The American Mathematical Monthly, Volume 128 (original) (raw)

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Volume 128, Number 1, 2021

Letter from the Editor

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    Susan Jane Colley:
    Letter from the Editor. 3

Original Articles

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    Michael Engen, Vincent Vatter:
    Containing All Permutations. 4-24
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    Joshua P. Bowman:
    Geometry and Algebra of the Deltoid Map. 25-39

MathBit

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    Paul Pollack, Enrique Treviño:
    Sums of Proper Powers. 40

Original Articles

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    Luca Brandolini, Leonardo Colzani, S. Robins, Giancarlo Travaglini:
    Pick's Theorem and Convergence of Multiple Fourier Series. 41-49
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    David Lowry-Duda, Miles H. Wheeler:
    Perturbing the Mean Value Theorem: Implicit Functions, the Morse Lemma, and Beyond. 50-61

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 61

Original Articles

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    Robert F. Brown:
    A Good Question Won't Go Away: An Example of Mathematical Research. 62-68

MathBit

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    Surinder Pal Singh Kainth:
    Perfect Metric Spaces of Increasingly Large Cardinality. 69

Notes

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    Daniel A. Klain:
    A Probabilistic Proof of the Spherical Excess Formula. 70-72
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    Xiaomin Chen, Fenglin Huang, Shuhan Zhou, Mingxuan Zou, Junchi Zuo:
    Foster, Turán, and Neighbors. 73-78

MathBit

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    Josh Hiller:
    Fibonacci's Bunny-pocalypse! 78

Notes

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    Erel Segal-Halevi, Warut Suksompong:
    How to Cut a Cake Fairly: A Generalization to Groups. 79-83
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    Przemyslaw Górka:
    Separability of a Metric Space Is Equivalent to the Existence of a Borel Measure. 84-86

MathBit

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    Hùng Viêt Chu:
    What's Special about the Perfect Number 6? 87

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 88-96

Volume 128, Number 2, 2021

Original Articles

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    Sonya Flaten, Paul D. Humke, Emily Olson, Thong Vo:
    Delicate Details of Filling Space. 99-114
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    Ian Thompson, Morris Davies, Miren Karmele Urbikain:
    Analysis of Series and Products. Part 1: The Euler-Maclaurin Formula. 115-124
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    Juan Tolosa:
    Length-Preserving Directions and Some Diophantine Equations. 125-139

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 139

Original Articles

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    Robert K. Moniot:
    Solution of an Odds Inversion Problem. 140-149

MathBit

Original Articles

MathBits

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    Ángel Plaza:
    Exponential Inequalities and Corollaries. 162

Notes

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    Eric L. Grinberg, Mehmet Orhon:
    Morley Trisectors and the Law of Sines with Reflections. 163-167
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    Dorin Andrica, Sorin Radulescu, George C. Turcas:
    On the Automorphism Group of Direct Products of Groups with Finite Exponent. 168-173
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    Hongjian Li, Pingzhi Yuan, Hairong Bai:
    Positive Rational Numbers of the Form φ ( m 2 ) / φ ( n 2 ). 174-176

MathBit

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    Matthew A. Niemiro:
    The Natural Logarithm Modulo 2. 177

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 178-186

Reviews

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    Darren B. Glass, Béla Bajnok, Carolyn Yackel, Edray Goins, Jenna P. Carpenter, Stephen Kennedy, Jeanette Shakalli, Ursula Whitcher, Dave Kung, Kathryn Kozak, Robert Ghrist, Andrew Gelman:
    Reviews. 187-192

Volume 128, Number 3, 2021

Gung and Hu Award

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    Nancy Ann Neudauer, Tevian Dray, George Berzsenyi, John Harris, Diane Lussier, Amy Shell-Gellasch, James Álvarez, Ruth Charney:
    Yeuh-Gin Gung and Dr. Charles Y. Hu Award for 2021 to Deanna Haunsperger for Distinguished Service. 195-197

Original Articles

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    Ian Thompson, Morris Davies, Miren Karmele Urbikain:
    Analysis of Series and Products. Part 2: The Trapezoidal Rule. 198-213

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 213

Original Articles

MathBit

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    Stephan Ramon Garcia, Matthew A. Myers:
    Composites in the Ulam Spiral. 238

Original Articles

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    Alexander Stasinski:
    A Uniform Proof of the Finiteness of the Class Group of a Global Field. 239-249

MathBit

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    Howard L. Ritter Jr.:
    A Pi in the Face of Tau. 249

Original Articles

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    Christian Elsholtz:
    Fermat's Last Theorem Implies Euclid's Infinitude of Primes. 250-257
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    Arnold T. Saunders, Hosam M. Mahmoud:
    Bar Bets and Generating Functions: The Distribution of the Separation of Two Distinct Card Ranks. 258-264

