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ORCIDThe American Mathematical Monthly, Volume 127
Volume 127, Number 1, 2020
- Susan Jane Colley:
Letter from the Editor. 3
- Frantisek Marko
, Semyon N. Litvinov:
Geometry of Figurate Numbers and Sums of Powers of Consecutive Natural Numbers. 4-22 - John M. Campbell, Jacopo D'Aurizio, Jonathan Sondow:
Hypergeometry of the Parbelos. 23-32 - Maria Bras-Amorós:
Increasingly Enumerable Submonoids of R : Music Theory as a Unifying Theme. 33-44 - Charles R. Johnson, Pietro Paparella:
Matricial Proofs of Some Classical Results about Critical Point Location. 45-53 - Alan D. Sokal:
How To Generalize (and Not To Generalize) the Chu-Vandermonde Identity. 54-62
- Vincent Vatter:
A Probabilistic Proof of a Lemma That Is Not Burnside's. 63
- Stefan Steinerberger:
The Best Way to Reconcile Your Past Is Exponentially. 64-69 - George Stoica:
Collisions and Angular Momentum for Singular Potentials. 70-71 - Jingyuan Zhang, Weigen Yan:
A New Proof of Foster's First Theorem. 72-74 - Wooyoung Chin:
A Probabilistic Proof of a Wallis-type Formula for the Gamma Function. 75-79 - Örs Rebák:
Generalization of a Ramanujan Identity. 80-83
- Zijian Diao:
An Elementary Proof of the Irrationality of e. 84
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and Solutions. 85-93
- Jeff Witmer:
Reviews. 94-96
Volume 127, Number 2, 2020
- Richard P. Stanley:
Some Linear Recurrences Motivated by Stern's Diatomic Array. 99-111 - Evan O'Dorney:
Visibly Irreducible Polynomials over Finite Fields. 112-124 - Mark B. Villarino:
Gauss on Gaussian Quadrature. 125-138
- Alfred Witkowski:
Bijections between (0, 1), (0, 1], and [0, 1]. 139
- Aled Walker, Alexander Walker:
Arithmetic Progressions with Restricted Digits. 140-150 - Mohammad Javaheri:
On Sets Closed Under the Cross Product and a Property of the Octahedron. 151-158
- Jesús Guillera:
When Ramanujan Meets Fibonacci and Lucas. 159
- Dorota Blinkiewicz, Bogdan Szydlo:
Minimal Perimeter Parallelograms Inscribed in a Pair of Confocal Ellipses. 160-165 - Xibao Hu, Yumin Zhong:
A Probabilistic Proof of a Recursion Formula for Sums of Powers. 166-168 - Timothy Trujillo:
Condorcet's Paradox and Ultrafilters. 169-174
- Seth Borgo:
Special Properties of Power Functions. 174
- Richard Ehrenborg:
The Wästlund Partition in Higher Dimensions. 175-178
- Daniel 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). 179-187
- Changjian Liu:
New Proof of a Gronwall-type Trigonometric Inequality. 188
- Darren B. Glass:
Reviews. 189-192
Volume 127, Number 3, 2020
- Nancy Ann Neudauer:
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2020 to Gerald J. Porter for Distinguished Service to Mathematics. 195-198
- Zvi Rosen, Jessica Sidman, Louis Theran:
Algebraic Matroids in Action. 199-216 - Zhaodong Cai, Matthew Faust, A. J. Hildebrand, Junxian Li, Yuan Zhang:
The Surprising Accuracy of Benford's Law in Mathematics. 217-237
- Richard Evan Schwartz, Serge Tabachnikov:
Descartes Circle Theorem, Steiner Porism, and Spherical Designs. 238-248
- Fred Kuczmarski:
Equal Zones and Tautochrones. 249-256
- Enrique Treviño:
Expected Number of Dice Rolls for the Sum to Reach n. 257
- Javier Sánchez-Reyes:
The Midpoints Between Roots Reveal the Quartic Equation. 258-262 - Zoltán Füredi, András Gyárfás:
An Extension of Mantel's Theorem to k-Graphs. 263-268 - Suk-Geun Hwang, Ki-Bong Nam:
A Determinant Proof of a Generalized Pythagorean Theorem. 269-272
- Christian Aebi:
A Short and Easy Proof of Morley's Congruence Theorem. 273
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and Solutions. 274-282
- Jason Rosenhouse:
Reviews. 283-288
Volume 127, Number 4, 2020
- John H. Conway, M. S. Paterson:
A Headache-Causing Problem. 291-296
- Steven Klee, Matthew T. Stamps:
Linear Algebraic Techniques for Spanning Tree Enumeration. 297-307 - Leonardo Bardomero, Matthias Beck:
Frobenius Coin-Exchange Generating Functions. 308-315 - Gregory P. Dresden, Saimon Islam, Prakriti Panthi, Anukriti Shrestha, Jiahao Zhang:
Polynomial Roots with Common Tails. 316-329
- Arpan Sadhukhan:
An Alternative Proof of Steinhaus's Theorem. 330
- Alberto A. Condori:
Maximum Principles for Matrix-Valued Analytic Functions. 331-343 - Juan Fernández-Sánchez, Wolfgang Trutschnig:
Nested Square Roots of 2 Revisited. 344-351
- Sue Geller:
Simply Not a Simple Group. 352-353 - Jesús Ferrer, Enrique Llorens-Fuster:
A Short Proof that Some Mappings of the Unit Ball of ℓ2 Are Never Nonexpansive. 354-358 - Kenichi Hirose:
Continuity of the Roots of a Polynomial. 359-363 - Sergey Sadov:
Gustafson's Isomorphism and the Zassenhaus Lemma via a Common Commutative Diagram. 364-370
- Walter Wyss:
Pythagoras Extended. 371
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and Solutions. 372-380
- Alex Kontorovich:
Reviews. 381-384
Volume 127, Number 5, 2020
- Norbert Hungerbühler:
The Inverse Caustic Problem. 387-400
- Steven W. Buchanan, Andrew J. Hetzel:
On the Success of Seriously Mishandling Euclid's Lemma. 401-410
- David Clark, Sophia Mancini, Jacob Van Hook:
Misère Tic-Tac-Toe on Projective Binary Steiner Triple Systems. 411-426
- Angel Plaza:
Harmonic, Logarithmic, and Arithmetic Means and Corollaries. 427
- Alexandru Tupan:
A Generalization of the Steiner Inellipse. 428-436 - Étienne Matheron:
Three Proofs of Tychonoff's Theorem. 437-443
- Vadim Ponomarenko:
Proof Techniques for the New Millennium. 443
- Vyacheslav M. Abramov:
Extension of the Bertrand-De Morgan Test and Its Application. 444-448 - Marc Chamberland:
When Are All the Zeros of a Polynomial Real and Distinct? 449-451 - Marijan Markovic:
Riesz's Theorem for Lumer's Hardy Spaces. 452-455 - Jitender Singh, Sanjeev Kumar:
A Generalization of Bevelacqua's Irreducibility Criterion. 456-459
- André Pierro de Camargo:
A New Proof of the Equivalence of the Cauchy Mean Value Theorem and the Mean Value Theorem. 460
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and Solutions. 461-469
- Fernando Q. Gouvêa:
Reviews. 470-477
- Susan Jane Colley:
Editor's Endnotes. 478-480
Volume 127, Number 6, 2020
- Brian S. Thomson:
The Bounded Convergence Theorem. 483-503 - J. J. P. Veerman:
Navigating Around Convex Sets. 504-517
- Marion Deutsche Cohen:
Portrait of the Mathematician as a First-Year Undergrad. 518
- Antonio Lei, Antoine Poulin:
On Certain Probabilistic Properties of Polynomials over the Ring of p-adic Integers. 519-529 - Shan Tai Chan, Yuan Yuan:
Finding the Determinant of a Matrix via Complex Analysis. 530-536
- Hyounggyu Choi:
Invariance of the Length and the Area of Cycloids. 537-544
- James M. Henle:
Paying Our Way Out of a Crisis. 544
- Cole Graham, Tadashi Tokieda, Vadim Ponomarenko:
An Entropy Proof of the Arithmetic Mean-Geometric Mean Inequality. 545-546 - Daniel Cao Labora:
When Is a Continuous Bijection a Homeomorphism? 547-553
- Marion Deutsche Cohen:
Portrait of the Mathematician as a New Mother. 553
- M. A. Nyblom:
Integer Part of the Partial Sums for the Divergent p-Series in Closed Form. 554-557 - Burghard Herrmann:
The Specified Three Distance Theorem. 558-562
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and solutions. 563-571
- Mark Levi:
A Water-Based Proof of the Cauchy-Schwarz Inequality. 572
- Tim Chartier:
Reviews. 573-576
Volume 127, Number 7, 2020
- Anders Aamand, Mikkel Abrahamsen, Mikkel Thorup:
Disks in Curves of Bounded Convex Curvature. 579-593
- Kristin Fritsch, Janin Heuer, Raman Sanyal, Nicole Schulz:
The Martin Gardner Polytopes. 594-601 - Christopher Ennis:
Between the Cracks: Filling Space with Polygonal Shapes. 602-617 - Kiana Mittelstaedt:
A Stochastic Approach to Eulerian Numbers. 618-628 - Noam Zimhoni:
A Forest of Eisensteinian Triangles. 629-637
- Sam Northshield:
A Short Proof of Fermat's Two-square Theorem. 638
- Christian Elsholtz:
Unconditional Prime-Representing Functions, Following Mills. 639-642 - Toby Alfred-Jones:
A Short Proof of the Uniform Smoothness of Certain Lebesgue Spaces. 643-648 - Warren P. Johnson:
Down with Weierstrass! 649-653 - Brian Hopkins, James A. Sellers:
Turning the Partition Crank. 654-657
- The Paul R. Halmos-Lester R. Ford Awards for 2019. 657
- George Stoica:
Components Used in the Stone-Weierstrass Theorem. 658
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and Solutions. 659-667
- Meredith L. Greer:
Reviews. 668-671
- Vadim Ponomarenko:
The Mathematical Association of America Prime. 672
Volume 127, Number 8, 2020
- Mark Krusemeyer, Daniel H. Ullman:
The Eightieth William Lowell Putnam Mathematical Competition. 675-687
- Ben Blum-Smith, Japheth Wood:
Chords of an Ellipse, Lucas Polynomials, and Cubic Equations. 688-705 - Rachel Eaton, Kurt Herzinger, Ian Pierce, Jeremy L. Thompson:
Numerical Semigroups and the Game of Sylver Coinage. 706-715
- Dennis L. Sun:
Wald's Identity and Geometric Expectation. 716
- Gary R. Lawlor:
l'Hôpital's Rule for Multivariable Functions. 717-725 - Louis Crane, David N. Yetter:
Tetrahedal Geometry from Areas. 726-733
- Alexandru Tupan:
A Simple Proof of the Siebeck-Marden Theorem. 734-736 - Benedikt Wirth:
Green's Function for the Neumann-Poisson Problem on n-Dimensional Balls. 737-743
- Surinder Pal Singh:
Null Subsets of All Sizes Inside Vitali Sets. 743
- Jackson Autry, Tara Gomes, Christopher O'Neill, Vadim Ponomarenko:
Elasticity in Apéry Sets. 744-749 - Karthik Chandrasekhar, Richard Ehrenborg, Frits Beukers:
A Counting Proof for When 2 Is a Quadratic Residue. 750-751
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and solutions. 752-761
- Gao-Wen Xi, Qiu-Ming Luo:
A Formula for the Stirling Numbers of the Second Kind. 762
- Kevin P. Knudson:
Discrete Morse Theory by Nicholas Scoville. 763-768
Volume 127, Number 9, 2020
- Louis Deaett:
Matroids and the Minimum Rank Problem for Matrix Patterns. 771-788 - Yuki Nakandakari, Shuichi Tsukuda:
An Elementary Proof That the Third Finite Subset Space of the Circle is the 3-Sphere. 789-805
- Angelina Y. M. Chin:
Counting Pairs to Find a Finite Field. 806
- Krzysztof Chris Ciesielski, Yichen Liu:
Distinct Continuous Maps with All Riemann Sums Equal. 807-819 - Anton A. Kutsenko:
An Entire Function Connected with the Approximation of the Golden Ratio. 820-826 - Benjamin Sambale:
On a Theorem of Ledermann and Neumann. 827-834
- Michael Mandler:
A Quick Proof of the Order-Extension Principle. 835
- Jens Marklof:
Delone Sets Generated by Square Roots. 836-840 - Vilmos Komornik:
A Short, Elementary Introduction to the Exponential Function. 841-846
- Dmitry Krachun, Zhi-Wei Sun:
Each Positive Rational Number Has the Form φ(m2)/φ(n2). 847-849
- Peter J. McGrath:
Bases for Second Order Linear ODEs. 849
- Dan Stefan Marinescu, Mihai Monea:
A Very Short Proof of the Hermite-Hadamard Inequalities. 850-851
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and solutions. 852-860
- Jo Boaler:
Mathematics for Human Flourishing. 861-864
Volume 127, Number 10, 2020
- Tevian Dray:
Using Embedding Diagrams to Visualize Curvature. 867-879 - Mikkel Abrahamsen, Jacob Holm, Eva Rotenberg, Christian Wulff-Nilsen:
Escaping an Infinitude of Lions. 880-896 - Hiroshi Maehara, Horst Martini:
Tangent Spheres of Tetrahedra and a Theorem of Grace. 897-910 - Adam Coffman, Yuan Zhang:
Vector Fields with Continuous Curl but Discontinuous Partial Derivatives. 911-917 - Ulrich Abel, Vitaliy Kushnirevych:
Reducing Multiple Integrals of Beukers's Type. 918-926
- George Stoica:
Two Uniqueness Theorems at Work. 927
- Bowen Yao:
A Note on Fraction Decompositions of Integers. 928-932 - Anatoly Eydelzon:
On a New Property of the Steiner Inellipse. 933-935 - Desmond MacHale:
Are There More Finite Rings than Finite Groups? 936-938
- Idris David Mercer:
Another Proof of the Infinitude of Primes. 938
- Daniel H. Ullman, Daniel J. Velleman, Douglas B. West:
Problems and Solutions. 944-952
- Lara 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. 953-957
- Susan Jane Colley:
Editor's Endnotes. 958-960
- Monthly Referees for 2020. i-iii
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