Journal: The American Mathematical Monthly

Volume 121, Issue 9

751 -- 753Fred Adler, Elizabeth S. Allman, Lisette G. de Pillis. A Letter from the Guest Editors
754 -- 770Jonathan R. Potts, Mark A. Lewis. A Mathematical Approach to Territorial Pattern Formation
771 -- 792Mike Steel. Tracing Evolutionary Links between Species
793 -- 809Roderick Edwards, Leon Glass. Dynamics in Genetic Networks
810 -- 823Hoa Nguyen, Ricardo Cortez, Lisa Fauci. Computing Flows Around Microorganisms: Slender-Body Theory and Beyond
824 -- 839David Terman. Mathematical Neuroscience
840 -- 856Trachette Jackson, Natalia Komarova, Kristin Swanson. Mathematical Oncology: Using Mathematics to Enable Cancer Discoveries
857 -- 867Laurie J. Heyer, Jeffrey L. Poet. Synthetic Biology: A New Frontier

Volume 121, Issue 8

663 -- 673Leonard F. Klosinski, Gerald L. Alexanderson, Mark Krusemeyer. The Seventy-Fourth William Lowell Putnam Mathematical Competition
674 -- 688Persi Diaconis, Xuancheng Shao, Kannan Soundararajan. Carries, Group Theory, and Additive Combinatorics
689 -- 699Marc Deléglise, Andrew Markoe. On the Maximum Arc Length of Monotonic Functions
700 -- 705David Borwein, Jonathan M. Borwein. Deriving New Sinc Results from Old
706 -- 710Michael Joswig, Günter M. Ziegler. Foldable Triangulations of Lattice Polygons
711 -- 716Jonathan Novak. Pólya's Random Walk Theorem
717 -- 722Michael Schramm, John Troutman, Daniel Waterman. Segmentally Alternating Series
722 -- 0John Molokach. Law of Cosines - A Proof Without Words
723 -- 726Mark H. Holmes. Connections Between Cubic Splines and Quadrature Rules
727 -- 733M. Scott Osborne. Hausdorffization and Such
734 -- 737Donald M. Davis. Binomial Coefficients Involving Infinite Powers of Primes
738 -- 745. Problems and Solutions
746 -- 748Brian M. Loft. The Cult of Pythagorus: Math and Myths. By Alberto A. Martínez. University of Pittsburgh Press, Pittsburgh, PA, 2012, xxii +264 pp., ISBN 978-0-8229-4418-8, $27.95

Volume 121, Issue 7

563 -- 589Erwan Brugallé, Kristin M. Shaw. A Bit of Tropical Geometry
589 -- 0Marcelo Brafman. Another Algebraic Pythagorean Proof
590 -- 598Bryan Brown, Michael Dairyko, Stephan Ramon Garcia, Bob Lutz, Michael Someck. Four Quotient Set Gems
600 -- 609Vinícius Gusmão Pereira de Sá, Celina M. Herrera de Figueiredo. Blind-friendly von Neumann's Heads or Tails
610 -- 618Richard Katz, Mike Krebs, Anthony Shaheen. Zero Sums on Unit Square Vertex Sets and Plane Colorings
618 -- 0Don Zagier. A Refinement of a Theorem of J. E. Littlewood
619 -- 624Rajendra Bhatia, Rajesh Sharma. Positive Linear Maps and Spreads of Matrices
625 -- 631Wen D. Chang, Russell A. Gordon. Trisecting Angles in Pythagorean Triangles
631 -- 0Diego Marques. Yet Another Direct Proof of the Uncountability of the Transcendental Numbers
632 -- 636Rom Pinchasi. Points Covered an Odd Number of Times by Translates
637 -- 639Meinolf Geck. On the Characterization of Galois Extensions
639 -- 0Samuel G. Moreno, Esther M. García-Caballero. Simpson's Rule and Sums of Powers
640 -- 643F. Dreher, T. Samuel. Continuous Images of Cantor's Ternary Set
644 -- 647Robert A. Beezer. Extended Echelon Form and Four Subspaces
648 -- 657. Problems and Solutions
658 -- 660Michael Barr. The Outer Limits of Reason. Noson Yanofsky. MIT Press, Cambridge, MA and London, England, 2013, xiv + 403 pp., ISBN 978-0-262-01935-4, $29.95