Notes

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    Frederick K. Dashiell Jr.:
    Countable Metric Spaces Without Isolated Points. 265-267
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    Hùng Viêt Chu:
    On Arithmetic Progressions of Powers in Cyclotomic Polynomials. 268-272
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    David M. Bradley:
    Note on Dirichlet's Sinc Integral. 273-274

MathBit

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    George Stoica:
    Widder-style Real Analytic Functions. 275

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 276-284

Reviews

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    Margaret Reese:
    Reviews. 285-288

Volume 128, Number 4, 2021

Original Articles

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    William Dunham:
    Euler and the Cubic Basel Problem. 291-301
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    Scott T. Chapman, Felix Gotti, Marly Gotti:
    When Is a Puiseux Monoid Atomic? 302-321
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    Aaron Melman:
    Zero Exclusion Sectors for Some Polynomials with Structured Coefficients. 322-336

MathBit

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    J. J. Bissell:
    Complex Numbers as Real Continued Fractions. 336

Original Articles

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    Jacqueline Anderson, Brian Camara, John Pike:
    Positional Voting and Doubly Stochastic Matrices. 337-351

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 351

Original Articles

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    Richard H. Hammack, Paul C. Kainen:
    A New View of Hypercube Genus. 352-359
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    Jacques Boulanger, Jean-Luc Chabert:
    An Elementary Proof of the Two-Generator Property for the Ring of Integer-Valued Polynomials. 360-366

Notes

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    Vilmos Komornik, Reinhard Schäfke:
    Leibniz, Newton, and Cauchy: A Complex Relationship. 367-369
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    Mark Levi, Tadashi Tokieda:
    A Communicating-Vessels Proof of Hölder's Inequality. 370
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    Tom Leinster:
    The Probability That an Operator Is Nilpotent. 371-375

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and solutions. 376-384

Volume 128, Number 5, 2021

Original Articles

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    Julie Rowlett, Max Blom, Henrik Nordell, Oliver Thim, Jack Vahnberg:
    Crystallographic Groups, Strictly Tessellating Polytopes, and Analytic Eigenfunctions. 387-406
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    Sarah Bockting-Conrad, Yevgenia Kashina, T. Kyle Petersen, Bridget Eileen Tenner:
    Sós Permutations. 407-422

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 422

Original Articles

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    Andrzej Komisarski:
    Nontransitive Random Variables and Nontransitive Dice. 423-434
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    Dov Samet:
    An Extension of Ceva's Theorem to n-Simplices. 435-445
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    Ignacio Bajo:
    Computing Moore-Penrose Inverses with Polynomials in Matrices. 446-456

MathBit

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    Aaron Crenshaw, Dalibor Froncek:
    Box-Object Redistribution Problem. 456

Notes

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    Lubica Holá:
    There are 2c Quasicontinuous Non-Lebesgue Measurable Functions. 457-460
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    Frantisek Marko, José L. Cereceda:
    A Note on the Geometry of Figurate Numbers. 461-463
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    David Conlon:
    Extremal Numbers of Cycles Revisited. 464-466

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 467-475

Reviews

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    David Nacin:
    Reviews. 476-478

Editor's Endnotes

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    Susan Jane Colley:
    Editor's Endnotes. 479-480

Volume 128, Number 6, 2021

Original Articles

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    Bruce E. Sagan, Vincent Vatter:
    Bijective Proofs of Proper Coloring Theorems. 483-499

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 499

Original Articles

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    Andrew J. Simoson:
    Ford Circles Strike Gold. 500-512
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    Cara D. Brooks, Alberto A. Condori, Nicholas Seguin:
    Polynomially Isometric Matrices in Low Dimensions. 513-524

MathBit

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    Vadim Ponomarenko:
    Grades Are Not Money. 524

Original Articles

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    William Johnston, Chloe M. Makdad:
    A Comparison of Norms: Bicomplex Root and Ratio Tests and an Extension Theorem. 525-533
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    András Bezdek, Zhenyue Guan, Mihály Hujter, Antal Joós:
    Cubes and Boxes Have Rupert's Passages in Every Nontrivial Direction. 534-542
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    Imre Bárány, Peter Frankl:
    How (Not) to Cut Your Cheese. 543-552

MathBit

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    Edward Coto Mora, Francesco Viganò:
    169 and Sums of Positive Squares. 553

Notes

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 563-571

Reviews

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    Debra K. Borkovitz:
    x + y: A Mathematician's Manifesto for Rethinking Gender. 572-576

Volume 128, Number 7, 2021

Original Articles

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    Christopher N. B. Hammond, Edward Omey:
    A Second Look at the Second Ratio Test. 579-596

MathBit

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    Robert Dawson:
    The Digital Rubáiyát. 597

Original Articles

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    Jeff Witmer:
    Simpson's Paradox, Visual Displays, and Causal Diagrams. 598-610
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    Jan E. Holly:
    What Type of Apollonian Circle Packing Will Appear? 611-629
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    Asaf Shapira, Mykhaylo Tyomkyn:
    Quasirandom Graphs and the Pantograph Equation. 630-639

