Journal: The American Mathematical Monthly

Volume 127, Issue 9

771 -- 788Louis Deaett. Matroids and the Minimum Rank Problem for Matrix Patterns
789 -- 805Yuki Nakandakari, Shuichi Tsukuda. An Elementary Proof That the Third Finite Subset Space of the Circle is the 3-Sphere
806 -- 0Angelina Y. M. Chin. Counting Pairs to Find a Finite Field
807 -- 819Krzysztof Chris Ciesielski, Yichen Liu. Distinct Continuous Maps with All Riemann Sums Equal
820 -- 826Anton A. Kutsenko. An Entire Function Connected with the Approximation of the Golden Ratio
827 -- 834Benjamin Sambale. On a Theorem of Ledermann and Neumann
835 -- 0Michael Mandler. A Quick Proof of the Order-Extension Principle
836 -- 840Jens Marklof. Delone Sets Generated by Square Roots
841 -- 846Vilmos Komornik. A Short, Elementary Introduction to the Exponential Function
847 -- 849Dmitry Krachun, Zhi-Wei Sun. Each Positive Rational Number Has the Form φ(m2)/φ(n2)
849 -- 0Peter J. McGrath. Bases for Second Order Linear ODEs
850 -- 851Dan Stefan Marinescu, Mihai Monea. A Very Short Proof of the Hermite-Hadamard Inequalities
852 -- 860Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and solutions
861 -- 864Jo Boaler. Mathematics for Human Flourishing

Volume 127, Issue 8

675 -- 687Mark Krusemeyer, Daniel H. Ullman. The Eightieth William Lowell Putnam Mathematical Competition
688 -- 705Ben Blum-Smith, Japheth Wood. Chords of an Ellipse, Lucas Polynomials, and Cubic Equations
706 -- 715Rachel Eaton, Kurt Herzinger, Ian Pierce, Jeremy Thompson. Numerical Semigroups and the Game of Sylver Coinage
716 -- 0Dennis L. Sun. Wald's Identity and Geometric Expectation
717 -- 725Gary R. Lawlor. l'Hôpital's Rule for Multivariable Functions
726 -- 733Louis Crane, David N. Yetter. Tetrahedal Geometry from Areas
734 -- 736Alexandru Tupan. A Simple Proof of the Siebeck-Marden Theorem
737 -- 743Benedikt Wirth. Green's Function for the Neumann-Poisson Problem on n-Dimensional Balls
743 -- 0Surinder-pal Singh. Null Subsets of All Sizes Inside Vitali Sets
744 -- 749Jackson Autry, Tara Gomes, Christopher O'Neill, Vadim Ponomarenko. Elasticity in Apéry Sets
750 -- 751Karthik Chandrasekhar, Richard Ehrenborg, Frits Beukers. A Counting Proof for When 2 Is a Quadratic Residue
752 -- 761Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and solutions
762 -- 0Gao-Wen Xi, Qiu-Ming Luo. A Formula for the Stirling Numbers of the Second Kind
763 -- 768Kevin P. Knudson. Discrete Morse Theory by Nicholas Scoville

Volume 127, Issue 7

579 -- 593Anders Aamand, Mikkel Abrahamsen, Mikkel Thorup. Disks in Curves of Bounded Convex Curvature
594 -- 601Kristin Fritsch, Janin Heuer, Raman Sanyal, Nicole Schulz. The Martin Gardner Polytopes
602 -- 617Christopher Ennis. Between the Cracks: Filling Space with Polygonal Shapes
618 -- 628Kiana Mittelstaedt. A Stochastic Approach to Eulerian Numbers
629 -- 637Noam Zimhoni. A Forest of Eisensteinian Triangles
638 -- 0Sam Northshield. A Short Proof of Fermat's Two-square Theorem
639 -- 642Christian Elsholtz. Unconditional Prime-Representing Functions, Following Mills
643 -- 648Toby Alfred-Jones. A Short Proof of the Uniform Smoothness of Certain Lebesgue Spaces
649 -- 653Warren P. Johnson. Down with Weierstrass!
654 -- 657Brian Hopkins 0001, James A. Sellers. Turning the Partition Crank
657 -- 0. The Paul R. Halmos-Lester R. Ford Awards for 2019
658 -- 0George Stoica. Components Used in the Stone-Weierstrass Theorem
659 -- 667Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and Solutions
668 -- 671Meredith L. Greer. Reviews
672 -- 0Vadim Ponomarenko. The Mathematical Association of America Prime