Volume 121, Issue 6

471 -- 485Alberto Facchini, Giulia Simonetta. Rational Numbers, Finite Cyclic Monoids, Divisibility Rules, and Numbers of Type 99...900...0
486 -- 498David Borwein, Jonathan M. Borwein, Brailey Sims. On the Solution of Linear Mean Recurrences
498 -- 0Josef Rukavicka. Rejection of Laplace's Demon
499 -- 505Charles W. Groetsch, S. A. Yost. Vertical Projection in a Resisting Medium: Reflections on Observations of Mersenne
506 -- 514J. Scott Carter, Daniel S. Silver, Susan G. Williams. Three Dimensions of Knot Coloring
514 -- 0Harris Kwong. An Alternate Proof of Sury's Fibonacci-Lucas Relation
515 -- 522Jose Pujol. On Hamilton's Nearly-Forgotten Early Work on the Relation between Rotations and Quaternions and on the Composition of Rotations
522 -- 0B. Sury. A Heuristic Argument for Hua's Identity Using Geometric Series
523 -- 528Tommy Wright. Lagrange's Identity and Congressional Apportionment
529 -- 533Chai Wah Wu. Pigeonholes and Repunits
534 -- 536Kevin K. Ferland. Record Crossword Puzzles
537 -- 540Michael Z. Spivey. A Combinatorial Proof for the Alternating Convolution of the Central Binomial Coefficients
541 -- 544Nikolai Nikolov, Blagovest Sendov. A Converse of the Gauss-Lucas Theorem
545 -- 546Yared Nigussie. Finding Your Seat Versus Tossing a Coin
547 -- 548Erich Badertscher. A Simple Direct Proof of Marden's Theorem
549 -- 556. Problems and Solutions
557 -- 560James A. Swenson. Which Numbers Are Real?. By Michael Henle. Mathematical Association of America, Washington, DC, 2012, x+219 pp., ISBN 978-0-88385-777-9, $53.00

Volume 121, Issue 5

379 -- 390Allison Henrich, Louis H. Kauffman. Unknotting Unknots
391 -- 402Alan F. Beardon, Ian Short. A Geometric Representation of Continued Fractions
403 -- 415Tom Leinster. Rethinking Set Theory
415 -- 0Allan J. Kroopnick. An Elementary Application of Brouwer's Fixed Point Theorem to Transition Matrices
416 -- 421Jon Grantham, Witold Jarnicki, John Rickert, Stan Wagon. Repeatedly Appending Any Digit to Generate Composite Numbers
422 -- 432Iddo Ben-Ari, Diana Hay, Alexander Roitershtein. On Wallis-type Products and Pólya's Urn Schemes
433 -- 437Paul Pollack, Enrique Treviño. The Primes that Euclid Forgot
438 -- 443Emmanuel Tsukerman. Solution of Sondow's Problem: A Synthetic Proof of the Tangency Property of the Parbelos
443 -- 0José Ángel Cid Araújo. A Difference Equation Leading to the Irrationality of √ 2
444 -- 0Nathan A. Carlson. A Connection between Furstenberg's and Euclid's Proofs of the Infinitude of Primes
445 -- 446Ming-Chia Li. An Elementary Proof of a Generalization of Banach's Mapping Theorem
447 -- 448M. L. Glasser. A Technique in Contour Integration
449 -- 454Kyle Luh, Nicholas Pippenger. Large-Deviation Bounds for Sampling without Replacement
455 -- 462. Problems and Solutions
463 -- 466Daniel Ullman. Math on Trial: How Mathematics Is Used and Abused in the Courtroom. By Leila Schneps and Coralie Colmez, Basic Books, New York, 2013, xi+256 pp., ISBN 978-0-465-03292-1, $26.99
467 -- 468. Editor's Endnotes