Award

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    The Paul R. Halmos-Lester R. Ford Awards for 2020. 639

Original Articles

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    Yusuf Z. Gürtas:
    Discriminants of Quadratics Generalized. 640-647

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 647

Notes

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    Hyounggyu Choi, Kyeonghoon Jeong:
    Concurrence of Three Area-Bisecting Cevians of a Triangle in Three Geometries. 648-651
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    Luca Studer:
    An Asymptotic Version of Frankl's Conjecture. 652-654
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    Pablo Amster:
    The Power of the Half Power. 655-657

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and solutions. 658-666

Reviews

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    Neil J. Calkin, Colm Mulcahy:
    Reviews. 667-672

Volume 128, Number 8, 2021

William Lowell Putnam Mathematical Competition

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    Mark Krusemeyer, Daniel H. Ullman, Paul Zeitz:
    The Eighty-First William Lowell Putnam Mathematical Competition. 675-686

Original Articles

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    Dominic Klyve, Erik R. Tou:
    A Prime Testing Algorithm from Leonhard Euler. 687-700
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    Vitaly Bergelson, Andrew Best, Alex Iosevich:
    Sums of Powers in Large Finite Fields: A Mix of Methods. 701-718
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    Bryan J. Freyberg:
    March Madness Magic: Constructing a Tournament with a Magic Cube. 719-725
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    Tomer Moran, Shay Moran, Shlomo Moran:
    Elementary Derivations of the Euclidean Hurwitz Algebras Adapted from Gadi Moran's last paper. 726-736
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    Alin Bostan, Fernando Chamizo, Mikael Persson Sundqvist:
    On an Integral Identity. 737-743

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 743

Notes

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    Asaf Cohen Antonir, Asaf Shapira:
    On Erdős's Method for Bounding the Partition Function. 744-747
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    Hannah Cairns:
    Perron's Theorem in an Hour. 748-752
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    Steven H. Weintraub:
    The Theorem of the Primitive Element. 753-754

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 755-763

Reviews

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    Justin Corvino:
    Curvature of Space and Time, with an Introduction to Geometric Analysis. 764-768

Volume 128, Number 9, 2021

Introduction

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    David H. Bailey, Scott Chapman:
    Introduction to the Special Issue. 772

Original Articles

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    David H. Bailey:
    Jonathan Borwein: Renaissance Mathematician. 773-779
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    Karl Dilcher:
    Analytic Continuations of Character and Alternating Tornheim Zeta Functions. 780-795
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    Heinz H. Bauschke, Sylvain Gretchko, Walaa M. Moursi, Matthew Saurette:
    Edelstein's Astonishing Affine Isometry. 796-809

MathBit

Original Articles

MathBit

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    Vadim Ponomarenko:
    100 Years Ago This Month in The American Mathematical Monthly. 855

Problems and Solutions

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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 856-864

Volume 128, Number 10, November 2021

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    Susan Jane Colley:
    Letter from the Editor. 867
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    Ryan Alvarado, Maia Averett, Benjamin Gaines, Christopher Jackson, Mary Leah Karker, Malgorzata Aneta Marciniak, Francis E. Su, Shanise Walker:
    The Game of Cycles. 868-887
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    Melvyn B. Nathanson:
    Sums of Finite Sets of Integers, II. 888-896
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    Li Zhou:
    Area Division of the Yellow Brick Road on the Regular Dodecahedron. 897
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    Ronaldo Garcia, Dan Reznik, Jair Koiller:
    New Properties of Triangular Orbits in Elliptic Billiards. 898-910
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    Robert Dawson, Pietro Milici, Frédérique Plantevin:
    Gardener's Hyperbolas and the Dragged-Point Principle. 911-921
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    Vadim Ponomarenko:
    Pollock's Generalized Tetrahedral Numbers Conjecture. 921
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    Juan Luis Varona:
    A Couple of Transcendental Prime-Representing Constants. 922-928
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    Claire Burrin, Matthew Issac:
    Infinitely Many Twin Prime Polynomials of Odd Degree. 929-935
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    Paul J. Campbell:
    Much Virtue in "If". 936
• 
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  • 
    Prapanpong Pongsriiam, Kittipong Subwattanachai:
    Arithmetic Progressions in the Values of a Quadratic Polynomial. 937-941
• 
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    Hojjat Farzadfard:
    The Fundamental Theorem of Algebra Via Newton's Identities. 942-945
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    Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
    Problems and Solutions. 946-954
• 
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  • 
  • 
    Bruce Torrence:
    Tessellations: Mathematics, Art, and Recreation: By Robert Fathauer. A K Peters/CRC Press, Boca Raton, FL, 2020. 464 pp., ISBN 978-0367185978. 955-959
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    Editor's Endnotes. 960

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