Volume 127, Issue 6

483 -- 503Brian S. Thomson. The Bounded Convergence Theorem
504 -- 517J. J. P. Veerman. Navigating Around Convex Sets
518 -- 0Marion Deutsche Cohen. Portrait of the Mathematician as a First-Year Undergrad
519 -- 529Antonio Lei, Antoine Poulin. On Certain Probabilistic Properties of Polynomials over the Ring of p-adic Integers
530 -- 536Shan Tai Chan, Yuan Yuan. Finding the Determinant of a Matrix via Complex Analysis
537 -- 544Hyounggyu Choi. Invariance of the Length and the Area of Cycloids
544 -- 0James Henle. Paying Our Way Out of a Crisis
545 -- 546Cole Graham, Tadashi Tokieda, Vadim Ponomarenko. An Entropy Proof of the Arithmetic Mean-Geometric Mean Inequality
547 -- 553Daniel Cao Labora. When Is a Continuous Bijection a Homeomorphism?
553 -- 0Marion Deutsche Cohen. Portrait of the Mathematician as a New Mother
554 -- 557M. A. Nyblom. Integer Part of the Partial Sums for the Divergent p-Series in Closed Form
558 -- 562Burghard Herrmann. The Specified Three Distance Theorem
563 -- 571Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and solutions
572 -- 0Mark Levi. A Water-Based Proof of the Cauchy-Schwarz Inequality
573 -- 576Tim Chartier. Reviews

Volume 127, Issue 5

387 -- 400Norbert Hungerbühler. The Inverse Caustic Problem
401 -- 410Steven W. Buchanan, Andrew J. Hetzel. On the Success of Seriously Mishandling Euclid's Lemma
411 -- 426David Clark, Sophia Mancini, Jacob Van Hook. Misère Tic-Tac-Toe on Projective Binary Steiner Triple Systems
427 -- 0Angel Plaza. Harmonic, Logarithmic, and Arithmetic Means and Corollaries
428 -- 436Alexandru Tupan. A Generalization of the Steiner Inellipse
437 -- 443Étienne Matheron. Three Proofs of Tychonoff's Theorem
443 -- 0Vadim Ponomarenko. Proof Techniques for the New Millennium
444 -- 448Vyacheslav M. Abramov. Extension of the Bertrand-De Morgan Test and Its Application
449 -- 451Marc Chamberland. When Are All the Zeros of a Polynomial Real and Distinct?
452 -- 455Marijan Markovic. Riesz's Theorem for Lumer's Hardy Spaces
456 -- 459Jitender Singh, Sanjeev Kumar. A Generalization of Bevelacqua's Irreducibility Criterion
460 -- 0André Pierro de Camargo. A New Proof of the Equivalence of the Cauchy Mean Value Theorem and the Mean Value Theorem
461 -- 469Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and Solutions
470 -- 477Fernando Q. Gouvêa. Reviews
478 -- 480Susan Jane Colley. Editor's Endnotes

Volume 127, Issue 4

291 -- 296John H. Conway, M. S. Paterson. A Headache-Causing Problem
297 -- 307Steven Klee, Matthew T. Stamps. Linear Algebraic Techniques for Spanning Tree Enumeration
308 -- 315Leonardo Bardomero, Matthias Beck. Frobenius Coin-Exchange Generating Functions
316 -- 329Gregory P. Dresden, Saimon Islam, Prakriti Panthi, Anukriti Shrestha, Jiahao Zhang. Polynomial Roots with Common Tails
330 -- 0Arpan Sadhukhan. An Alternative Proof of Steinhaus's Theorem
331 -- 343Alberto A. Condori. Maximum Principles for Matrix-Valued Analytic Functions
344 -- 351Juan Fernández-Sánchez, Wolfgang Trutschnig. Nested Square Roots of 2 Revisited
352 -- 353Sue Geller. Simply Not a Simple Group
354 -- 358Jesús Ferrer, Enrique Llorens-Fuster. A Short Proof that Some Mappings of the Unit Ball of ℓ2 Are Never Nonexpansive
359 -- 363Kenichi Hirose. Continuity of the Roots of a Polynomial
364 -- 370Sergey Sadov. Gustafson's Isomorphism and the Zassenhaus Lemma via a Common Commutative Diagram
371 -- 0Walter Wyss. Pythagoras Extended
372 -- 380Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and Solutions
381 -- 384Alex Kontorovich. Reviews

Volume 127, Issue 3

195 -- 198Nancy Ann Neudauer. Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2020 to Gerald J. Porter for Distinguished Service to Mathematics
199 -- 216Zvi Rosen, Jessica Sidman, Louis Theran. Algebraic Matroids in Action
217 -- 237Zhaodong Cai, Matthew Faust, A. J. Hildebrand, Junxian Li, Yuan Zhang. The Surprising Accuracy of Benford's Law in Mathematics
238 -- 248Richard Evan Schwartz, Serge Tabachnikov. Descartes Circle Theorem, Steiner Porism, and Spherical Designs
249 -- 256Fred Kuczmarski. Equal Zones and Tautochrones
257 -- 0Enrique Treviño. Expected Number of Dice Rolls for the Sum to Reach n
258 -- 262Javier Sánchez-Reyes. The Midpoints Between Roots Reveal the Quartic Equation
263 -- 268Zoltán Füredi, András Gyárfás. An Extension of Mantel's Theorem to k-Graphs
269 -- 272Suk-Geun Hwang, Ki-Bong Nam. A Determinant Proof of a Generalized Pythagorean Theorem
273 -- 0Christian Aebi. A Short and Easy Proof of Morley's Congruence Theorem
274 -- 282Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and Solutions
283 -- 288Jason Rosenhouse. Reviews

