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The American Mathematical Monthly, Volume 122
Volume 122, Number 1, January 2015
- Scott T. Chapman:
A Letter from the Editor: 2015 is the Centennial Year of the MAA. 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 - Titu Andreescu, Vladimir Georgiev
, Oleg Mushkarov:
Napoleon Polygons. 24-29 - Kenneth S. Williams:
Historical Remark on Ramanujan′s Tau Function. 30-35 - Branko Curgus, Robert I. Jewett:
Somewhat Stochastic Matrices. 36-42 - Michael Hardy:
Stereographic Trigonometric Identities. 43-47 - Xianzu Lin:
Infinitely Many Primes in the Arithmetic Progression kn-1. 48-51 - P. Mark Kayll:
Deranged Matchings: Enumeration by Integration!! 51 - Francis C. Motta, Patrick D. Shipman, 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 - 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 - Problems and Solutions. 75-82
- Edward F. Schaefer:
The Mathematics of Encryption: An Elementary Introduction. 83-88
Volume 122, Number 2, February 2015
- Yves Nievergelt:
Backward Analysis Explained with Monthly Payments. 91-120 - Christopher O'Neill, 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 - Carlos A. Catalá de la Torre:
A New Proof for a Sharp van der Corput's Lemma. 138-142 - Sahin Koçak:
Dihedral Angles of the Regular n-Simplex. 143 - Arseniy V. Akopyan:
Geometry of the Cardioid. 144-150 - Marcelo Brafman:
Another Algebraic Pythagorean Proof. 150 - G. Molinari:
Elementary Prime Identities. 151-154 - Joachim Gräter, Karl-Joachim Wirths:
On Elementary Bounds for ∑k=n∞ 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, Esther M. García-Caballero:
A Geometric Proof of Morrie's Law. 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 - Problems and Solutions. 175-182
- Gerald B. Folland:
Hidden Harmony - Geometric Fantasies: The Rise of Complex Function Theory. 183-188
Volume 122, Number 3, March 2015
- 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, 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, Esther M. García-Caballero:
A Geometric Proof of Morrie's Law. 233 - Jaap Eising
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, 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 ℝn onto ℝn. 268-271 - Mizan R. Khan, 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 Horák:
Partitioning ℝn into Connected Components. 280-283 - Konstantinos Gaitanas:
An Explicit Formula for the Prime Counting Function Which is Valid Infinitely Often. 283 - Problems and Solutions. 284-291
- Reuben Hersh:
How Humans Learn to Think Mathematically. Exploring the Three Worlds of Mathematics. 292-296
Volume 122, Number 4, April 2015
- Vadim Ponomarenko
A Base Conversion Surprise. - Richard Montgomery:
The Three-Body Problem and the Shape Sphere. 299-321 - Rebekah Ann Gilbert:
A Fine Rediscovery. 322-331 - Juliá Cufí, Agustí Reventó, Carlos J. Rodríz:
Curvature for Polygons. 332-337 - Karl Dilcher, 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, Brian R. Hunt:
Absolute Continuity of a Function and Uniform Integrability of Its Divided Differences. 362-366 - Michal Adamaszek
Face Numbers of Down-Sets. 367-370 - Dirk Huylebrouck
Generalizing Wallis' Formula. 371-372 - Mehmet Kiliç:
A New Geometric Proof for Morley's Theorem. 373-376 - Hidefumi Katsuura:
A New Infinite Series Representation of lnk. 376 - Maxim Arnold
Cyclic Evasion in the Three Bug Problem. 377-380 - Dorde Baralic
A Short Proof of the Bradley Theorem. 381-385 - Byron Schmuland:
Linear Recurrences via Probability. 386-389 - Problems and Solutions. 390-397
- Will Traves:
Perspectives in Projective Geometry. A Guided Tour Through Real and Complex Geometry. 398-402
Volume 122, Number 5, May 2015
- Donald G. Saari:
Mathematics and the "Dark Matter" Puzzle. 407-423 - Alex Chin, Gary Gordon, Kellie J. MacPhee
Pick a Tree - Any Tree. 424-432 - Christian Aebi
Generalizations of Wilson's Theorem for Double-, Hyper-, Sub- and Superfactorials. 433-443 - Óscar Ciaurri, Luis M. Navas
A Simple Computation of ζ (2k). 444-451 - Nam Gu Heo:
A New Proof of the Pythagorean Theorem. 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 - Ivan Izmestiev
A Porism for Cyclic Quadrilaterals, Butterfly Theorems, and Hyperbolic Geometry. 467-475 - Maria Bras-Amorós
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 - 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 - Ádám Besenyei:
The Brocard Angle and a Geometrical Gem from Dmitriev and Dynkin. 495-499 - Problems and Solutions. 500-507
- Gerald B. Folland:
A History in Sum: 150 Years of Mathematics at Harvard (1825-1975) by Steve Nadis and Shing-Tung Yau. 508-510
