . . . . . . 648--657
Michael Barr Book Review: \booktitleThe Outer Limits
of Reason, Noson Yanofsky. MIT Press,
Cambridge, MA and London, England, 2013,
xiv + 403 pp., ISBN 978-0-262-01935-4,
\$29.95} . . . . . . . . . . . . . . . . 658--660
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 659--662
Leonard F. Klosinski and
Gerald L. Alexanderson and
Mark Krusemeyer The Seventy-Fourth William Lowell Putnam
Mathematical Competition . . . . . . . . 663--673
Persi Diaconis and
Xuancheng Shao and
Kannan Soundararajan Carries, Group Theory, and Additive
Combinatorics . . . . . . . . . . . . . 674--688
Marc Deléglise and
Andrew Markoe On the Maximum Arc Length of Monotonic
Functions . . . . . . . . . . . . . . . 689--699
David Borwein and
Jonathan Borwein Deriving New Sinc Results from Old . . . 700--705
Michael Joswig and
Günter M. Ziegler Foldable Triangulations of Lattice
Polygons . . . . . . . . . . . . . . . . 706--710
Jonathan Novak Pólya's Random Walk Theorem . . . . . . . 711--716
Michael Schramm and
John Troutman and
Daniel Waterman Segmentally Alternating Series . . . . . 717--722
John Molokach Law of Cosines --- A Proof Without Words 722--722
Mark H. Holmes Connections Between Cubic Splines and
Quadrature Rules . . . . . . . . . . . . 723--726
M. Scott Osborne Hausdorffization and Such . . . . . . . 727--733
Donald M. Davis Binomial Coefficients Involving Infinite
Powers of Primes . . . . . . . . . . . . 734--737
Anonymous Problems and Solutions . . . . . . . . . 738--745
Brian M. Loft Book Review: \booktitleThe Cult of
Pythagorus: Math and Myths, by Alberto
A. Martínez. University of Pittsburgh
Press, Pittsburgh, PA, 2012, xxii + 264
pp., ISBN 978-0-8229-4418-8, \$27.95} 746--748
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 747--750
Anonymous Front Matter . . . . . . . . . . . . . . 747--750
Fred Adler and
Elizabeth S. Allman and
Lisette G. de Pillis A Letter from the Guest Editors . . . . 751--753
Jonathan R. Potts and
Mark A. Lewis A Mathematical Approach to Territorial
Pattern Formation . . . . . . . . . . . 754--770
Mike Steel Tracing Evolutionary Links between
Species . . . . . . . . . . . . . . . . 771--792
Roderick Edwards and
Leon Glass Dynamics in Genetic Networks . . . . . . 793--809
Hoa Nguyen and
Ricardo Cortez and
Lisa Fauci Computing Flows Around Microorganisms:
Slender-Body Theory and Beyond . . . . . 810--823
David Terman Mathematical Neuroscience . . . . . . . 824--839
Trachette Jackson and
Natalia Komarova and
Kristin Swanson Mathematical Oncology: Using Mathematics
to Enable Cancer Discoveries . . . . . . 840--856
Laurie J. Heyer and
Jeffrey L. Poet Synthetic Biology: A New Frontier . . . 857--867
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 867--870
Anonymous Front Matter . . . . . . . . . . . . . . 867--870
Peter J. Giblin and
J. Paul Warder Evolving Evolutoids . . . . . . . . . . 871--889
Pieter Moree Numerical Semigroups, Cyclotomic
Polynomials, and Bernoulli Numbers . . . 890--902
Lei Ni A Perron-type Theorem on the Principal
Eigenvalue of Nonsymmetric Elliptic
Operators . . . . . . . . . . . . . . . 903--908
Pete L. Clark and
Niels J. Diepeveen Absolute Convergence in Ordered Fields 909--916
William F. Trench An Unnoticed Consequence of Szeg\Ho's
Distribution Theorem . . . . . . . . . . 917--921
Jack Button and
Maurice Chiodo and
Mariano Zeron-Medina Laris Coset Intersection Graphs for Groups . . 922--926
Sam Northshield Complex Descartes Circle Theorem . . . . 927--931
Pallab Kanti Dey and
R. Thangadurai The Length of an Arithmetic Progression
Represented by a Binary Quadratic Form 932--936
Marshall Hampton Cosines and Cayley, Triangles and
Tetrahedra . . . . . . . . . . . . . . . 937--941
Felipe Acker A Note on the Spectral Theorem in the
Finite-Dimensional Real Case . . . . . . 942--945
Anonymous Problems and Solutions . . . . . . . . . 946--953
Anonymous Problems and Solutions . . . . . . . . . 946--953
Genevieve S. Walsh Book Review: \booktitleMostly Surfaces,
By Richard Evan Schwartz. American
Mathematical Society, Providence, RI,
2010, xiii + 314 pp., ISBN
978-0-8218-5368-9, \$47.00} . . . . . . 954--956
Anonymous Editor's Endnotes . . . . . . . . . . . 957--959
Anonymous Monthly Referees for 2014 . . . . . . . 960--962
Jonathan Sondow From the \booktitleMonthly Over 100
Years Ago \ldots . . . . . . . . . . . . 963--963
Jonathan Sondow From the Monthly Over 100 Years
Ago\ldots . . . . . . . . . . . . . . . 963--963
Amrik Singh Nimbran One More Proof of the Irrationality of $
\sqrt 2 $ . . . . . . . . . . . . . . . 964--964
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2
Scott T. Chapman A Letter from the Editor: 2015 is the
Centennial Year of the MAA . . . . . . . 3--3
David E. Zitarelli The First 100 Years of the MAA . . . . . 4--23
Frank Swenton Simultaneous Proof of the First
Fundamental Theorem of Calculus and
Integrability of Continuous Functions 23--23
Titu Andreescu and
Vladimir Georgiev and
Oleg Mushkarov and
Vladimir Georgiev and
Oleg Mushkarov Napoleon Polygons . . . . . . . . . . . 24--29
Kenneth S. Williams Historical Remark on Ramanujan's Tau
Function . . . . . . . . . . . . . . . . 30--35
Branko \'Curgus and
Robert I. Jewett and
Robert I. Jewett Somewhat Stochastic Matrices . . . . . . 36--42
Michael Hardy Stereographic Trigonometric Identities 43--47
Xianzu Lin Infinitely Many Primes in the Arithmetic
Progression $ k n - 1 $ . . . . . . . . 48--51
P. Mark Kayll Deranged Matchings: Enumeration by
Integration!! . . . . . . . . . . . . . 51--51
Francis C. Motta and
Patrick D. Shipman and
Bethany Springer A Point of Tangency Between
Combinatorics and Differential Geometry 52--55
Hossein Hosseini Giv The Axiom of Choice, Well-Ordering, and
Well-Classification . . . . . . . . . . 56--59
R. Ehrenhorg An Unbiased Marriage Theorem . . . . . . 59--59
Ignacio Ojeda Kronecker Square Roots and the Block Vec
Matrix . . . . . . . . . . . . . . . . . 60--64
Pablo A. Panzone On a Formula of S. Ramanujan . . . . . . 65--69
Edward S. Letzter Continuity is an Adjoint Functor . . . . 70--74
Anonymous Problems and Solutions . . . . . . . . . 75--82
Edward F. Schaefer Book Review: \booktitleThe Mathematics
of Encryption: An Elementary
Introduction, Reviewed work(s): The
Mathematics of Encryption: An Elementary
Introduction. By Margaret Cozzens and
Steven J. Miller. American Mathematical
Society, Providence, RI, 2013, xviii +
332 pp., ISBN 978-0-8218-8321-1,
\$49.00} . . . . . . . . . . . . . . . . 83--88
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 87--90
Yves Nievergelt Backward Analysis Explained with Monthly
Payments . . . . . . . . . . . . . . . . 91--120
Christopher O'Neill and
Roberto Pelayo and
Roberto Pelayo How Do You Measure Primality? . . . . . 121--137
Aydin Shukurov The Power System is Never a Basis in the
Space of Continuous Functions . . . . . 137--137
Carlos A. Catalá de la Torre A New Proof for a Sharp van der Corput's
Lemma . . . . . . . . . . . . . . . . . 138--142
S. Koçak Dihedral Angles of the Regular
$n$-Simplex . . . . . . . . . . . . . . 143--143
Arseniy V. Akopyan Geometry of the Cardioid . . . . . . . . 144--150
Marcelo Brafman Another Algebraic Pythagorean Proof . . 150--150
G. Molinari Elementary Prime Identities . . . . . . 151--154
Joachim Gräter and
Karl-Joachim Wirths and
Karl-Joachim Wirths On Elementary Bounds for $ \sum
\nolimits_{k = n}^\infty {k^{-s}} $ . . 155--158
Paul Pollack An Easy Generalization of Euler's
Theorem on the Series of Prime
Reciprocals . . . . . . . . . . . . . . 159--163
Daniel Drucker A Comprehensive Pythagorean Theorem for
all Dimensions . . . . . . . . . . . . . 164--168
Samuel G. Moreno and
Esther M. García-Caballero A Geometric Proof of Morrie's Law . . . 168--168
Bao Qin Li Two Elementary Properties of Entire
Functions . . . . . . . . . . . . . . . 169--172
Xiongping Dai From the First Borel--Cantelli Lemma to
Poincaré's Recurrence Theorem . . . . . . 173--174
Anonymous Problems and Solutions . . . . . . . . . 175--182
Gerald B. Folland Book Review: \booktitleHidden
Harmony---Geometric Fantasies: The Rise
of Complex Function Theory, By Umberto
Bottazzini and Jeremy Gray. Springer,
New York, 2013, xvii + 848 pp., ISBN
978-1-4614-5724-4, \$189.00 (hardcover),
ISBN 978-1-4614-5725-1, \$149.00 (eBook) 183--188
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 189--190
Jennifer J. Quinn Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2015 to W. James Lewis for
Distinguished Service to Mathematics . . 191--194
Jonathan M. Borwein and
Scott T. Chapman I Prefer Pi: A Brief History and
Anthology of Articles in the American
Mathematical Monthly . . . . . . . . . . 195--216
David Peifer Max Dehn and the Origins of Topology and
Infinite Group Theory . . . . . . . . . 217--233
Samuel G. Moreno and
Esther M. García-Caballero A Geometric Proof of Morrie's Law . . . 233--233
Jaap Eising and
David Radcliffe and
Jaap Top A Simple Answer to Gelfand's Question 234--245
Doreen De Leon Using Undetermined Coefficients to Solve
Certain Classes of Variable-Coefficient
Equations . . . . . . . . . . . . . . . 246--255
Matthias Beck and
Neville Robbins Variations on a Generating-Function
Theme: Enumerating Compositions with
Parts Avoiding an Arithmetic Sequence 256--263
Anton Petrunin Area Minimizing Polyhedral Surfaces are
Saddle . . . . . . . . . . . . . . . . . 264--267
William Goldbloom Bloch Open Discontinuous Maps From $ \mathbb
