Journal: The American Mathematical Monthly

Volume 123, Issue 9

0 -- 0. Editorial Board
847 -- 848Scott T. Chapman. A Letter From the Editor: Jonathan M. Borwein (1951-2016)
849 -- 870Paul Baginski, Ryan Rodriguez, George J. Schaeffer, Yiwei She. Finding Elements With Given Factorization Lengths and Multiplicities
871 -- 883Lyle Ramshaw. Stråhle's Equal-Tempered Triumph
884 -- 893Jean C. Cortissoz. A Note on Harmonic Functions on Surfaces
894 -- 899Uuganbaatar Ninjbat. Another Memorable Mongolian Olympiad Problem: A Two-Colored Rectangular Lattice
900 -- 908Joshua Brown Kramer, Jonathan Cutler, A. J. Radcliffe. The Multistep Friendship Paradox
909 -- 918Sean Eastman, Selwyn Hollis, Kawee Numpacharoen, Jared Schlieper. The Volume of the Spatial Region Corresponding to n × n Correlation Matrices
919 -- 0Ivica Martinjak. Two Extensions of the Sury's Identity
920 -- 923Bernd Schomburg. Primitivity and Orbit Decomposition
924 -- 927Adrian W. Dudek. On the Success of Mishandling Euclid's Lemma
928 -- 930Alan J. Hoffman, Chai Wah Wu. A Simple Proof of a Generalized Cauchy - Binet Theorem
931 -- 935Nicolae Anghel. Optimal Bounds for the Roots of Polynomials
936 -- 939Anthony J. Bevelacqua. A Family of Non-Euclidean PIDs
940 -- 0Kuldeep Kumar Kataria. An Alternate Proof of the Binomial Theorem
941 -- 948. Problems and Solutions
949 -- 952Jeffrey Nunemacher, Gerald B. Folland. Reviews

Volume 123, Issue 8

0 -- 0. Editorial Board
739 -- 752Leonard F. Klosinski, Gerald L. Alexanderson, Mark Krusemeyer. The Seventy-Sixth William Lowell Putnam Mathematical Competition
753 -- 776Jeffrey C. Lagarias. Erdős, Klarner, and the 3x + 1 Problem
777 -- 788Dvij Bajpai, Daniel J. Velleman. Anonymity in Predicting the Future
789 -- 801Philippe Caldero, Jérôme Germoni. Equilateral Triangles and the Fano Plane
802 -- 807T. S. Michael, Val Pinciu. The Art Gallery Theorem, Revisited
808 -- 813Lon Mitchell, Michael A. Jones, Brittany Shelton. Abelian and Non-Abelian Triangle Mysteries
814 -- 816Yong Kong, Shaowei Zhang. The Adventitious Angles Problem: The Lonely Fractional Derived Angle
817 -- 820Jesús Jerónimo-Castro, C. Yee-Romero. Maximal Isoptic Chords of Convex Curves
821 -- 824Olivier de La Grandville. An Alternate Derivation of the Euler-Poisson Equation
824 -- 0J. A. Grzesik. Yet Another Analytic Proof of Napoleon's Theorem
825 -- 830Bálint Farkas, Sven-Ake Wegner. Variations on Barbălat's Lemma
831 -- 839. Problems and Solutions
840 -- 843Jeffrey Nunemacher, Mark Kidwell. Reviews
843 -- 0Halil Mutuk. A Physical Proof for Cauchy's Inequality

Volume 123, Issue 7

0 -- 0. Editorial Board
627 -- 642Laura Florescu, Lionel Levine, Yuval Peres. The Range of a Rotor Walk
643 -- 656Lawrence Zalcman. A Tale of Three Theorems
657 -- 682Márton Balázs, Áron Folly. An Electric Network for Nonreversible Markov Chains
683 -- 688Vincent Coll, Jeff Dodd. A Characteristic Averaging Property of the Catenary
689 -- 698Dennis Ivanov, Serge Tabachnikov. The Six Circles Theorem Revisited
699 -- 700Arnon Avron, Nachum Dershowitz. Cayley's Formula: A Page From The Book
701 -- 703Michael Hardy. On Tangents and Secants of Infinite Sums
704 -- 709Alex Kasman. Factorization of a Matrix Differential Operator Using Functions in Its Kernel
710 -- 715Brian D. Sittinger. Computing ζ(2m) by Using Telescoping Sums
716 -- 721Yuanyuan Yao, Wenxia Li. Generating Iterated Function Systems for the Vicsek Snowflake and the Koch Curve
722 -- 730. Problems and Solutions
731 -- 736Jeffrey Nunemacher, Matthew Richey. Reviews