Volume 121, Issue 4

283 -- 298Andrew J. Simoson. Periodicity Domains and the Transit of Venus
299 -- 317Daniel J. Velleman. A Drug-Induced Random Walk
318 -- 331Alexei Yu. Uteshev. Analytical Solution for the Generalized Fermat-Torricelli Problem
331 -- 0Samuel J. Ferguson. A One-Sentence Line-of-Sight Proof of the Extreme Value Theorem
332 -- 337Martin Kovár, Alena Chernikava. On the Proof of the Existence of Undominated Strategies in Normal Form Games
338 -- 343Chao-Ping Chen, Junesang Choi. x Based on the Partition Function
344 -- 349Steffen Eger. Stirling's Approximation for Central Extended Binomial Coefficients
350 -- 352Thorsten Neuschel. A New Proof of Stirling's Formula
353 -- 354Ralph M. Krause. Zeta(2) Once Again
355 -- 358Andrea M. Hyde, Paul D. Lee, Blair K. Spearman. 2 + 3) Solvable Modulo Any Integer
359 -- 360B. Sury. Macaulay Expansion
361 -- 364Jerry J. Koliha. Evaluating Lebesgue Integrals Efficiently with the FTC
365 -- 372. Problems and Solutions
373 -- 376Jeffrey Nunemacher. Encounters with Chaos and Fractals, 2nd edition. By Denny Gulick. Chapman and Hall/CRC Press, Boca Raton, 2012, xvi + 371 pp., ISBN 978-1-58488-517-7, $79.95

Volume 121, Issue 3

187 -- 190Kenneth A. Ross, Ann E. Watkins. Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2014 to Joan Leitzel for Distinguished Service to Mathematics
191 -- 206David H. Bailey, Jonathan M. Borwein. Pi Day Is Upon Us Again and We Still Do Not Know if Pi Is Normal
207 -- 212Stephan Berendonk. The Length of Spirographic Curves
213 -- 221Alec S. Cooper, Oleg Pikhurko, John R. Schmitt, Gregory S. Warrington. Martin Gardner's Minimum No-3-in-a-Line Problem
222 -- 228Aleksander Maliszewski, Marcin Szyszkowski. Level Sets on Disks
229 -- 236Junesang Choi, Hari M. Srivastava. Series Involving the Zeta Functions and a Family of Generalized Goldbach-Euler Series
236 -- 0B. Sury. A Polynomial Parent to a Fibonacci-Lucas Relation
237 -- 243Trevor Hyde. A Wallis Product on Clovers
244 -- 248Mircea Merca. On Some Power Sums of Sine or Cosine
249 -- 253William Johnston. 2(ℝ)
254 -- 257Gerd Herzog. A Proof of Lie's Product Formula
258 -- 259Kenneth Lange. Hadamard's Determinant Inequality
259 -- 0Sahin Koçak, M. Limoncu. Mean of the Mean of the Mean ..
260 -- 262Justin Tatch Moore. Justin Tatch Moore
263 -- 265Marc Chamberland, Doron Zeilberger. A Short Proof of McDougall's Circle Theorem
266 -- 273. Problems and Solutions
274 -- 278Mark Kozek. Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media. Edited by Jessica K. Sklar and Elizabeth S. Sklar; Foreword by Keith Devlin. McFarland, Jefferson, NC, 2012, viii + 345 pp., ISBN 978-0-7864-4978-1, $45