{R}^n $ onto $ \mathbb {R}^n $ . . . . . 268--271
Mizan R. Khan and
Richard Magner An Application of Modular Hyperbolas to
Quadratic Residues . . . . . . . . . . . 272--274
Marius Tarnauceanu Finite Groups With a Certain Number of
Cyclic Subgroups . . . . . . . . . . . . 275--276
John Konvalina Powers of Matrices and Algebraic
Centrosymmetry . . . . . . . . . . . . . 277--279
Peter Horak Partitioning $ \mathbb {R}^n $ into
Connected Components . . . . . . . . . . 280--283
Konstantinos Gaitanas An Explicit Formula for the Prime
Counting Function Which is Valid
Infinitely Often . . . . . . . . . . . . 283--283
Anonymous Problems and Solutions . . . . . . . . . 284--291
Reuben Hersh Book Review: \booktitleHow Humans Learn
to Think Mathematically. Exploring the
Three Worlds of Mathematics . . . . . . 292--296
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 297--298
Richard Montgomery The Three-Body Problem and the Shape
Sphere . . . . . . . . . . . . . . . . . 299--321
Rebekah Ann Gilbert A Fine Rediscovery . . . . . . . . . . . 322--331
Juliá Cufí and
Agustí Reventó and
Carlos J. RodrÍz Curvature for Polygons . . . . . . . . . 332--337
Karl Dilcher and
Larry Ericksen The Polynomials of Mahler and Roots of
Unity . . . . . . . . . . . . . . . . . 338--353
Altino F. Santos A New Metric on Spherical $f$-Tilings 354--361
Patrick M. Fitzpatrick and
Brian R. Hunt Absolute Continuity of a Function and
Uniform Integrability of Its Divided
Differences . . . . . . . . . . . . . . 362--366
Vadim Ponomarenko A Base Conversion Surprise . . . . . . . 366 402--366
Michal Adamaszek Face Numbers of Down-Sets . . . . . . . 367--370
Dirk Huylebrouck Generalizing Wallis' Formula . . . . . . 371--372
Mehmet Kilic A New Geometric Proof for Morley's
Theorem . . . . . . . . . . . . . . . . 373--376
Hidefumi Katsuura A New Infinite Series Representation of
$ \ln k $ . . . . . . . . . . . . . . . 376--376
Maxim Arnold and
Vadim Zharnitsky Cyclic Evasion in the Three Bug Problem 377--380
\Ethorde Barali\'c A Short Proof of the Bradley Theorem . . 381--385
Byron Schmuland Linear Recurrences via Probability . . . 386--389
Anonymous Problems and Solutions . . . . . . . . . 390--397
Will Traves Book Review: \booktitlePerspectives in
Projective Geometry. A Guided Tour
Through Real and Complex Geometry . . . 398--402
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 405--406
Donald G. Saari Mathematics and the ``Dark Matter''
Puzzle . . . . . . . . . . . . . . . . . 407--423
Alex Chin and
Gary Gordon and
Kellie MacPhee and
Charles Vincent Pick a Tree --- Any Tree . . . . . . . . 424--432
Christian Aebi and
Grant Cairns Generalizations of Wilson's Theorem for
Double-, Hyper-, Sub- and
Superfactorials . . . . . . . . . . . . 433--443
Óscar Ciaurri and
Luis M. Navas and
Francisco J. Ruiz and
Juan L. Varona A Simple Computation of $ \zeta (2 k) $ 444--451
Nam Gu Heo A New Proof of the Pythagorean Theorem 451--451
Jeffrey A. Boyle Using Rolling Circles to Generate
Caustic Envelopes Resulting from
Reflected Light . . . . . . . . . . . . 452--466
Sam Northshield A One-Line Proof of the Infinitude of
Primes . . . . . . . . . . . . . . . . . 466--466
Ivan Izmestiev A Porism for Cyclic Quadrilaterals,
Butterfly Theorems, and Hyperbolic
Geometry . . . . . . . . . . . . . . . . 467--475
Maria Bras-Amorós and
Marta Pujol Side Lengths of Equiangular Polygons (as
seen by a coding theorist) . . . . . . . 476--478
Iosif Pinelis Relationships Between the First Four
Moments . . . . . . . . . . . . . . . . 479--481
Janusz Januszewski An Upper Bound for Some Coloring Problem 481--481
Meinolf Geck Eigenvalues of Real Symmetric Matrices 482--483
Bogdan Veklych A One-Formula Proof of the Nonvanishing
of $L$-Functions of Real Characters at
$1$ . . . . . . . . . . . . . . . . . . 484--485
Jesús Jerónimo Castro The Volume of the Convex Hull of a Body
and its Homothetic Copies . . . . . . . 486--489
J. Michael Steele Explaining a Mysterious Maximal
Inequality --- and a Path to the Law of
Large Numbers . . . . . . . . . . . . . 490--494
Michael Hardy Using Infinitesimals to Differentiate
Secant and Tangent . . . . . . . . . . . 494--494
Ádám Besenyei The Brocard Angle and a Geometrical Gem
from Dmitriev and Dynkin . . . . . . . . 495--499
Anonymous Problems and Solutions . . . . . . . . . 500--507
Gerald B. Folland Book Review: \booktitleA History in Sum:
150 Years of Mathematics at Harvard
(1825--1975), By Steve Nadis and
Shing-Tung Yau. Harvard University
Press, Cambridge, 2013, xviii + 249 pp.,
ISBN 978-0-674-72500-3, \$39.95} . . . . 508--510
Anonymous Editor's Endnotes . . . . . . . . . . . 511--512
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 513--514
Dennis D. A. Epple and
Jason Siefken Collapse: A Fibonacci and Sturmian Game 515--527
Kenneth S. Williams A ``Four Integers'' Theorem and a ``Five
Integers'' Theorem . . . . . . . . . . . 528--536
Lorenz Halbeisen and
Norbert Hungerbühler A Simple Proof of Poncelet's Theorem (on
the Occasion of Its Bicentennial) . . . 537--551
Aaditya Salgarkar and
Rishi Mehta Alternate Derivation for the Parity of
the $ n^{\rm th} $ Triangular Number . . 551--551
Nicholas J. Werner Covering Numbers of Finite Rings . . . . 552--566
J. Rooin and
A. Alikhani A Geometric Proof of the Beppo--Levi
Inequality . . . . . . . . . . . . . . . 566--566
Alan Haynes and
Sara Munday Diophantine Approximation and Coloring 567--580
Haryono Tandra A Proof of the Replacement Theorem by
the Notion of Maximal Elements . . . . . 580--580
Satomi Murakami and
Hiroki Ohwa Periodic Points of Some Discontinuous
Mappings . . . . . . . . . . . . . . . . 581--586
Vadim Ponomarenko Asymptotic Formula for $ (1 + 1 / x)^x
$, Revisited . . . . . . . . . . . . . . 587--587
Virgil Barnard A Proof of Quadratic Reciprocity . . . . 588--592
Daniel Daners Uniform Continuity of Continuous
Functions on Compact Metric Spaces . . . 592--592
Iosif Pinelis On the Hölder and Cauchy--Schwarz
Inequalities . . . . . . . . . . . . . . 593--595
José Gascón Another Proof That the Real Numbers $
\mathbb {R} $ Are Uncountable . . . . . 596--597
Haryono Tandra A Simple Modified Version for Ferguson's
Proof of the Extreme Value Theorem . . . 598--598
Mircea Merca An Alternative to Faulhaber's Formula 599--601
Tommaso Drammatico A New Proof of the Equality of Mixed
Second Partial Derivatives . . . . . . . 602--603
Anonymous Problems and Solutions . . . . . . . . . 604--612
Marion Cohen Book Review: \booktitleMathematicians on
Creativity. Edited by Peter Borwein,
Peter Liljedahl, and Helen Zhai, The
Mathematical Association of America,
Washington DC, 2014, xviii + 199 pp,
ISBN 978-0-88385-574-4, \$30.00} . . . . 613--616
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 616--618
Manya Raman-Sundström A Pedagogical History of Compactness . . 619--635
Carl Pomerance Divisors of the Middle Binomial
Coefficient . . . . . . . . . . . . . . 636--644
Neil Ashby Isosynchronous Paths on a Rotating
Surface . . . . . . . . . . . . . . . . 645--659
Matthias Beck and
Ana Berrizbeitia and
Michael Dairyko and
Claudia Rodriguez and
Amanda Ruiz and
Schuyler Veeneman Parking Functions, Shi Arrangements, and
Mixed Graphs . . . . . . . . . . . . . . 660--673
Pablo G. Barrientos A Family of Eventually Expanding
Piecewise Linear Maps of the Interval 674--680
Robert Cowen Deleting Edges from Ramsey Minimal
Examples . . . . . . . . . . . . . . . . 681--683
Diego Marques A New Fibonacci--Lucas Relation . . . . 683--683
Hans J. H. Tuenter A Double Binomial Sum: Putnam $ 35$-A4
Revisited . . . . . . . . . . . . . . . 684--689
Michael D. Hirschhorn Wallis's Product and the Central
Binomial Coefficient . . . . . . . . . . 689--689
James E. McClure and
Alec McGail An Elementary Treatment of the
Construction of the Free Product of
Groups . . . . . . . . . . . . . . . . . 690--692
Óscar Ciaurri Euler's Product Expansion for the Sine:
An Elementary Proof . . . . . . . . . . 693--695
Edward Omey On Xiang's Observations Concerning the
Cauchy--Schwarz Inequality . . . . . . . 696--698
Samuel G. Moreno The Dramatic and Ultimate Shortening of
a Doctoral Dissertation in Mathematics 699--699
Anonymous Problems and Solutions . . . . . . . . . 700--707
Joseph Malkevitch Book Review: \booktitleThe Mathematical
Coloring Book . . . . . . . . . . . . . 708--712
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 713--714
Leonard F. Klosinski and
Gerald L. Alexanderson and
Mark Krusemeyer The Seventy-Fifth William Lowell Putnam
Mathematical Competition . . . . . . . . 715--725
California Jack Cassidy Early Round Bluffing in Poker . . . . . 726--744
Tom M. Apostol and
Mamikon A. Mnatsakanian Volume/Surface Area Relations for
$n$-Dimensional Spheres, Pseudospheres,
and Catenoids . . . . . . . . . . . . . 745--756
P. Pollack and
J. Vandehey Besicovitch, Bisection, and the
Normality of $ 0. (1)(4)(9)(16)(25) $ 757--765
Shui-Hung Hou and
Edwin Hou On a Recursion Formula Related to
Confluent Vandermonde . . . . . . . . . 766--772
Syahida Che Dzul-Kifli and
Chris Good On Devaney Chaos and Dense Periodic
Points: Period $3$ and Higher Implies
Chaos . . . . . . . . . . . . . . . . . 773--780
Cristinel Mortici Funny Forms of the Mean Value Theorem 780--780
Tadashi Tokieda A Viscosity Proof of the Cauchy--Schwarz
Inequality . . . . . . . . . . . . . . . 781--781
Tomasz Kania A Short Proof of the Fact That the
Matrix Trace Is the Expectation of the