Volume 123, Issue 6

0 -- 0. Editorial Board
519 -- 541Jennifer M. Johnson, János Kollár. Arcology
542 -- 556Steve Butler, Persi Diaconis, Ron Graham 0001. The Mathematics of the Flip and Horseshoe Shuffles
557 -- 573Valerio De Angelis, Dominic Marcello. Wilf's Conjecture
574 -- 582F. Adrián F. Tojo. A Hyperbolic Analog of the Phasor Addition Formula
583 -- 591Pablo A. Panzone. Tiling the Plane with Different Hexagons and Triangles
592 -- 596Franklin H. J. Kenter. How to Win Your Betting Pool with Jensen's Inequality and the Law of Large Numbers
597 -- 599Erhan Gürel. On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products
600 -- 604Hunter Swan. Expected Number of Vertices of a Hypercube Slice
604 -- 0Peter McCauley. Proofs Without Using Limits of Both Calculus Power Rules
605 -- 608Pham Duy Khanh, Marc Lassonde. Quasiconvex Linear Perturbations and Convexity
609 -- 612Ariel Amir, Mikhail Lemeshko, Tadashi Tokieda. Surprises in Numerical Expressions of Physical Constants
613 -- 620. Problems and Solutions
621 -- 624Jeffrey Nunemacher, Leslie Hogben, Mark Hunacek. Reviews

Volume 123, Issue 5

0 -- 0. Editorial Board
415 -- 426Søren Eilers. The LEGO Counting Problem
427 -- 438Harold P. Boas. Mocposite Functions
439 -- 447Tom M. Apostol, Mamikon A. Mnatsakanian. A New Look at Surfaces of Constant Curvature
448 -- 470Jaime Cruz-Sampedro, Margarita Tetlalmatzi-Montiel. Hardy's Reduction for a Class of Liouville Integrals of Elementary Functions
470 -- 0Piotr Josevich. An Alternative Approach to the Product Rule
471 -- 480Gary L. Mullen, Daniel Panario, David Thomson. Fast and Simple Modular Interpolation Using Factorial Representation
481 -- 0Iosif Pinelis. On Measurable Semigroups in ℝ
482 -- 485Arseniy Sheydvasser. A Corrigendum to Unreasonable Slightness
486 -- 490Karl Dilcher, Christophe Vignat. Euler and the Strong Law of Small Numbers
490 -- 0Tim Hsu. Rational Nonaxis Points on the Unit Circle Have Irrational Angles
491 -- 496Iosif Pinelis. Explicit Additive Decomposition of Norms on ℝ2
497 -- 501Michael Gaul, Fred Kuczmarski. Parabolas and Archimedes' 2/3-Property
502 -- 503Peter McGrath. An Extremely Short Proof of the Hairy Ball Theorem
504 -- 511. Problems and Solutions
512 -- 514Jeffrey Nunemacher, Gerald L. Alexanderson. Reviews
515 -- 516Scott T. Chapman. Editor's End Notes

Volume 123, Issue 4

0 -- 0. Editorial Board
311 -- 337Paul-Jean Cahen, Jean-Luc Chabert. What You Should Know About Integer-Valued Polynomials
338 -- 346Keith Johnson, Kira Scheibelhut. Rational Polynomials That Take Integer Values at the Fibonacci Numbers
347 -- 362Gary Brookfield. Factoring Forms
363 -- 375Grant Cairns, Yuri Nikolayevsky, Gavin Rossiter. Conewise Linear Periodic Maps of the Plane with Integer Coefficients
376 -- 381Mohamed Ayad, Omar Kihel, Jesse Larone. When Does a Given Polynomial with Integer Coefficients Divide Another?
382 -- 386Neil J. Calkin, Beth Novick, Hayato Ushijima-Mwesigwa. What Moser Could Have Asked: Counting Hamilton Cycles in Tournaments
386 -- 0Nuno Luzia. A Proof of The Pythagorean Theorem After Descartes
387 -- 391Ovidiu Costin, Neil Falkner, Jeffery D. McNeal. Some Generalizations of the Riemann-Lebesgue Lemma
392 -- 397Peter S. Landweber, Emanuel A. Lazar, Neel Patel. On Fiber Diameters of Continuous Maps
397 -- 0Daniel López-Aguayo. Irrationality via Maximality
398 -- 0Dennis S. Bernstein, Khaled F. Aljanaideh, Arthur E. Frazho. Laurent Series and ℓp Sequences
399 -- 406. Problems and Solutions
407 -- 412Jeffrey Nunemacher, Thomas Garrity. Reviews

Volume 123, Issue 3

0 -- 0. Editorial Board
211 -- 213Jennifer J. Quinn. Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2016 to George Berzsenyi for Distinguished Service to Mathematics
214 -- 240Karen Hunger Parshall. Mathematics and the Politics of Race: The Case of William Claytor (Ph.D., University of Pennsylvania, 1933)
241 -- 257John P. Boyd 0001. Correcting Three Errors in Kantorovich & Krylov's Approximate Methods of Higher Analysis
258 -- 266Boris M. Bekker, Oleg A. Ivanov, Alexander S. Merkurjev. Milnor's Lemma, Newton's Method, and Continued Fractions
267 -- 273Clark Kimberling, Kenneth B. Stolarsky. Slow Beatty Sequences, Devious Convergence, and Partitional Divergence
274 -- 279Steve Butler, Ron Graham 0001, Richard Stong. Inserting Plus Signs and Adding
280 -- 286Tom Mertens, Jeff Weeks. Electromagnetism in a Multiconnected Universe
287 -- 291Jeffrey S. Ovall. The Laplacian and Mean and Extreme Values
292 -- 295Peter McGrath. On the Smooth Jordan Brouwer Separation Theorem
295 -- 0José L. Ramírez. An Identity of Carlitz and Its Generalization
296 -- 303. Problems and Solutions
304 -- 308Jeffrey Nunemacher, Craig H. Jackson. Reviews