Volume 127, Issue 2

99 -- 111Richard P. Stanley. Some Linear Recurrences Motivated by Stern's Diatomic Array
112 -- 124Evan O'Dorney. Visibly Irreducible Polynomials over Finite Fields
125 -- 138Mark B. Villarino. Gauss on Gaussian Quadrature
139 -- 0Alfred Witkowski. Bijections between (0, 1), (0, 1], and [0, 1]
140 -- 150Aled Walker, Alexander Walker. Arithmetic Progressions with Restricted Digits
151 -- 158Mohammad Javaheri. On Sets Closed Under the Cross Product and a Property of the Octahedron
159 -- 0Jesús Guillera. When Ramanujan Meets Fibonacci and Lucas
160 -- 165Dorota Blinkiewicz, Bogdan Szydlo. Minimal Perimeter Parallelograms Inscribed in a Pair of Confocal Ellipses
166 -- 168Xibao Hu, Yumin Zhong. A Probabilistic Proof of a Recursion Formula for Sums of Powers
169 -- 174Timothy Trujillo. Condorcet's Paradox and Ultrafilters
174 -- 0Seth Borgo. Special Properties of Power Functions
175 -- 178Richard Ehrenborg. The Wästlund Partition in Higher Dimensions
179 -- 187Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and Solutions (with the collaboration of Paul Bracken, Ezra A. Brown Zachary Franco Christian Friesen László Lipták Rick Luttmann Frank B. Miles Lenhard Ng Kenneth Stolarsky Richard Stong Stan Wagon Lawrence Washington Elizabeth Wilmer Fuzhen Zhang and Li Zhou)
188 -- 0Changjian Liu. New Proof of a Gronwall-type Trigonometric Inequality
189 -- 192Darren B. Glass. Reviews

Volume 127, Issue 10

0 -- 0. Monthly Referees for 2020
867 -- 879Tevian Dray. Using Embedding Diagrams to Visualize Curvature
880 -- 896Mikkel Abrahamsen, Jacob Holm, Eva Rotenberg, Christian Wulff-Nilsen. Escaping an Infinitude of Lions
897 -- 910Hiroshi Maehara, Horst Martini. Tangent Spheres of Tetrahedra and a Theorem of Grace
911 -- 917Adam Coffman 0001, Yuan Zhang. Vector Fields with Continuous Curl but Discontinuous Partial Derivatives
918 -- 926Ulrich Abel, Vitaliy Kushnirevych. Reducing Multiple Integrals of Beukers's Type
927 -- 0George Stoica. Two Uniqueness Theorems at Work
928 -- 932Bowen Yao. A Note on Fraction Decompositions of Integers
933 -- 935Anatoly Eydelzon. On a New Property of the Steiner Inellipse
936 -- 938Desmond MacHale. Are There More Finite Rings than Finite Groups?
938 -- 0Idris Mercer. Another Proof of the Infinitude of Primes
939 -- 943Xiumei Li, Min Sha. A Proof of Sondow's Conjecture on the Smarandache Function
944 -- 952Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and Solutions
953 -- 957Lara Pudwell. An Introduction to Undergraduate Research in Computational and Mathematical Biology Edited by Hannah Callender Highlander, Alex Capaldi, and Carrie Diaz Eaton; and A Project-Based Guide to Undergraduate Research in Mathematics. Edited by Pamela Harris, Erik Insko, and Aaron Wootton
958 -- 960Susan Jane Colley. Editor's Endnotes

Volume 127, Issue 1

3 -- 0Susan Jane Colley. Letter from the Editor
4 -- 22Frantisek Marko, Semyon N. Litvinov. Geometry of Figurate Numbers and Sums of Powers of Consecutive Natural Numbers
23 -- 32John M. Campbell, Jacopo D'Aurizio, Jonathan Sondow. Hypergeometry of the Parbelos
33 -- 44Maria Bras-Amorós. Increasingly Enumerable Submonoids of R : Music Theory as a Unifying Theme
45 -- 53Charles R. Johnson, Pietro Paparella. Matricial Proofs of Some Classical Results about Critical Point Location
54 -- 62Alan D. Sokal. How To Generalize (and Not To Generalize) the Chu-Vandermonde Identity
63 -- 0Vincent Vatter. A Probabilistic Proof of a Lemma That Is Not Burnside's
64 -- 69Stefan Steinerberger. The Best Way to Reconcile Your Past Is Exponentially
70 -- 71George Stoica. Collisions and Angular Momentum for Singular Potentials
72 -- 74Jingyuan Zhang, Weigen Yan. A New Proof of Foster's First Theorem
75 -- 79Wooyoung Chin. A Probabilistic Proof of a Wallis-type Formula for the Gamma Function
80 -- 83Örs Rebák. Generalization of a Ramanujan Identity
84 -- 0Zijian Diao. An Elementary Proof of the Irrationality of e
85 -- 93Daniel H. Ullman, Daniel J. Velleman, Douglas B. West. Problems and Solutions
94 -- 96Jeff Witmer. Reviews