Numerical Values . . . . . . . . . . . . 782--783
Levent Alpoge van der Waerden and the Primes . . . . . 784--785
Raphaël Cerf and
Matthias Gorny An Exponential Inequality for Symmetric
Random Variables . . . . . . . . . . . . 786--789
Melvyn B. Nathanson Pairs of Matrices in $ {\rm GL}_2
(R_{\geq 0}) $ That Freely Generate . . 790--792
Zsolt Lengvárszky Pythagoras by Integral . . . . . . . . . 792--792
Tamás Titkos A Simple Proof of the Lebesgue
Decomposition Theorem . . . . . . . . . 793--794
Haryono Tandra A New Proof of the Change of Variable
Theorem for the Riemann Integral . . . . 795--799
Jonathan Borwein and
Scott Chapman I Prefer Pi: Addenda . . . . . . . . . . 800--800
Anonymous Problems and Solutions . . . . . . . . . 801--808
Ferebee Tunno Book Review: \booktitleReviews . . . . . 809--812
Tamás Titkos How to Make Equivalent Measures? . . . . 812--812
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 813--814
Zhiqin Lu and
Julie Rowlett The Sound of Symmetry . . . . . . . . . 815--835
Péter Hajnal and
László I. Szabó and
Vilmos Totik Convex Polygons and Common Transversals 836--844
Titu Andreescu and
Vladimir Georgiev and
Oleg Mushkarov Correction to ''Napoleon Polygons'' . . 844--844
Qingchun Ren and
Jürgen Richter-Gebert and
Bernd Sturmfels Cayley--Bacharach Formulas . . . . . . . 845--854
J. Roberto Hasfura-Buenaga Kronecker's Diophantine Approximation
and the Asymptotics of Solutions of
Difference Equations . . . . . . . . . . 855--861
Zbigniew Nitecki Cantorvals and Subsum Sets of Null
Sequences . . . . . . . . . . . . . . . 862--870
Robert O. Stanton Sets Closed Under the Division Algorithm 871--879
George E. Andrews and
Aviezri S. Fraenkel and
James A. Sellers Characterizing the Number of $m$-ary
Partitions Modulo $m$ . . . . . . . . . 880--885
Thomas J. Osler A Product of Nested Radicals for the AGM 886--887
Rafael de la Llave Computing Some Integrals by Computing
Derivatives . . . . . . . . . . . . . . 888--889
Dmitry Ryabogin A Lemma of Nakajima and Süss on Convex
Bodies . . . . . . . . . . . . . . . . . 890--892
Elias Lampakis A New Proof of Euler's Inequality . . . 892--892
Nguyen S. Hoang A Limit Comparison Test for General
Series . . . . . . . . . . . . . . . . . 893--896
Hamid Reza Daneshpajouh A New Proof of $ \aleph_0$-Resolvability
of a Metric Space Without an Isolated
Point . . . . . . . . . . . . . . . . . 897--898
Anonymous Problems and Solutions . . . . . . . . . 899--906
Robin Hartshorne Book Review: \booktitleReviews . . . . . 907--911
Michael Henle Book Review: \booktitleReviews . . . . . 912--915
Anonymous Statement of Ownership . . . . . . . . . 916--916
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 917--918
Zhaiming Shen and
Lasse Rempe-Gillen The Exponential Map Is Chaotic: An
Invitation to Transcendental Dynamics 919--940
Fred Kuczmarski and
James Kuczmarski Hanging Around in Non-Uniform Fields . . 941--957
Andrzej Nowicki Strong Divisibility and LCM-Sequences 958--966
Jesús Jerónimo Castro On Convex Curves Which Have Many
Inscribed Triangles of Maximum Area . . 967--971
Sebastian M. Cioaba and
Peter J. Cameron A Graph Partition Problem . . . . . . . 972--982
Jaime Gaspar All Triangles at Once . . . . . . . . . 982--982
Guram Bezhanishvili and
David Pengelley What Does ``Less Than or Equal'' Really
Mean? . . . . . . . . . . . . . . . . . 983--989
Haryono Tandra A Simple Proof of the Uniform Continuity
of Real-Valued Continuous Functions on
Compact Intervals . . . . . . . . . . . 989--989
Mehmet Kiliç and
Sahin Koçak On Products of Uniquely Geodesic Spaces 990--994
Sadi Abu-Saymeh and
Mowaffaq Hajja and
Hellmuth Stachel Equicevian Points of a Triangle . . . . 995--1000
Weimin Peng A Generalized Liouville Theorem for
Entire Functions . . . . . . . . . . . . 1001--1002
Atsushi Yamamori Yet Another Proof of Poincaré's Theorem 1003--1004
Kenneth Lange Polya's Random Walk Theorem Revisited 1005--1007
José Luis Cereceda Newton's Interpolation Polynomial for
the Sums of Powers of Integers . . . . . 1007--1007
Jun-Ming Zhu A Semi-Finite Proof of Jacobi's Triple
Product Identity . . . . . . . . . . . . 1008--1009
Anonymous Problems and Solutions . . . . . . . . . 1010--1017
Michael Harris Book Review: \booktitleReviews . . . . . 1018--1022
Anonymous Editor's Endnotes . . . . . . . . . . . 1023--1025
Anonymous Monthly Referees for 2015 . . . . . . . 1026--1028
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2
Richard D. Neidinger A Fair-Bold Gambling Function Is Simply
Singular . . . . . . . . . . . . . . . . 3--18
Adrien Kassel and
David B. Wilson The Looping Rate and Sandpile Density of
Planar Graphs . . . . . . . . . . . . . 19--39
J. Ángel Cid and
Rodrigo López Pouso Integration by Parts and by Substitution
Unified with Applications to Green's
Theorem and Uniqueness for ODEs . . . . 40--52
M. Ram Murty and
Chester Weatherby A Generalization of Euler's Theorem for
$ \zeta (2 k) $ . . . . . . . . . . . . 53--65
Shivarajkumar Beyond Schur's Conjecture . . . . . . . 66--70
Yaroslav Shitov The Diameter of Chess Grows
Exponentially . . . . . . . . . . . . . 71--77
Daniel J. Velleman Monthly Gems . . . . . . . . . . . . . . 77--77
Michael C. Slattery On a Property Motivated by Groups with a
Specified Number of Subgroups . . . . . 78--81
Oleg Viro Pictorial Calculus for Isometries . . . 82--87
Konstantinos Gaitanas A Partial Solution of Representing $1$
as a Sum of $n$ Distinct Unit Fractions 87--87
David G. Radcliffe A Function That Is Surjective on Every
Interval . . . . . . . . . . . . . . . . 88--89
Thomas Osler Iterations for the Lemniscate Constant
Resembling the Archimedean Algorithm for
Pi . . . . . . . . . . . . . . . . . . . 90--93
Kuldeep Kumar Kataria A Probabilistic Proof of the Multinomial
Theorem . . . . . . . . . . . . . . . . 94--96
Xiaoxue Li A Synthetic Approach to a USAMO Problem 96--96
Anonymous Problems and Solutions . . . . . . . . . 97--105
Darren B. Glass Book Review: \booktitleReviews . . . . . 106--112
József Sándor A Note on the Logarithmic Mean . . . . . 112--112
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 113--114
Francis C. Motta and
Patrick D. Shipman and
Bethany D. Springer Optimally Topologically Transitive
Orbits in Discrete Dynamical Systems . . 115--135
Ian Morrison and
David Swinarski Can You Play a Fair Game of Craps with a
Loaded Pair of Dice? . . . . . . . . . . 136--148
Deborah A. Kent and
David J. Muraki A Geometric Solution of a Cubic by Omar
Khayyam \ldots in Which Colored Diagrams
Are Used Instead of Letters for the
Greater Ease of Learners . . . . . . . . 149--160
Mariano Suárez-Álvarez Cyclic Extensions Are Radical . . . . . 160--160
Josh Hiller Old Friends in Unexpected Places: Pascal
(and Other) Matrices in $ {\rm GL}_n(C)
$ . . . . . . . . . . . . . . . . . . . 161--167
John Brillhart and
Richard Blecksmith and
Mike Decaro Using Conic Sections to Factor Integers 168--174
Michael Z. Spivey Probabilistic Proofs of a Binomial
Identity, Its Inverse, and
Generalizations . . . . . . . . . . . . 175--180
E. W. Dekking and
F. M. Dekking Helge von Koch's Snowflake Curve
Revisited . . . . . . . . . . . . . . . 181--184
Jonathan Baker Strong Convexity Does Not Imply Radial
Unboundedness . . . . . . . . . . . . . 185--188
Xin-Jie Sun On Sums of Three Pentagonal Numbers . . 189--191
Jeffrey Lutgen A Combinatorial Proof of an Alternating
Convolution Identity for Multichoose
Numbers . . . . . . . . . . . . . . . . 192--196
Anonymous Problems and Solutions . . . . . . . . . 197--204
Jeffrey Nunemacher Book Review: \booktitleReviews . . . . . 205--208
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 209--210
Jennifer J. Quinn Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2016 to George Berzsenyi for
Distinguished Service to Mathematics . . 211--213
Karen Hunger Parshall Mathematics and the Politics of Race:
The Case of William Claytor (Ph.D.,
University of Pennsylvania, 1933) . . . 214--240
John P. Boyd Correcting Three Errors in Kantorovich &
Krylov's Approximate Methods of Higher
Analysis . . . . . . . . . . . . . . . . 241--257
Boris M. Bekker and
Oleg A. Ivanov and
Alexander S. Merkurjev Milnor's Lemma, Newton's Method, and
Continued Fractions . . . . . . . . . . 258--266
Clark Kimberling and
Kenneth B. Stolarsky Slow Beatty Sequences, Devious
Convergence, and Partitional Divergence 267--273
Steve Butler and
Ron Graham and
Richard Stong Inserting Plus Signs and Adding . . . . 274--279
Tom Mertens and
Jeff Weeks Electromagnetism in a Multiconnected
Universe . . . . . . . . . . . . . . . . 280--286
Jeffrey S. Ovall The Laplacian and Mean and Extreme
Values . . . . . . . . . . . . . . . . . 287--291
Peter McGrath On the Smooth Jordan Brouwer Separation
Theorem . . . . . . . . . . . . . . . . 292--295
José L. Ramírez An Identity of Carlitz and Its
Generalization . . . . . . . . . . . . . 295--295
Anonymous Problems and Solutions . . . . . . . . . 296--303
Craig H. Jackson Book Review: \booktitleReviews . . . . . 304--308
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 309--310
Paul-Jean Cahen and
Jean-Luc Chabert What You Should Know About
Integer-Valued Polynomials . . . . . . . 311--337
Keith Johnson and
Kira Scheibelhut Rational Polynomials That Take Integer
Values at the Fibonacci Numbers . . . . 338--346
Gary Brookfield Factoring Forms . . . . . . . . . . . . 347--362
Grant Cairns and
Yuri Nikolayevsky and
Gavin Rossiter Conewise Linear Periodic Maps of the