Volume 123, Issue 2

115 -- 135Francis C. Motta, Patrick D. Shipman, Bethany Springer. Optimally Topologically Transitive Orbits in Discrete Dynamical Systems
136 -- 148Ian Morrison, David Swinarski. Can You Play a Fair Game of Craps with a Loaded Pair of Dice?
149 -- 160Deborah A. Kent, David J. Muraki. A Geometric Solution of a Cubic by Omar Khayyam... in Which Colored Diagrams Are Used Instead of Letters for the Greater Ease of Learners
160 -- 0Mariano Suárez-Álvarez. Cyclic Extensions Are Radical
161 -- 167Josh Hiller. Old Friends in Unexpected Places: Pascal (and Other) Matrices in GLn(ℂ)
168 -- 174Richard Blecksmith, John Brillhart, Michael Decaro. Using Conic Sections to Factor Integers
175 -- 180Michael Z. Spivey. Probabilistic Proofs of a Binomial Identity, Its Inverse, and Generalizations
181 -- 184E. W. Dekking, F. M. Dekking. Helge von Koch′s Snowflake Curve Revisited
185 -- 188Jonathan Baker. Strong Convexity Does Not Imply Radial Unboundedness
189 -- 191Xin-Jie Sun. On Sums of Three Pentagonal Numbers
192 -- 196Jeffrey Lutgen. A Combinatorial Proof of an Alternating Convolution Identity for Multichoose Numbers
197 -- 204. Problems and Solutions
205 -- 208Jeffrey Nunemacher. Reviews

Volume 123, Issue 10

0 -- 0. Editorial Board
955 -- 958Scott T. Chapman. A Letter from the Editor: The Long and Winding Road
959 -- 0. Single Digit NFL Scores
960 -- 988Alfred Geroldinger. Sets of Lengths
989 -- 1000Anton A. Klyachko, Anton N. Vassilyev. Balanced Factorizations
1001 -- 1012Melvyn B. Nathanson. Cantor Polynomials and the Fueter-Pólya Theorem
1013 -- 1032Aaron M. Broussard, Martin E. Malandro, Abagayle Serreyn. Optimizing the Video Game Multi-Jump: Player Strategy, AI, and Level Design
1033 -- 1038Jeffrey C. Lagarias, Takumi Murayama, D. Harry Richman. Dilated Floor Functions That Commute
1039 -- 1044Stephan Ramon Garcia, Florian Luca. Quotients of Fibonacci Numbers
1045 -- 1048Richard Ehrenborg, Alex Happ. Parking Cars of Different Sizes
1049 -- 0. Corrigendum to "A New Proof of the Change of Variable Theorem for the Riemann Integral"
1050 -- 1057. Problems and Solutions
1058 -- 1061Jeffrey Nunemacher, Chris A. Marx. Reviews
1062 -- 1066. Monthly Referees for 2016

Volume 123, Issue 1

3 -- 18Richard D. Neidinger. A Fair-Bold Gambling Function Is Simply Singular
19 -- 39Adrien Kassel, David B. Wilson 0002. The Looping Rate and Sandpile Density of Planar Graphs
40 -- 52José Ángel Cid, Rodrigo López Pouso. Integration by Parts and by Substitution Unified with Applications to Green's Theorem and Uniqueness for ODEs
53 -- 65M. Ram Murty, Chester Weatherby. A Generalization of Euler's Theorem for ζ(2k)
66 -- 70Shivarajkumar. Beyond Schur's Conjecture
71 -- 76Yaroslav Shitov. The Diameter of Chess Grows Exponentially
77 -- 0Daniel J. Velleman. Monthly Gems
78 -- 81Michael C. Slattery. On a Property Motivated by Groups with a Specified Number of Subgroups
82 -- 87Oleg Viro. Pictorial Calculus for Isometries
87 -- 0Konstantinos Gaitanas. A Partial Solution of Representing 1 as a Sum of n Distinct Unit Fractions
88 -- 89David G. Radcliffe. A Function That Is Surjective on Every Interval
90 -- 93Thomas Osler. Iterations for the Lemniscate Constant Resembling the Archimedean Algorithm for Pi
94 -- 96Kuldeep Kumar Kataria. A Probabilistic Proof of the Multinomial Theorem
96 -- 0Xiaoxue Li. A Synthetic Approach to a USAMO Problem
97 -- 105. Problems And Solutions
106 -- 111Jeffrey Nunemacher, Darren B. Glass. Reviews
112 -- 0József Sándor. A Note on the Logarithmic Mean