Volume 122, Number 6, June 2015
- Dennis D. A. Epple, 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, Norbert Hungerbühler:
A Simple Proof of Poncelet's Theorem (on the Occasion of Its Bicentennial). 537-551 - Aaditya Salgarkar, Rishi Mehta:
Alternate Derivation for the Parity of the nth Triangular Number. 551 - Nicholas J. Werner
Covering Numbers of Finite Rings. 552-566 - Jamal Rooin, Akram Alikhani:
A Geometric Proof of the Beppo-Levi Inequality. 566 - Alan Haynes, Sara Munday
Diophantine Approximation and Coloring. 567-580 - Haryono Tandra:
A Proof of the Replacement Theorem by the Notion of Maximal Elements. 580 - Satomi Murakami, Hiroki Ohwa:
Periodic Points of Some Discontinuous Mappings. 581-586 - Vadim Ponomarenko
Asymptotic Formula for (1 + 1/x)x, Revisited. 587 - Virgil Barnard:
A Proof of Quadratic Reciprocity. 588-592 - Daniel Daners
Uniform Continuity of Continuous Functions on Compact Metric Spaces. 592 - Iosif Pinelis:
On the Hölder and Cauchy-Schwarz Inequalities. 593-595 - José Gascón:
Another Proof That the Real Numbers ℝ Are Uncountable. 596-597 - Haryono Tandra:
A Simple Modified Version for Ferguson's Proof of the Extreme Value Theorem. 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 - Problems and Solutions. 604-612
- Marion Cohen:
Mathematicians on Creativity. 613-616
Volume 122, Number 7, 2015
- 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, Ana Berrizbeitia, Michael Dairyko, Claudia Rodriguez, Amanda Ruiz, 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
- 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
- James E. McClure, 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 - Problems and Solutions. 700-707
- Jeffrey Nunemacher, Joseph Malkevitch:
Reviews. 708-712
Volume 122, Number 8, 2015
- Leonard F. Klosinski, Gerald L. Alexanderson, Mark Krusemeyer:
The Seventy-Fifth William Lowell Putnam Mathematical Competition. 715-725 - Jack Cassidy:
Early Round Bluffing in Poker. 726-744 - Tom M. Apostol, Mamikon A. Mnatsakanian:
Volume/Surface Area Relations for n-Dimensional Spheres, Pseudospheres, and Catenoids. 745-756 - Paul Pollack, Joseph Vandehey:
Besicovitch, Bisection, and the Normality of 0.(1)(4)(9)(16)(25) ... 757-765 - Shui-Hung Hou, Edwin S. H. Hou:
On a Recursion Formula Related to Confluent Vandermonde. 766-772 - Syahida Che Dzul-Kifli, 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
- Tadashi Tokieda:
A Viscosity Proof of the Cauchy-Schwarz Inequality. 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, Matthias Gorny:
An Exponential Inequality for Symmetric Random Variables. 786-789 - Melvyn B. Nathanson:
Pairs of Matrices in GL2(R≥0) That Freely Generate. 790-792
- Zsolt Lengvárszky:
Pythagoras by Integral. 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 M. Borwein, Scott T. Chapman:
I Prefer Pi: Addenda. 800
- Problems and Solutions. 801-808
- Jeffrey Nunemacher, Ferebee Tunno:
Reviews. 809-812
- Tamás Titkos:
How to Make Equivalent Measures? 812
Volume 122, Number 9, 2015
- Zhiqin Lu, Julie Rowlett
The Sound of Symmetry. 815-835 - Péter Hajnal
Convex Polygons and Common Transversals. 836-844 - Titu Andreescu, Vladimir Georgiev, Oleg Mushkarov:
Correction to "Napoleon Polygons". 844 - Qingchun Ren, Jürgen Richter-Gebert
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, Aviezri S. Fraenkel, 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
- Nguyen S. Hoang:
A Limit Comparison Test for General Series. 893-896 - Hamid Reza Daneshpajouh
A New Proof of ℵ0-Resolvability of a Metric Space Without an Isolated Point. 897-898
- Problems and Solutions. 899-906
- Jeffrey Nunemacher, Robin Hartshorne:
Reviews. 907-911 - Jeffrey Nunemacher, Michael Henle:
Reviews. 912-915
Volume 122, Number 10, 2015
- Zhaiming Shen
The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics. 919-940 - Fred Kuczmarski, 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
A Graph Partition Problem. 972-982 - Jaime Gaspar:
All Triangles at Once. 982 - Guram Bezhanishvili, 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
- Mehmet Kiliç, Sahin Koçak:
On Products of Uniquely Geodesic Spaces. 990-994 - Sadi Abu-Saymeh, Mowaffaq Hajja, 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
- Junming Zhu:
A Semi-Finite Proof of Jacobi′s Triple Product Identity. 1008-1009
- Problems and Solutions. 1010-1017
- Jeffrey Nunemacher, Michael Harris:
Reviews. 1018-1022
- Scott T. Chapman:
Editor's Endnotes. 1023-1025
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