Plane with Integer Coefficients . . . . 363--375
Mohamed Ayad and
Omar Kihel and
Jesse Larone When Does a Given Polynomial with
Integer Coefficients Divide Another? . . 376--381
Neil J. Calkin and
Beth Novick and
Hayato Ushijima-Mwesigwa What Moser Could Have Asked: Counting
Hamilton Cycles in Tournaments . . . . . 382--386
Nuno Luzia A Proof of The Pythagorean Theorem After
Descartes . . . . . . . . . . . . . . . 386--386
Ovidiu Costin and
Neil Falkner and
Jeffery D. McNeal Some Generalizations of the
Riemann--Lebesgue Lemma . . . . . . . . 387--391
Peter S. Landweber and
Emanuel A. Lazar and
Neel Patel On Fiber Diameters of Continuous Maps 392--397
Daniel López-Aguayo Irrationality via Maximality . . . . . . 397--397
Dennis S. Bernstein and
Khaled F. Aljanaideh and
Arthur E. Frazho Laurent Series and $ l^p $ Sequences . . 398--398
Anonymous Problems and Solutions . . . . . . . . . 399--406
Thomas Garrity Book Review: \booktitleReviews . . . . . 407--412
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 413--414
Sòren Eilers The LEGO Counting Problem . . . . . . . 415--426
Harold P. Boas Mocposite Functions . . . . . . . . . . 427--438
Tom M. Apostol and
Mamikon A. Mnatsakanian A New Look at Surfaces of Constant
Curvature . . . . . . . . . . . . . . . 439--447
Jaime Cruz-Sampedro and
Margarita Tetlalmatzi-Montiel Hardy's Reduction for a Class of
Liouville Integrals of Elementary
Functions . . . . . . . . . . . . . . . 448--470
Piotr Josevich An Alternative Approach to the Product
Rule . . . . . . . . . . . . . . . . . . 470--470
G. L. Mullen and
D. Panario and
D. Thomson Fast and Simple Modular Interpolation
Using Factorial Representation . . . . . 471--480
Iosif Pinelis On Measurable Semigroups in $R$ . . . . 481--481
Arseniy Sheydvasser A Corrigendum to Unreasonable Slightness 482--485
Karl Dilcher and
Christophe Vignat Euler and the Strong Law of Small
Numbers . . . . . . . . . . . . . . . . 486--490
Tim Hsu and
San José Rational Nonaxis Points on the Unit
Circle Have Irrational Angles . . . . . 490--490
Iosif Pinelis Explicit Additive Decomposition of Norms
on $ R^2 $ . . . . . . . . . . . . . . . 491--496
Michael Gaul and
Fred Kuczmarski Parabolas and Archimedes' $ 2 /
3$-Property . . . . . . . . . . . . . . 497--501
Peter McGrath An Extremely Short Proof of the Hairy
Ball Theorem . . . . . . . . . . . . . . 502--503
Anonymous Problems and Solutions . . . . . . . . . 504--511
Gerald L. Alexanderson Book Review: \booktitleReviews . . . . . 512--514
Anonymous Editor's End Notes . . . . . . . . . . . 515--516
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 517--518
Jennifer M. Johnson and
János Kollár Arcology . . . . . . . . . . . . . . . . 519--541
Steve Butler and
Persi Diaconis and
Ron Graham The Mathematics of the Flip and
Horseshoe Shuffles . . . . . . . . . . . 542--556
Valerio De Angelis and
Dominic Marcello Wilf's Conjecture . . . . . . . . . . . 557--573
F. Adrián F. Tojo A Hyperbolic Analog of the Phasor
Addition Formula . . . . . . . . . . . . 574--582
Pablo A. Panzone Tiling the Plane with Different Hexagons
and Triangles . . . . . . . . . . . . . 583--591
Franklin H. J. Kenter How to Win Your Betting Pool with
Jensen's Inequality and the Law of Large
Numbers . . . . . . . . . . . . . . . . 592--596
Erhan Gürel On the Occurrence of Perfect Squares
Among Values of Certain Polynomial
Products . . . . . . . . . . . . . . . . 597--599
Hunter Swan Expected Number of Vertices of a
Hypercube Slice . . . . . . . . . . . . 600--604
Peter McCauley Proofs Without Using Limits of Both
Calculus Power Rules . . . . . . . . . . 604--604
Pham Duy Khanh and
Marc Lassonde Quasiconvex Linear Perturbations and
Convexity . . . . . . . . . . . . . . . 605--608
Ariel Amir and
Mikhail Lemeshko and
Tadashi Tokieda Surprises in Numerical Expressions of
Physical Constants . . . . . . . . . . . 609--612
Anonymous Problems and Solutions . . . . . . . . . 613--620
Leslie Hogben and
Mark Hunacek Book Review: \booktitleReviews . . . . . 621--624
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 625--626
Laura Florescu and
Lionel Levine and
Yuval Peres The Range of a Rotor Walk . . . . . . . 627--642
Lawrence Zalcman A Tale of Three Theorems . . . . . . . . 643--656
Márton Balázs and
Áron Folly An Electric Network for Nonreversible
Markov Chains . . . . . . . . . . . . . 657--682
Vincent E. Coll and
Jeff Dodd A Characteristic Averaging Property of
the Catenary . . . . . . . . . . . . . . 683--688
Dennis Ivanov and
Serge Tabachnikov The Six Circles Theorem Revisited . . . 689--698
Arnon Avron and
Nachum Dershowitz Cayley's Formula: A Page From The Book 699--700
Michael Hardy On Tangents and Secants of Infinite Sums 701--703
Alex Kasman Factorization of a Matrix Differential
Operator Using Functions in Its Kernel 704--709
Brian D. Sittinger Computing $ \zeta (2 m) $ by using
Telescoping Sums . . . . . . . . . . . . 710--715
Yuanyuan Yao and
Wenxia Li Generating Iterated Function Systems for
the Vicsek Snowflake and the Koch Curve 716--721
Anonymous Problems and Solutions . . . . . . . . . 722--730
Matthew Richey Book Review . . . . . . . . . . . . . . 731--736
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 737--738
Leonard F. Klosinski and
Gerald L. Alexanderson and
Mark Krusemeyer The Seventy-Sixth William Lowell Putnam
Mathematical Competition . . . . . . . . 739--752
Jeffrey C. Lagarias Erd\Hos, Klarner, and the $ 3 x + 1 $
Problem . . . . . . . . . . . . . . . . 753--776
Dvij Bajpai and
Daniel J. Velleman Anonymity in Predicting the Future . . . 777--788
Philippe Caldero and
Jérôme Germoni Equilateral Triangles and the Fano Plane 789--801
T. S. Michael and
Val Pinciu The Art Gallery Theorem, Revisited . . . 802--807
Lon Mitchell and
Michael A. Jones and
Brittany Shelton Abelian and Non-Abelian Triangle
Mysteries . . . . . . . . . . . . . . . 808--813
Yong Kong and
Shaowei Zhang The Adventitious Angles Problem: The
Lonely Fractional Derived Angle . . . . 814--816
J. Jerónimo-Castro and
C. Yee-Romero Maximal Isoptic Chords of Convex Curves 817--820
Olivier de La Grandville An Alternate Derivation of the
Euler--Poisson Equation . . . . . . . . 821--824
J. A. Grzesik Yet Another Analytic Proof of Napoleon's
Theorem . . . . . . . . . . . . . . . . 824--824
Bálint Farkas and
Sven-Ake Wegner Variations on Barbalat's Lemma . . . . . 825--830
Anonymous Problems and Solutions . . . . . . . . . 831--839
Mark Kidwell Book Review . . . . . . . . . . . . . . 840--843
Halil Mutuk A Physical Proof for Cauchy's Inequality 843--843
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 845--846
Scott T. Chapman A Letter From the Editor: Jonathan M.
Borwein (1951--2016) . . . . . . . . . . 847--848
Paul Baginski and
Ryan Rodriguez and
George J. Schaeffer and
Yiwei She Finding Elements With Given
Factorization Lengths and Multiplicities 849--870
Lyle Ramshaw Stråhle's Equal-Tempered Triumph . . . . 871--883
Jean C. Cortissoz A Note on Harmonic Functions on Surfaces 884--893
Uuganbaatar Ninjbat Another Memorable Mongolian Olympiad
Problem: A Two-Colored Rectangular
Lattice . . . . . . . . . . . . . . . . 894--899
Josh Brown Kramer and
Jonathan Cutler and
A. J. Radcliffe The Multistep Friendship Paradox . . . . 900--908
Sean Eastman and
Selwyn Hollis and
Kawee Numpacharoen and
Jared Schlieper The Volume of the Spatial Region
Corresponding to $ n \times n $
Correlation Matrices . . . . . . . . . . 909--918
Ivica Martinjak Two Extensions of the Sury's Identity 919--919
Bernd Schomburg Primitivity and Orbit Decomposition . . 920--923
Adrian W. Dudek On the Success of Mishandling Euclid's
Lemma . . . . . . . . . . . . . . . . . 924--927
Alan J. Hoffman and
Chai Wah Wu A Simple Proof of a Generalized
Cauchy--Binet Theorem . . . . . . . . . 928--930
Nicolae Anghel Optimal Bounds for the Roots of
Polynomials . . . . . . . . . . . . . . 931--935
Anthony J. Bevelacqua A Family of Non-Euclidean PIDs . . . . . 936--939
Kuldeep Kumar Kataria An Alternate Proof of the Binomial
Theorem . . . . . . . . . . . . . . . . 940--940
Anonymous Problems and Solutions . . . . . . . . . 941--948
Gerald B. Folland Book Review . . . . . . . . . . . . . . 949--952
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 953--954
Scott T. Chapman A Letter from the Editor: The Long and
Winding Road . . . . . . . . . . . . . . 955--958
Franco Bradshaw Single Digit NFL Scores . . . . . . . . 959--959
Alfred Geroldinger Sets of Lengths . . . . . . . . . . . . 960--988
Anton A. Klyachko and
Anton N. Vassilyev Balanced Factorizations . . . . . . . . 989--1000
Melvyn B. Nathanson Cantor Polynomials and the Fueter--Pólya
Theorem . . . . . . . . . . . . . . . . 1001--1012
Aaron M. Broussard and
Martin E. Malandro and
Abagayle Serreyn Optimizing the Video Game Multi-Jump:
Player Strategy, AI, and Level Design 1013--1032
Jeffrey C. Lagarias and
Takumi Murayama and
D. Harry Richman Dilated Floor Functions That Commute . . 1033--1038
Stephan Ramon Garcia and
Florian Luca Quotients of Fibonacci Numbers . . . . . 1039--1044
Richard Ehrenborg and
Alex Happ Parking Cars of Different Sizes . . . . 1045--1048
Anonymous Corrigendum to ''A New Proof of the
Change of Variable Theorem for the
Riemann Integral'' . . . . . . . . . . . 1049--1049
Anonymous Problems and Solutions . . . . . . . . . 1050--1057
Chris A. Marx Book Review: \booktitleA First Course in
the Calculus of Variations. By Mark Kot.