Volume 121, Issue 2

95 -- 108Eric C. Chi, Kenneth Lange. A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization
109 -- 119Vincent Coll, Mike Harrison. Two Generalizations of a Property of the Catenary
120 -- 135Pantelis A. Damianou. A Beautiful Sine Formula
136 -- 144Ron Evans, Lihua Huang, Tuan Nguyen. Keeler's Theorem and Products of Distinct Transpositions
144 -- 0Jaime Gaspar. Non-recursive Polynomial Formula for the Sum of the Powers of the Integers
145 -- 149David Grant. The Quadratic Gauss Sum Redux
149 -- 0Miles Dillon Edwards. A Possibly New Proof of the Law of Cos
150 -- 153Yuly Billig, John D. Dixon. An Eigenvalue Theorem for Systems of Polynomial Equations
154 -- 157Hongwei Lou. A Short Proof of Stirling's Formula
158 -- 161Richard Ehrenborg. Hamiltonian Cycles on Archimedean Solids Are Twisting Free
162 -- 164Chua Cheong Siong. A Simple Proof of Ljunggren's Binomial Congruence
164 -- 0Daniel J. Velleman. Monthly Gems
165 -- 166Peter J. McGrath. Another Proof of Clairaut's Theorem
167 -- 169Hossein Hosseini Giv. Proving the Banach-Alaoglu Theorem via the Existence of the Stone-Čech Compactification
170 -- 177. Problems and Solutions
178 -- 182Harold P. Boas. Invitation to Classical Analysis, American Mathematical Society, Providence, RI, 2012, xiii + 392 pp., ISBN 978-0-8218-6932-1, $74.00. by Peter Duren
183 -- 0Peter D. Lax. Numbers and Functions: From a Classical Experimental Mathematicians Point of View, American Mathematical Society, Providence, RI, 2012, 504 pp., ISBN 978-0821887950, $58. by Victor H. Moll

Volume 121, Issue 10

871 -- 889Peter J. Giblin, John Paul Warder. Evolving Evolutoids
890 -- 902Pieter Moree. Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers
903 -- 908Lei Ni. A Perron-type Theorem on the Principal Eigenvalue of Nonsymmetric Elliptic Operators
909 -- 916Pete L. Clark, Niels J. Diepeveen. Absolute Convergence in Ordered Fields
917 -- 921William F. Trench. An Unnoticed Consequence of Szegö's Distribution Theorem
922 -- 926Jack Button, Maurice Chiodo, Mariano Zeron-Medina Laris. Coset Intersection Graphs for Groups
927 -- 931Sam Northshield. Complex Descartes Circle Theorem
932 -- 936Pallab Kanti Dey, R. Thangadurai. The Length of an Arithmetic Progression Represented by a Binary Quadratic Form
937 -- 941Marshall Hampton. Cosines and Cayley, Triangles and Tetrahedra
942 -- 945Felipe Acker. A Note on the Spectral Theorem in the Finite-Dimensional Real Case
946 -- 953. Problems and Solutions
954 -- 956Genevieve Walsh. Mostly Surfaces. By Richard Evan Schwartz. American Mathematical Society, Providence, RI, 2010, xiii+ 314 pp., ISBN 978-0-8218-5368-9, $47.00
957 -- 959. Editor′s Endnotes
960 -- 962. Monthly Referees for 2014
963 -- 0Jonathan Sondow. Monthly Over 100 Years Ago..
964 -- 0Amrik Singh Nimbran. One More Proof of the Irrationality of √2

Volume 121, Issue 1

3 -- 4Scott T. Chapman. A Letter from the Editor: What's In a Color?
5 -- 17Melvyn B. Nathanson. Additive Systems and a Theorem of de Bruijn
18 -- 32Mario Ponce, Patricio Santibáñez. On Equidistant Sets and Generalized Conics: The Old and the New
33 -- 44Anthony Mendes, Kent E. Morrison. Guessing Games
45 -- 59Chris D. Lynd. Using Difference Equations to Generalize Results for Periodic Nested Radicals
60 -- 68J. A. Conejero, P. Jiménez-Rodríguez, Gustavo A. Muñoz-Fernández, Juan B. Seoane-Sepúlveda. When the Identity Theorem "Seems" to Fail
69 -- 72Ádám Besenyei. Peano's Unnoticed Proof of Borel's Theorem
73 -- 74Steven H. Weintraub. Values of Polynomials over Integral Domains
75 -- 77Bao Qin Li. A Direct Proof and a Transcendental Version of the Fundamental Theorem of Algebra via Cauchy's Theorem
78 -- 80Samuel Clowes Huneke. An Inductive Proof of Hex Uniqueness
81 -- 82Karim Boulabiar. C(Ω)
83 -- 90. Problems and Solutions
91 -- 92Kenneth A. Ross. In the Dark on the Sunny Side: a Memoir of an Out-of-Sight Mathematician, Mathematical Association of America, Washington, DC, 2012, 206 pp., ISBN 978-0883855812, $50. by Larry Baggett