Student Mathematical Library Vol 72,
American Mathematical Society,
Providence, Rhode Island, 2014, x + 298
pp., ISBN 978-1-4704-1495-5, \$50} . . . 1058--1061
Anonymous Monthly Referees for 2016 . . . . . . . 1062--1066
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2
Susan Jane Colley Letter from the Editor . . . . . . . . . 3--3
Ryan Blair and
Marion Campisi and
Jesse Johnson and
Scott A. Taylor and
Maggy Tomova Neighbors of Knots in the Gordian Graph 4--23
Robert J. Vanderbei The Falling Slinky . . . . . . . . . . . 24--36
Antonio Cafure and
Eda Cesaratto Irreducibility Criteria for Reciprocal
Polynomials and Applications . . . . . . 37--53
Joseph A. Gallian Seventy-Five Years of the Putnam
Mathematical Competition* . . . . . . . 54--59
Saveliy Ustuzhanin A Novel Way to Prove the Irrationality
of $ \sqrt 2 $ . . . . . . . . . . . . . 59--59
Nicolae Anghel On a 2015 Putnam Problem Related to a
Double Recursion . . . . . . . . . . . . 60--69
Ian Stewart Why Do All Triangles Form a Triangle? 70--73
Cezar Lupu A New Proof of the Finsler--Hadwiger
Inequality . . . . . . . . . . . . . . . 73--73
Yusuf Z. Gürtas Chebyshev Polynomials and the Minimal
Polynomial of $ \cos (2 \pi / n) $ . . . 74--78
Eli Shamir and
Benny Sudakov Two-Sided, Unbiased Version of Hall's
Marriage Theorem . . . . . . . . . . . . 79--80
Bart van Munster Hausdorffization and Homotopy . . . . . 81--82
Anonymous Problems and Solutions . . . . . . . . . 83--91
Jason Rosenhouse Reviews . . . . . . . . . . . . . . . . 92--95
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 98--98
Annalisa Crannell and
Marc Frantz and
Fumiko Futamura The Image of a Square . . . . . . . . . 99--115
Allen Stenger Experimental Math for Math Monthly
Problems . . . . . . . . . . . . . . . . 116--131
Michael Maltenfort Characterizing Additive Systems . . . . 132--148
Bisharah Libbus and
Gordon Simons and
Yi-Ching Yao Rotating Multiple Sets of Labeled Points
to Bring Them Into Close Coincidence: A
Generalized Wahba Problem . . . . . . . 149--160
Scott Ginebaugh Generalized Infinite Products for Powers
of $ e^{1 / k} $ . . . . . . . . . . . . 161--165
Christian Aebi and
Grant Cairns Sums of Quadratic Residues and
Nonresidues . . . . . . . . . . . . . . 166--169
Idris Mercer Another Proof That There Are Infinitely
Many Primes . . . . . . . . . . . . . . 169--169
Chatchawan Panraksa and
Pornrat Ruengrot A Note on Average of Roots of Unity . . 170--174
Charles Audet Maximal Area of Equilateral Small
Polygons . . . . . . . . . . . . . . . . 175--178
Anonymous Problems and Solutions . . . . . . . . . 179--187
Alan Baker The Philosophies of Mathematics . . . . 188--192
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 194--194
Annalisa Crannell and
Doug Ensley Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2017 to Martha Siegel for
Distinguished Service to Mathematics . . 195--197
Pete L. Clark The Euclidean Criterion for Irreducibles 198--216
Joseph Bak and
Strashimir G. Popvassilev The Evolution of Cauchy's Closed Curve
Theorem and Newman's Simple Proof . . . 217--231
Jonathan Sondow and
Kieren MacMillan Primary Pseudoperfect Numbers,
Arithmetic Progressions, and the
Erd\Hos--Moser Equation . . . . . . . . 232--240
Koji Momihara and
Masashi Shinohara Distance Sets on Circles . . . . . . . . 241--254
Michael Weiss Where Are the Rational Squares? . . . . 255--259
Shubhodip Mondal Surjectivity of Maps Induced on Matrices
by Polynomials and Entire Functions . . 260--264
Dirk Huylebrouck A New Regular (Compound) Polyhedron (of
Infinite Kepler--Poinsot Type) . . . . . 265--268
Joseph Plante A Proof of Bonnet's Version of the Mean
Value Theorem by Methods of Cauchy . . . 269--273
Anonymous Problems and Solutions . . . . . . . . . 274--281
Dominic Lanphier Book Review: \booktitleSumming it Up:
From One Plus One to Modern Number
Theory . . . . . . . . . . . . . . . . . 282--288
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 290--290
Paul E. Becker and
Martin Derka and
Sheridan Houghten and
Jennifer Ulrich Build a Sporadic Group in Your Basement 291--305
John P. Boyd and
Houjun Wang Convergent Power Series for Boundary
Value Problems and Eigenproblems with
Application to Atmospheric and Oceanic
Tides . . . . . . . . . . . . . . . . . 306--323
Arno Berger More Grade School Triangles . . . . . . 324--336
Hiroshi Maehara and
Horst Martini On Lexell's Theorem . . . . . . . . . . 337--344
Antonio Avilés and
Grzegorz Plebanek A Little Ado about Rectangles . . . . . 345--350
Trevor D. Wooley A Superpowered Euclidean Prime Generator 351--352
Carl McTague On the Greatest Common Divisor of
Binomial Coefficients . . . . . . . . . 353--356
Mehtaab S. Sawhney A Telescoping Proof of the AM--GM
Inequality . . . . . . . . . . . . . . . 356--356
David E. Speyer A Counting Proof of a Theorem of
Frobenius . . . . . . . . . . . . . . . 357--359
Evelyn R. Easdale and
Jolene E. Fleming and
Bogdan D. Suceava Convergence for Series With Terms
Defined by a Recurrence Relation . . . . 360--364
Christian Elsholtz Golomb's Conjecture on Prime Gaps . . . 365--368
Anonymous Problems and Solutions . . . . . . . . . 369--378
Marion Cohen Book Review: \booktitleMom the Chemistry
Professor: Personal Accounts and Advice
from Chemistry Professors Who Are
Mothers . . . . . . . . . . . . . . . . 379--383
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 386--386
Maria Deijfen and
Alexander E. Holroyd and
James B. Martin Friendly Frogs, Stable Marriage, and the
Magic of Invariance . . . . . . . . . . 387--402
Juan Monterde and
David Rochera Holditch's Ellipse Unveiled . . . . . . 403--421
Frantisek Marko and
Semyon Litvinov On the Steiner--Routh Theorem for
Simplices . . . . . . . . . . . . . . . 422--435
Marek Balcerzak and
Michal Poplawski and
Julia Wódka Local Extrema and Nonopenness Points of
Continuous Functions . . . . . . . . . . 436--443
Jeremiah Farrell and
William Johnston Mathematical Evolution . . . . . . . . . 444--444
Péter E. Frenkel and
József Pelikán On the Greatest Common Divisor of the
Value of Two Polynomials . . . . . . . . 446--450
Valerio De Angelis The Stern Diatomic Sequence via
Generalized Chebyshev Polynomials . . . 451--455
Melvyn B. Nathanson Subalgebras of a Polynomial Ring That
Are Not Finitely Generated . . . . . . . 456--458
Beniamin Bogosel A Geometric Proof of the Siebeck--Marden
Theorem . . . . . . . . . . . . . . . . 459--463
Haryono Tandra A More Direct Proof of the Extreme Value
Theorem . . . . . . . . . . . . . . . . 464--464
Anonymous Problems and Solutions . . . . . . . . . 465--474
Reuben Hersh Book Review: \booktitleElements of
Mathematics: From Euclid to Gödel . . . . 475--478
Anonymous Editor's Endnotes . . . . . . . . . . . 480--480
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 481--482
Francis Edward Su Mathematics for Human Flourishing . . . 483--493
Andrey Kupavskii and
János Pach From Tarski's Plank Problem to
Simultaneous Approximation . . . . . . . 494--505
David Aldous and
Weijian Han Introducing Nash Equilibria via an
Online Casual Game That People Actually
Play . . . . . . . . . . . . . . . . . . 506--517
Grant Cairns Equitable Candy Sharing . . . . . . . . 518--526
Finbarr Holland On the Limiting Behavior of Solutions of
Linear Difference Equations . . . . . . 527--534
Paul Carter and
David Lowry-Duda On Functions Whose Mean Value Abscissas
Are Midpoints, with Connections to
Harmonic Functions . . . . . . . . . . . 535--542
Darren B. Glass Klein Four Actions on Graphs and Sets 543--547
Mikhail A. Patrakeev Dissection of an Equilateral Triangle
into Five Congruent Open Sets . . . . . 547--547
Heinrich Steinlein Fermat's Little Theorem and Gauss
Congruence: Matrix Versions and Cyclic
Permutations . . . . . . . . . . . . . . 548--553
Mircea Merca The Riemann Zeta Function With Even
Arguments as Sums Over Integer
Partitions . . . . . . . . . . . . . . . 554--557
Lee K. Jones An Elementary Derivation of the
Numerical Integration Bounds in
Beginning Calculus . . . . . . . . . . . 558--561
Romeo Mestrovi\'c A Very Short Proof of the Infinitude of
Primes . . . . . . . . . . . . . . . . . 562--562
Anonymous Problems and Solutions . . . . . . . . . 563--571
Jeffrey Nunemacher Book Review: \booktitleVector Calculus,
Linear Algebra, and Differential Forms:
A Unified Approach (5th Edition) . . . . 572--575
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 577--578
Peter Winkler The Sleeping Beauty Controversy . . . . 579--587
Arseniy Akopyan and
Vladislav Vysotsky On the Lengths of Curves Passing Through
Boundary Points of a Planar Convex Shape 588--596
Moa Apagodu and
Doron Zeilberger Using the ``Freshman's Dream'' to Prove
Combinatorial Congruences . . . . . . . 597--608
Philip P. West and
Brian D. Sittinger A Further Stroll into the Eisenstein
Primes . . . . . . . . . . . . . . . . . 609--620
John C. Bowers and
Philip L. Bowers A Menger Redux: Embedding Metric Spaces
Isometrically in Euclidean Space . . . . 621--636
David A. Levin and
Yuval Peres Counting Walks and Graph Homomorphisms
via Markov Chains and Importance
Sampling . . . . . . . . . . . . . . . . 637--641
Anonymous The Other Moore Method . . . . . . . . . 641--641
Christian Axler and
Thomas Leßmann On the First $k$-Ramanujan Prime . . . . 642--646
Amrik Singh Nimbran An Infinite Product for the Square Root
of an Integer . . . . . . . . . . . . . 647--650
Tomasz Kania On Bases That Are Closed Under
Multiplication . . . . . . . . . . . . . 651--653
Óscar Ciaurri Maria Gaetana Agnesi Meets Johannes
Kepler . . . . . . . . . . . . . . . . . 654--658
Jitender Singh Another Proof of the Binomial Theorem 658--658
Anonymous Problems and Solutions . . . . . . . . . 659--666
Calvin Jongsma Book Review: \booktitleSourcebook in the
Mathematics of Medieval Europe and North
Africa . . . . . . . . . . . . . . . . . 667--672
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 673--674
Leonard F. Klosinski and
Gerald L. Alexanderson and
Mark Krusemeyer The Seventy-Seventh William Lowell
Putnam Mathematical Competition . . . . 675--687
Soham Basu and
Daniel J. Velleman On Gauss's First Proof of the
Fundamental Theorem of Algebra . . . . . 688--694
Bernd C. Kellner and
Jonathan Sondow Power-Sum Denominators . . . . . . . . . 695--709
Hugo Parlier and
Samuel Zappa Distances in Domino Flip Graphs . . . . 710--722
Stephan Ramon Garcia Linearly Independent Spanning Sets . . . 722--722
Ulrich Abel and
Linda Beukemann and
Vitaliy Kushnirevych Rolling Curves: An Old Proof of the
Roulette Lemma . . . . . . . . . . . . . 723--736
David J. Platt and
Timothy S. Trudgian On the Sum of Two Squares and At Most
Two Powers of 2 . . . . . . . . . . . . 737--740
Jens Marklof and
Andreas Strömbergsson The Three Gap Theorem and the Space of
Lattices . . . . . . . . . . . . . . . . 741--745
Zoltán Kánnai A One-to-One Popcorn Function . . . . . 746--748
Stasys Jukna Minkowski Complexity of Sets: An Easy
Lower Bound . . . . . . . . . . . . . . 749--753
Anonymous Problems and Solutions . . . . . . . . . 754--762
Anonymous Problems for Metagrobologists: A
Collection of Puzzles with Real
Mathematical, Logical, or Scientific
Content; One Hundred Prisoners and A
Light Bulb . . . . . . . . . . . . . . . 763--768
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 769--770
Scott T. Chapman and
Joseph A. Gallian From the Guest Editors . . . . . . . . . 771--771
Anonymous About the Cover . . . . . . . . . . . . 772--772
Paul-Jean Cahen and
Jean-Luc Chabert and
Kiran S. Kedlaya Bhargava's Early Work: The Genesis of
$P$-Orderings . . . . . . . . . . . . . 773--790
Colin Adams Turning Knots into Flowers and Related
Undergraduate Research . . . . . . . . . 791--806
Cesar E. Silva On Mixing-Like Notions in Infinite
Measure . . . . . . . . . . . . . . . . 807--825
Adrian Chun Pong Chu Dihedral Angle of the Regular
$n$-Simplex via Menelaus' Theorem . . . 826--826
Yufei Zhao Extremal Regular Graphs: Independent
Sets and Graph Homomorphisms . . . . . . 827--843
Rishi Nath Advances in the Theory of Cores and
Simultaneous Core Partitions . . . . . . 844--861
Nathan Kaplan Counting Numerical Semigroups . . . . . 862--875
Carlos Castillo-Chavez and
Christopher Kribs and
Benjamin Morin Student-Driven Research at the
Mathematical and Theoretical Biology
Institute . . . . . . . . . . . . . . . 876--892
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 893--894
Peter Frankl and
Amram Meir and
János Pach Decomposition of a Cube into Nearly
Equal Smaller Cubes . . . . . . . . . . 895--904
Michael Barnsley and
Andrew Vince Self-Similar Polygonal Tiling . . . . . 905--921
Emmanuel Tsukerman and
Ellen Veomett Brunn--Minkowski Theory and Cauchy's
Surface Area Formula . . . . . . . . . . 922--929
Yann Bugeaud and
Andrej Dujella and
Tomislav Pejkovi\'c and
Bruno Salvy Absolute Real Root Separation . . . . . 930--936
Martin Kreh ``Lights Out'' and Variants . . . . . . 937--950
Andrew Granville Squares in Arithmetic Progressions and
Infinitely Many Primes . . . . . . . . . 951--954
Joshua Cooper and
Anton Swifton Throwing a Ball as Far as Possible,
Revisited . . . . . . . . . . . . . . . 955--959
Sunil K. Chebolu and
Keir Lockridge How Many Units Can a Commutative Ring
Have? . . . . . . . . . . . . . . . . . 960--965
Jen\Ho Szigeti and
Leon vanWyk A Constructive Elementary Proof of the
Skolem--Noether Theorem for Matrix
Algebras . . . . . . . . . . . . . . . . 966--968
Umberto Cerruti and
Nadir Murru If the Primes are Finite, Then All of
Them Divide the Number One . . . . . . . 969--969
Anonymous Problems and Solutions . . . . . . . . . 970--978
Anonymous Book Review: \booktitleFrom Music to
Mathematics: Exploring the Connections,
Gareth E. Roberts. Johns Hopkins
University Press, Baltimore, MD, 2016.
Price: \$49.95 ISBN: 978-1-4214-1918-3} 979--982
Anonymous Editor's Endnotes . . . . . . . . . . . 983--985
Anonymous Monthly Referees For 2017 . . . . . . . 986--988
Anonymous Back Matter . . . . . . . . . . . . . . ??
Adrian Rice Partnership, Partition, and Proof: The
Path to the Hardy--Ramanujan Partition
Formula . . . . . . . . . . . . . . . . 3--15
Harold P. Boas Cauchy's Residue Sore Thumb . . . . . . 16--28
Anonymous 100 Years Ago This Month in
\booktitleThe American Mathematical
Monthly, Edited by Vadim Ponomarenko . . 28--28
Kristen Mazur and
Mutiara Sondjaja and
Matthew Wright and
Carolyn Yarnall Approval Voting in Product Societies . . 29--43
David Treeby Further Thoughts on a Paradoxical Tower 44--60
Carl D. Meyer Rank My Update, Please . . . . . . . . . 61--64
Alok Shukla A Short Proof of Cayley's Tree Formula 65--68
John Clifford and
Kelly Jabbusch and
Michael Lachance Preimages of the Numerical Range . . . . 69--74
Giuseppe De Marco An Almost Everywhere Constant Function
Surjective on Every Interval . . . . . . 75--76
Tamás Titkos The Singular Part as Fixed Point . . . . 77--80
Jitender Singh A Noninductive Proof of de Moivre's
Formula . . . . . . . . . . . . . . . . 80--80
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 81--89
Geoffrey Dietz The Mathematics Lover's Companion:
Masterpieces for Everyone . . . . . . . 90--95
Bruce C. Berndt and
Sun Kim and
Alexandru Zaharescu The Circle Problem of Gauss and the
Divisor Problem of Dirichlet --- Still
Unsolved . . . . . . . . . . . . . . . . 99--114
Michael Maltenfort Pascal Functions . . . . . . . . . . . . 115--129
C. Bryan Dawson A New Extension of the Riemann Integral 130--140
Marcin Kulczycki and
Dominik Kwietniak and
Jian Li Entropy of Subordinate Shift Spaces . . 141--148
Cara D. Brooks and
Alberto A. Condori A Resolvent Criterion for Normality . . 149--156
Jonathan Sondow Lorentz Stöer's \booktitleGeometria et
Perspectiva . . . . . . . . . . . . . . 157--157
Aaron Melman Optimality of a Polynomial Multiplier 158--163
Rom Pinchasi A Theorem on Unit Segments on the Real
Line . . . . . . . . . . . . . . . . . . 164--168
Ralph Howard and
Virginia Johnson and
George F. McNulty A Functional Equation Characterization
of Archimedean Ordered Fields . . . . . 169--172
Christopher Stuart An Inequality Involving $ \sin (n) $ . . 173--174
Wenchang Chu Partial Fractions and Riesz'
Interpolation Formula for Trigonometric
Polynomials . . . . . . . . . . . . . . 175--178
Anonymous Problems and Solutions . . . . . . . . . 179--187
Robert Cowen Review: \booktitleA Beginner's Guide to
Mathematical Logic, By Raymond M.
Smullyan. Dover, Mineola, NY, 2014. vi +
284 pp.
store.doverpublications.com/0486492370.html ISBN: 978-0-486-49237-7, \$19.95. \booktitle{A Beginner's Further Guide to Mathematical Logic}. By Raymond M. Smullyan. World Scientific, Hackensack, NJ, 2017. x + 278 pp. worldscientific.com/worldscibooks/10.1142/9865 ISBN: 978-981-4725-72-9, \$24.00 (paperback) 188--192
Annalisa Crannell Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2018 to David Bressoud for
Distinguished Service to Mathematics . . 195--197
Sam Vandervelde The Worpitzky Numbers Revisited . . . . 198--206
Russell A. Gordon and
José Carlos Santos An Interesting Construction Problem . . 207--221
Ángel Plaza The Harmonic Series Diverges . . . . . . 222--222
Gilbert Strang Multiplying and Factoring Matrices . . . 223--230
David Salwinski The Continuous Binomial Coefficient: an
Elementary Approach . . . . . . . . . . 231--244
Maxim Gilula A Class of Simple Rearrangements of the
Alternating Harmonic Series . . . . . . 245--256
Kevin Woods AdaM and GrahaM Play the Stock Market 257--257
Leo Goldmakher and
Paul Pollack Refinements of Lagrange's Four-Square
Theorem . . . . . . . . . . . . . . . . 258--263
Peter Shiu A Footnote to the Three Gaps Theorem . . 264--266
Andrew Leahy The Method of Archimedes in the
Seventeenth Century . . . . . . . . . . 267--272
Marcin Mazur An Inequality for the Volume of a
Tetrahedron . . . . . . . . . . . . . . 273--275
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 276--283
Darren Glass The Joy of SET . . . . . . . . . . . . . 284--288
David Broaddus and
Stephen Lovett and
Dawson Miller and
Caitlin Smith Seeing Curvature on Specular Surfaces 291--305
Larry Carter and
Stan Wagon The Mensa Correctional Institute . . . . 306--319
Maria Bras-Amorós A Decoding Approach to Reed--Solomon
Codes from Their Definition . . . . . . 320--338
Chungwu Ho and
Seth Zimmerman On Certain Dense, Uncountable Subsets of
the Real Line . . . . . . . . . . . . . 339--346
Eli Leher is Not 1.41421356237 or Anything of the
Sort . . . . . . . . . . . . . . . . . . 346--346
Matthias Keller and
Yehuda Pinchover and
Felix Pogorzelski An Improved Discrete Hardy Inequality 347--350
Brian Lubeck and
Vadim Ponomarenko Subsums of the Harmonic Series . . . . . 351--355
Vaibhav Pandey and
Sagar Shrivastava and
Balasubramanian Sury A Dedekind Domain with Nontrivial Class
Group . . . . . . . . . . . . . . . . . 356--359
Mark B. Villarino The Error in an Alternating Series . . . 360--364
José A. Adell and
Alberto Lekuona Binomial Identities and Moments of
Random Variables . . . . . . . . . . . . 365--369
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 370--378
Laura Taalman Review: \booktitleVisualizing
Mathematics With $3$D Printing by Henry
Segerman and Pasta by Design by George
Legendre . . . . . . . . . . . . . . . . 379--384
Joe Buhler and
Ron Graham and
Al Hales Maximally Nontransitive Dice . . . . . . 387--399
Jonathan M. Borwein and
Robert M. Corless Gamma and Factorial in the Monthly . . . 400--424
Abílio Lemos and
Pedro H. A. de Oliveira Suggested Corrections for ``A Principal
Ideal Domain That Is Not a Euclidean
Domain'' . . . . . . . . . . . . . . . . 425--425
Daniel de la Fuente and
Rafael Ramírez-Uclés and
Juan F. Ruiz-Hidalgo A Visual Model of the Lorentz Triangular
Moduli Space . . . . . . . . . . . . . . 426--432
João Lita da Silva On One Type of Generalized Vandermonde
Determinants . . . . . . . . . . . . . . 433--442
Chris D. Lynd and
James Wright Sharpe Sequences Generated by Powers of the
$k$-th-order Fibonacci Recurrence
Relation . . . . . . . . . . . . . . . . 443--446
Augustine O. Munagi Set Partitions with Isolated Singletons 447--452
A. G. Smirnov A Gronwall-type Trigonometric Inequality 453--456
Youssef Azouzi Cluster Points of Slow Sequences . . . . 457--461
Eugene Curtin Another Short Proof of the Hairy Ball
Theorem . . . . . . . . . . . . . . . . 462--463
Iago Rodríguez-Quintana A Beautiful Continued Fraction for $ \pi
$ . . . . . . . . . . . . . . . . . . . 463--463
Anuj Jakhar An Irreducibility Criterion for
Polynomials with Integer Coefficients 464--465
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 466--475
Avner Ash Review: \booktitlePrime Numbers and the
Riemann Hypothesis by Barry Mazur and
William Stein . . . . . . . . . . . . . 476--480
Andrew Granville Using Dynamical Systems to Construct
Infinitely Many Primes . . . . . . . . . 483--496
Ying Chai and
Liping Yuan and
Tudor Zamfirescu Rupert Property of Archimedean Solids 497--504
Greg Huber and
Kay Pechenick Shultz and
John E. Wetzel The $n$-Cube is Rupert . . . . . . . . . 505--512
Mark B. Villarino and
William Gasarch and
Kenneth W. Regan Hilbert's Proof of His Irreducibility
Theorem . . . . . . . . . . . . . . . . 513--530
Philip de Castro and
Desiree Domini and
Tom Edgar and
Devon M. Johnson and
Steven Klee and
Ranjani Sundaresan Counting Binomial Coefficients Divisible
by a Prime Power . . . . . . . . . . . . 531--540
Peter McGrath A Note Regarding Hopf's Umlaufsatz . . . 541--544
Angelina Y. M. Chin Finite Rings of Odd Order with Few
Nilpotent and Idempotent Elements . . . 545--548
Shamil Asgarli A New Proof of Warning's Second Theorem 549--553
Jitender Singh A Short Proof That Lebesgue Outer
Measure of an Interval Is Its Length . . 553--553
Yves Coud\`ene A Strange Inequality Concerning
Alternating Series . . . . . . . . . . . 554--557
Kapil R. Shenvi Pause Basel Problem: a Solution Motivated by
the Power of a Point . . . . . . . . . . 558--560
Samuel G. Moreno and
Esther M. García-Caballero A Characterization of Bernoulli
Differential Equations . . . . . . . . . 561--561
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 562--570
Jason Rosenhouse Reviews . . . . . . . . . . . . . . . . 571--576
Ian Morrison Sacks of Dice with Fair Totals . . . . . 579--592
Edray H. Goins and
Pamela E. Harris and
Bethany Kubik and
Aba Mbirika Lattice Point Visibility on Generalized
Lines of Sight . . . . . . . . . . . . . 593--601
Andrew Gard The Wild Goose Chase Problem . . . . . . 602--611
Ghada Al-Afifi and
Mowaffaq Hajja and
Ahmad Hamdan Another $n$-Dimensional Generalization
of Pompeiu's Theorem . . . . . . . . . . 612--622
Melvyn B. Nathanson An Elementary Proof for the Krull
Dimension of a Polynomial Ring . . . . . 623--637
Allan Berele and
Stefan Catoiu Nonuniqueness of Sixpartite Points . . . 638--642
Scott T. Chapman What Happens When the Division Algorithm
``Almost'' Works . . . . . . . . . . . . 643--647
George Stoica When Must a Flat Function be Identically
0? . . . . . . . . . . . . . . . . . . . 648--649
Marian Gencev On a Proof of the Inequality Between the
Arithmetic and Geometric Means . . . . . 650--652
Daniel L. Reinholz Peer Feedback for Learning Mathematics 653--658
Enrique Treviño A short proof of a sum of powers formula 659--659
Gerald A. Edgar and
Daniel Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 660--668
Alex Meadows Reviews . . . . . . . . . . . . . . . . 669--672
Mark Krusemeyer and
Daniel H. Ullman The Seventy-Eighth William Lowell Putnam
Mathematical Competition . . . . . . . . 675--688
Stephanie Chan Rational Right Triangles of a Given Area 689--703
John Pearson Vi\`ete's Formula, Knar's Formula, and
the Geometry of the Gamma Function . . . 704--714
Erik Talvila You Know You're a Mathematician If
\ldots . . . . . . . . . . . . . . . . . 714--714
Alejandro H. Morales and
Igor Pak and
Greta Panova Why Is Pi Less Than Twice Phi? . . . . . 715--723
J. J. P. Veerman Social Balance and the Bernoulli
Equation . . . . . . . . . . . . . . . . 724--732
Naoki Shioji Simple Proofs of the Uniform Convexity
of $ L^p $ and the Riesz Representation
Theorem for $ L^p $ . . . . . . . . . . 733--738
Krzysztof Chris Ciesielski Monsters in Calculus . . . . . . . . . . 739--744
Aalok Thakkar Infinitude of Primes Using Formal
Languages . . . . . . . . . . . . . . . 745--749
T. N. L. Patterson Sines, Cosines, Square Roots, and Binary
Bits . . . . . . . . . . . . . . . . . . 750--754
Mark Stander The Smallest Solution to $ A B = C $,
Where $A$, $B$, and $C$ are Square
Matrices Composed of Distinct Primes . . 754--754
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 755--763
Russell Merris Reviews . . . . . . . . . . . . . . . . 764--768
Steven J. Brams and
Mehmet S. Ismail and
D. Marc Kilgour and
Walter Stromquist Catch-Up: a Rule That Makes Service
Sports More Competitive . . . . . . . . 771--796
Kenneth S. Williams Everything You Wanted To Know About $ a
x^2 + b y^2 + c z^2 + d t^2 $ But Were
Afraid To Ask . . . . . . . . . . . . . 797--810
Titu Andreescu and
Oleg Mushkarov Quadratic Forms, Chebyshev Polynomials,
and Geometric Inequalities . . . . . . . 811--819
Matthew C. H. Tointon The Mahler Conjecture in Two Dimensions
via the Probabilistic Method . . . . . . 820--828
Lee Sallows A Self-Descriptive Crossword Puzzle . . 829--829
Yuliy Baryshnikov and
Robert Ghrist Stokes's Theorem, Data, and the Polar
Ice Caps . . . . . . . . . . . . . . . . 830--834
Davit Harutyunyan When the Cauchy Inequality Becomes a
Formula . . . . . . . . . . . . . . . . 835--838
Pedro Ribeiro Another Proof of the Famous Formula for
the Zeta Function at Positive Even
Integers . . . . . . . . . . . . . . . . 839--841
Paolo Leonetti A Characterization of Convex Functions 842--844
Joseph Plante Cubic Equations from an Analytic Point
of View . . . . . . . . . . . . . . . . 845--849
Bryan Park On the Divergence of the Prime Harmonic
Series . . . . . . . . . . . . . . . . . 850--850
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 851--859
Marion Cohen Reviews . . . . . . . . . . . . . . . . 860--864
Lee Sallows Solution to the Self-Descriptive
Crossword Puzzle . . . . . . . . . . . . 864--864
Noah Giansiracusa and
Cameron Ricciardi Geometry in the Courtroom . . . . . . . 867--877
Boris Alexeev and
Dustin G. Mixon An Impossibility Theorem for
Gerrymandering . . . . . . . . . . . . . 878--884
Pisheng Ding On the Lengths of Level Curves . . . . . 885--900
Achim Clausing Ducci Matrices . . . . . . . . . . . . . 901--921
Chen Zheng and
Zhijun Zhou A Generalization of a \booktitleMonthly
Problem . . . . . . . . . . . . . . . . 922--922
J. A. Hocutt and
P. L. Robinson Everywhere Differentiable, Nowhere
Continuous Functions . . . . . . . . . . 923--928
Mircea Merca and
Maxie D. Schmidt A Partition Identity Related to
Stanley's Theorem . . . . . . . . . . . 929--933
Lior Bary-Soroker and
Ofir Gorodetsky Roots of Polynomials and the Derangement
Problem . . . . . . . . . . . . . . . . 934--938
José Antonio Torné and
Juan Luis Varona The Lindemann Theorem for Matrices . . . 939--940
Peng Liu and
Shibo Liu On the Surjectivity of Smooth Maps into
Euclidean Spaces and the Fundamental
Theorem of Algebra . . . . . . . . . . . 941--943
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 944--952
Robert M. Guralnick and
Gary M. Seitz Reviews . . . . . . . . . . . . . . . . 953--955
Susan Jane Colley Editor Editor's Endnotes . . . . . . . . . . . 956--957
Anonymous \booktitleMonthly Referees for 2018 . . 958--960
Susan Jane Colley Letter from the Editor . . . . . . . . . 3--3
Jayadev S. Athreya and
Bruce Reznick and
Jeremy T. Tyson Cantor Set Arithmetic . . . . . . . . . 4--17
Florian Frick and
Kelsey Houston-Edwards and
Frédéric Meunier Achieving Rental Harmony with a
Secretive Roommate . . . . . . . . . . . 18--32
Javier Sánchez-Reyes The Joukowsky Map Reveals the Cubic
Equation . . . . . . . . . . . . . . . . 33--40
Daniel P. Bossaller and
Sergio R. López-Permouth On the Associativity of Infinite Matrix
Multiplication . . . . . . . . . . . . . 41--52
Waldemar Pompe Concurrent Lines in the Napoleon-style
Configurations . . . . . . . . . . . . . 53--59
Benjamin Sambale Pseudo Sylow Numbers . . . . . . . . . . 60--65
William Cocke and
Geetha Venkataraman On the Number of Elements of Maximal
Order in a Group . . . . . . . . . . . . 66--69
Dylan Fridman and
Juli Garbulsky and
Bruno Glecer and
James Grime and
Massi Tron Florentin A Prime-Representing Constant . . . . . 70--73
José Manuel Rodríguez Caballero A Characterization of the Hypotenuses of
Primitive Pythagorean Triangles Using
Partitions into Consecutive Parts . . . 74--77
Vadim Ponomarenko Help with the Jumble . . . . . . . . . . 77--77
John Donnelly On a Conjecture of Fickett . . . . . . . 78--80
K. Kuhapatanakul and
K. Thongsing Generalizations of the Fibonacci--Lucas
Relations . . . . . . . . . . . . . . . 81--81
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 82--90
Tullia Dymarz Reviewed by Reviews . . . . . . . . . . . . . . . . 91--96
Pamela Gorkin Four Theorems with Their Foci on
Ellipses . . . . . . . . . . . . . . . . 99--111
Arpan Sadhukhan A Simple Construction to Prove
Mycielski's Theorem . . . . . . . . . . 112--112
Jason Cantarella and
Tom Needham and
Clayton Shonkwiler and
Gavin Stewart Random Triangles and Polygons in the
Plane . . . . . . . . . . . . . . . . . 113--134
Mowaffaq Hajja and
Jonathan Sondow Newton Quadrilaterals, the Associated
Cubic Equations, and Their Rational
Solutions . . . . . . . . . . . . . . . 135--150
J. Jerónimo-Castro and
C. Yee-Romero Characterizations of the Euclidean Ball
by Intersections with Planes and Slabs 151--157
Maxim Arnold and
Anatoly Eydelzon On Matrix Pythagorean Triples . . . . . 158--160
Jayadev S. Athreya and
David Aulicino A Trajectory from a Vertex to Itself on
the Dodecahedron . . . . . . . . . . . . 161--162
Paolo Leonetti Convergence Rates of Subseries . . . . . 163--167
B. Sury A Ring-theoretic Approach to Bound the
Totient Function . . . . . . . . . . . . 167--167
Nicholas Phat Nguyen A Note on Cyclotomic Integers . . . . . 168--172
Dorin Andrica and
Vlad Crisan The Smallest Nontrivial Solution to $
x_k \equiv 1 (\bmod n) $ and Related
Sequences . . . . . . . . . . . . . . . 173--178
Robert G. Donnelly and
Molly W. Dunkum The Group Action Tri-cycle Theorem . . . 179--179
Edited by Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West and
with the collaboration of Paul Bracken Problems and Solutions . . . . . . . . . 180--188
Reviewed by Bruce Berndt Reviews . . . . . . . . . . . . . . . . 189--192
Joanne Peeples and
James Álvarez and
Ruth Charney and
John Harris and
Jim Lewis and
Nancy Neudauer Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2019 to Philip Uri Treisman
for Distinguished Service to Mathematics 195--198
Daniel H. Ullman and
Daniel J. Velleman Differences of Bijections . . . . . . . 199--216
J.-P. Allouche Two Binomial Identities of Ruehr
Revisited . . . . . . . . . . . . . . . 217--225
K. Soundararajan Equidistribution of Zeros of Polynomials 226--236
Oscar M. Perdomo The Round Taylor Method . . . . . . . . 237--251
V. P. Ramesh and
R. Thangadurai and
R. Thatchaayini A Note on Gauss's Theorem on Primitive
Roots . . . . . . . . . . . . . . . . . 252--254
Shirley Llamado Yap A Theodorus Construction . . . . . . . . 255--259
Jean Mawhin Simple Proofs of the Hadamard and
Poincaré--Miranda Theorems Using the
Brouwer Fixed Point Theorem . . . . . . 260--263
Neil Falkner Hahn's Proof of the Hahn Decomposition
Theorem, and Related Matters . . . . . . 264--268
Tamás Forgács and
Jack Luong and
Joshua Williamson A Note on Infinite Series with
Recursively Defined Terms . . . . . . . 269--274
Bill Rounds Euclid's Lemma and the Square Root of 2 274--274
Russell A. Gordon Comments on ``Subsums of the Harmonic
Series'' . . . . . . . . . . . . . . . . 275--279
Edited by Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 280--288
Deborah E. Seacrest and
Tyler Seacrest The Prisoner Shouting Puzzle and
Variations . . . . . . . . . . . . . . . 291--305
Alan D. Taylor and
Stan Wagon A Paradox Arising from the Elimination
of a Paradox . . . . . . . . . . . . . . 306--318
Finbarr Holland and
Roger Smyth Cardioids and Self-inversive Cubic
Polynomials . . . . . . . . . . . . . . 319--329
Scott T. Chapman So What Is Class Number 2? . . . . . . . 330--339
M. G. Mahmoudi A Geometric Interpretation of the
Simplicity of $ {\rm SO}(3) $ . . . . . 340--350
Simon Demers The Smallest Number That Cannot Be
Collapsed Using Fewer Than 6 Plus Signs
is 3003344034004 . . . . . . . . . . . . 351--351
Makoto Ozawa and
Scott A. Taylor Two More Proofs that the Kinoshita Graph
is Knotted . . . . . . . . . . . . . . . 352--357
Péter Kórus Notes on Projectile Motion . . . . . . . 358--360
M. L. Glasser A Note on Beukers's and Related Double
Integrals . . . . . . . . . . . . . . . 361--363
Stasys Jukna Coin Flipping Cannot Shorten Arithmetic
Computations . . . . . . . . . . . . . . 364--366
Stephan Berendonk A Napoleonic Theorem for Trapezoids . . 367--369
Edited by Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West and
with the collaboration of Paul Bracken Problems and Solutions . . . . . . . . . 370--378
Lowell Beineke Reviews . . . . . . . . . . . . . . . . 379--384
Bruce Torrence Passing the Buck and Firing Fibonacci:
Adventures with the Stochastic Abacus 387--399
Dmitri V. Fomin Is the Multiset of $n$ Integers Uniquely
Determined by the Multiset of Its
$s$-sums? . . . . . . . . . . . . . . . 400--417
Tim Antonelli A Surprising Link Between Integer
Partitions and Euler's Number $e$ . . . 418--429
Niels Juul Munch A Chebyshev Theorem for Ellipses in the
Complex Plane . . . . . . . . . . . . . 430--436
Anonymous The Hardest Jumbles . . . . . . . . . . 436--436
Thomas R. Cameron The Determinant from Signed Volume to
the Laplace Expansion . . . . . . . . . 437--447
Olivier Schneegans How Close to 10 Is $ \pi^2 $ ? . . . . . 448--448
Gerd Herzog and
Peer Chr. Kunstmann Korovkin's Theorem for Functionals and
Limits for Box Integrals . . . . . . . . 449--454
Edited by Vadim Ponomarenko 100 Years Ago This Month in
\booktitleThe American Mathematical
Monthly . . . . . . . . . . . . . . . . 454--454
R. R. Andruszkiewicz and
K. Pryszczepko A Curious Characterization of Subrings
of the Field $ \mathbb {Q} $ and
Applications . . . . . . . . . . . . . . 455--458
Raymond Mortini A Simpler Proof of Cohen's Factorization
Theorem . . . . . . . . . . . . . . . . 459--463
Aleksander B\laszczyk A Simple Proof of Sierpi\'nski's Theorem 464--466
Angel Plaza $k$-th Power of a Partial Sum . . . . . 467--467
Edited by Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West and
with the collaboration of Paul Bracken Problems and Solutions . . . . . . . . . 468--476
Reviewed by Thomas Ratliff Reviews . . . . . . . . . . . . . . . . 477--479
Anonymous Solution to the Hardest Jumbles . . . . 479--479
Susan Jane Colley Editor's Endnotes . . . . . . . . . . . 480--480
Colin Adams and
Allison Henrich and
Kate Kearney and
Nicholas Scoville Knots Related by Knotoids . . . . . . . 483--490
Ronaldo Garcia Elliptic Billiards and Ellipses
Associated to the 3-Periodic Orbits . . 491--504
Tiffany Kolba and
Anthony Coniglio and
Sarah Sparks and
Daniel Weithers Noise-Induced Stabilization of Perturbed
Hamiltonian Systems . . . . . . . . . . 505--518
José Hernández Santiago The Group-Theoretic Analog of
Kuratowski's Closure-Complement Theorem 519--526
Jennifer Brooks An Interesting Family of Symmetric
Polynomials . . . . . . . . . . . . . . 527--540
Judy Holdener and
Emily Rachfal Perfect and Deficient Perfect Numbers 541--546
David Treeby Relativity . . . . . . . . . . . . . . . 546--546
K. C. Ciesielski and
M. E. Martínez-Gómez and
J. B. Seoane-Sepúlveda ``Big'' Continuous Restrictions of
Arbitrary Functions . . . . . . . . . . 547--552
Jonathan M. Fraser Almost Arithmetic Progressions in the
Primes and Other Large Sets . . . . . . 553--558
Hunter Swan Nonnegative Eigenvectors of Symmetric
Matrices . . . . . . . . . . . . . . . . 559--560
Jacques Gélinas and
Alexander G. Smirnov Integral Representation for Derivatives
of $ \cos (x) $ . . . . . . . . . . . . 561--561
Edited by Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 562--570
Dominic Lanphier Reviews . . . . . . . . . . . . . . . . 571--576
John B. Little The Many Lives of the Twisted Cubic . . 579--592
Kristopher Tapp Measuring Political Gerrymandering . . . 593--609
Athanase Papadopoulos Three Theorems of Menelaus . . . . . . . 610--619
Anonymous The Paul R. Halmos-Lester R. Ford Awards
for 2018 . . . . . . . . . . . . . . . . 619--619
Anatolii Grinshpan and
Hugo J. Woerdeman A Linear-algebraic Proof of Hilbert's
Ternary Quartic Theorem . . . . . . . . 620--627
Michael Maltenfort Decimal Selection Functions . . . . . . 628--634
Malik Younsi Peano Curves in Complex Analysis . . . . 635--640
Graham Jameson and
Peter R. Mercer The Logarithmic Mean Revisited . . . . . 641--645
Marc Chamberland and
Eugene A. Herman Arctangent Formulas and Pi . . . . . . . 646--650
Ioulia N. Baoulina Integer Ratios of Consecutive
Alternating Power Sums . . . . . . . . . 651--654
Yossi Lonke Shadows of Cube Vertices . . . . . . . . 655--656
Christian Aebi 53 Is the Smallest Prime That Is Not the
Sum or Difference of Powers of the First
Two Prime Numbers . . . . . . . . . . . 657--657
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 658--666
Karl-Dieter Crisman Reviews . . . . . . . . . . . . . . . . 667--672
Mark Krusemeyer and
Daniel H. Ullman The Seventy-Ninth William Lowell Putnam
Mathematical Competition . . . . . . . . 675--687
Carl Pomerance and
Chris Spicer Proof of the Sheldon Conjecture . . . . 688--698
Niels Lauritzen and
Jesper Funch Thomsen A Euclidean Algorithm for Integer
Matrices . . . . . . . . . . . . . . . . 699--699
Rainer Hegselmann and
Ulrich Krause Consensus and Fragmentation of Opinions
with a Focus on Bounded Confidence . . . 700--716
Erik Talvila Fourier Transform Inversion Using an
Elementary Differential Equation and a
Contour Integral . . . . . . . . . . . . 717--727
Florian Luca and
Pantelimon Stanica Perfect Squares as Concatenation of
Consecutive Integers . . . . . . . . . . 728--734
James East and
Ron Niles Integer Triangles of Given Perimeter: a
New Approach via Group Theory . . . . . 735--739
Harold W. Ellingsen Jr. A Fresh Look at Highly Composite Numbers 740--741
Fiachra Knox and
Bojan Mohar and
David R. Wood A Golden Ratio Inequality for Vertex
Degrees of Graphs . . . . . . . . . . . 742--747
Misha Kutzman and
Vadim Ponomarenko Count to Six in Six Languages . . . . . 747--747
Ashish Goyal and
Hemant Kalra and
Deepak Gumber On the Probability That an Automorphism
Fixes a Group Element . . . . . . . . . 748--753
André Pierro de Camargo A Straightforward Approach to the
Product Rule . . . . . . . . . . . . . . 754--754
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 755--763
Priscilla Bremser Reviews . . . . . . . . . . . . . . . . 764--768
Lionel Ponton The Calkin--Wilf Tree of a Quadratic
Surd . . . . . . . . . . . . . . . . . . 771--785
Rick Mabry Fibonacci Numbers, Integer Compositions,
and Nets of Antiprisms . . . . . . . . . 786--801
Peter Shiu On Erd\Hos's Last Equation . . . . . . . 802--808
G. J. O. Jameson Operator-valued Extensions of
Matrix-norm Inequalities . . . . . . . . 809--815
Fredrik Ekström Dimension of Random Limsup Sets . . . . 816--824
Seth Zimmerman and
Chungwu Ho Partitioning the Real Line into an
Uncountable Collection of Everywhere
Uncountably Dense Sets . . . . . . . . . 825--834
Antonín Slavík Unbiased Version of Hall's Marriage
Theorem in Matrix Form . . . . . . . . . 835--837
Manor Mendel A Simple Proof of the
Johnson--Lindenstrauss Extension Theorem 838--840
Enrique Treviño Probabilistic Proof that $ 1 + 2 +
\cdots + n = n (n + 1) / 2 $ . . . . . . 840--840
Franz Embacher and
Hans Humenberger A Note on the Stammler Hyperbola . . . . 841--844
Iris Gaber and
Arieh Lev and
Romina Zigdon Insights and Observations on Teaching
the Intermediate Value Theorem . . . . . 845--849
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 850--858
Benjamin Braun and
Santiago de León and
Kyle Franz and
Sami Sultan Base-$b$ Representations . . . . . . . . 859--859
Nicholas Scoville Reviews . . . . . . . . . . . . . . . . 860--864
Norbert Henze and
Günter Last Absent-Minded Passengers . . . . . . . . 867--875
Vitaly Bergelson and
Joseph Vandehey A Hot Spot Proof of the Generalized Wall
Theorem . . . . . . . . . . . . . . . . 876--890
Hugues Bellemare and
Yves Langlois and
Thomas Ransford A Positivity Conjecture Related to the
Riemann Zeta Function . . . . . . . . . 891--904
Balázs Gerencsér and
Viktor Harangi Too Acute to Be True: The Story of Acute
Sets . . . . . . . . . . . . . . . . . . 905--914
Mark Huber Halving the Bounds for the Markov,
Chebyshev, and Chernoff Inequalities
Using Smoothing . . . . . . . . . . . . 915--927
Bogdan Veklych A Minimalist Proof of the Law of
Quadratic Reciprocity . . . . . . . . . 928--928
Gérard Lavau The Truncated Tetrahedron Is Rupert . . 929--932
Meinolf Geck Eigenvalues and Polynomial Equations . . 933--935
Bernardo de la Calle Ysern Asymptotically Stable Equilibria of
Gradient Systems . . . . . . . . . . . . 936--939
B. Sury Lower Bound for the Least Common
Multiple . . . . . . . . . . . . . . . . 940--942
François Huppé and
Vadim Ponomarenko Primes in $ (0, n] $ vs. $ (n, m] $ . . 942--942
Anuj Jakhar A Useful Irreducibility Result for
Integer Polynomials . . . . . . . . . . 943--944
Hongwei Lou Remark on ``When Must a Flat Function be
Identically 0?'' . . . . . . . . . . . . 945--945
Gerald A. Edgar and
Daniel H. Ullman and
Douglas B. West Problems and Solutions . . . . . . . . . 946--954
Dylan A. King and
Thomas C. Martinez and
Steven J. Miller and
Chenyang Sun Reviews . . . . . . . . . . . . . . . . 955--958
Marion Deutsche Cohen End . . . . . . . . . . . . . . . . . . 958--958
Susan Jane Colley Editor's Endnotes . . . . . . . . . . . 959--960
Anonymous \booktitleMonthly Referees for 2019 . . i--iv