The American Mathematical Monthly, Volume 119

Volume 119, Number 1, January 2012

Articles

• 
  Scott Chapman:
  A Letter from the Editor. 3
• 
  Daniel Brinkman, Peter J. Olver:
  Invariant Histograms. 4-24
• 
  Thomas Bauer, Mirel Caibar, Gary Kennedy:
  Zariski Decomposition: A New (Old) Chapter of Linear Algebra. 25-41
• 
  Dan Kalman, Mark McKinzie:
  Another Way to Sum a Series: Generating Functions, Euler, and the Dilog Function. 42-51

Notes

• 
  Costas J. Efthimiou:
  A Class of Periodic Continued Radicals. 52-58
• 
  Parames Laosinchai, Bhinyo Panijpan:
  A Geometric Interpretation of Pascal's Formula for Sums of Powers of Integers. 58-64
• 
  Pete L. Clark:
  Covering Numbers in Linear Algebra. 65-67

Problems and solutions

• 
  Problems and Solutions. 68-75

Reviews

• 
  Alan Durfee:
  Review: An Introduction to the Mathematics of Money. Springer, New York, 2007, xii + 300 pp., ISBN 978-0-387-34432-4. $79.95. by David Lovelock, Marilou Mendel, and A. Larry Wright. 76-82

Volume 119, Number 2, February 2012

Articles

• 
  Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas:
  Solving a Generalized Heron Problem by Means of Convex Analysis. 87-99
• 
  Sam Vandervelde:
  Jacobi Sum Matrices. 100-114
• 
  Donald J. Bindner, Martin J. Erickson:
  Alcuin's Sequence. 115-121
• 
  Burkard Polster, Marty Ross, David Treeby:
  A Case of Continuous Hangover. 122-139

Notes

• 
  David A. Herron:
  Riemann Maps and Diameter Distance. 140-147
• 
  Cristinel Mortici:
  A Power Series Approach to Some Inequalities. 147-151
• 
  Julian Rosen, Zachary Scherr, Benjamin Weiss, Michael E. Zieve:
  Chebyshev Mappings of Finite Fields. 151-155
• 
  Igor Pak, Rom Pinchasi:
  Collapsing Walls Theorem. 156-160

Problems and solutions

• 
  Problems and Solutions. 161-168

Reviews

• 
  José Ferreirós:
  Review: Roads to Infinity. The mathematics of truth and proof. A K Peters, Natick, MA, 2010. xi + 203 pp., ISBN 978-1-56881-466-7. $39.95 by John Stillwell. 169-176

Volume 119, Number 3, March 2012

Articles

• 
  Ann E. Watkins:
  Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2012 to John Ewing for Distinguished Service to Mathematics. 179-182
• 
  Jessica Sidman:
  An Introduction to Algebraic Geometry: Polygons, Parameterizations, and Equations. 183-198
• 
  Daniel Daners:
  The Mercator and Stereographic Projections, and Many in Between. 199-210
• 
  Yves Nievergelt:
  Real and Generic Data without Unconstrained Best-Fitting Verhulst Curves and Sufficient Conditions for Median Mitscherlich and Verhulst Curves to Exist. 211-234

Notes

• 
  William C. Waterhouse:
  Square Root as a Homomorphism. 235-239
• 
  Michael P. Cohen:
  Sample Means of Independent Standard Cauchy Random Variables Are Standard Cauchy: A New Approach. 240-244
• 
  Daniel Reem:
  Character Analysis Using Fourier Series. 245-246

Problems and solutions

• 
  Problems and Solutions. 247-254

Reviews

• 
  Gerald L. Alexanderson:
  Review: Loving and Hating Mathematics: Challenging the Myths of Mathematical Life. Princeton University Press, Princeton, NJ, 2011, xii + 416 pp. ISBN 978-0-691-14247-0, $29.95. by Reuben Hersh and Vera John-Steiner. 255-259

Volume 119, Number 4, April 2012

Articles

• 
  Rachel Wells Hall, Dmitri Tymoczko:
  Submajorization and the Geometry of Unordered Collections. 263-283
• 
  Stephen McAdam:
  Unknowable Matters: How Nature's Speed Limit on Communication Relates to Quantum Physics. 284-299
• 
  Barry J. Cox, Stan Wagon:
  Drilling for Polygons. 300-312
• 
  Kenneth Hicks, Xiang-dong Hou, Gary L. Mullen:
  Sums of Reciprocals of Polynomials over Finite Fields. 313-317
• 
  Evgeny Lakshtanov, Vera Roshchina:
  On Finiteness in the Card Game of War. 318-323
• 
  Djurdje Cvijovic, Hari M. Srivastava:
  Limit Representations of Riemann's Zeta Function. 324-330

Notes

• 
  Christian Elsholtz:
  Prime Divisors of Thin Sequences. 331-333
• 
  Isaac Edward Leonard, A. C. F. Liu:
  A Familiar Recurrence Occurs Again. 333-336
• 
  Robbert Fokkink:
  Tossing Coins to Guess a Secret Number. 337-339
• 
  Lizhou Chen:
  A Generalization of the Cayley-Hamilton Theorem. 340-342
• 
  Randall McCutcheon:
  Monochromatic Permutation Quadruples - A Schur Thing in S_n. 342-343

Problems and solutions

• 
  Problems and Solutions. 344-351

Reviews

• 
  Bonnie Shulman:
  Review: Population Games and Evolutionary Dynamics. MIT Press, Cambridge, MA, 2011, xxv + 589 pp., ISBN 978-0-262-19587-4, $65. by William H. Sandholm. 352-356

Volume 119, Number 5, May 2012

Articles

• 
  Tony Gilbert:
  Lost Mail: The Missing Envelope in the Problem of the Minimal Surface of Revolution. 359-372
• 
  Frits Beukers, Florian Luca, Frans Oort:
  Power Values of Divisor Sums. 373-380
• 
  Hassan Boualem, Robert Brouzet:
  On What Is the Almost-Near Principle. 381-397
• 
  Serge Tabachnikov:
  The (Un)equal Tangents Problem. 398-405
• 
  Lance Bryant, James Hamblin, Lenny Jones:
  A Variation on the Money-Changing Problem. 406-414

Notes

• 
  David Callan:
  Flexagons Lead to a Catalan Number Identity. 415-419
• 
  R. D. Arthan:
  Aronszajn's Criterion for Euclidean Space. 419-422
• 
  Joseph E. Borzellino, Morgan Sherman:
  When Is a Trigonometric Polynomial Not a Trigonometric Polynomial? 422-425

Problems and solutions

• 
  Problems and Solutions. 426-433

Reviews

• 
  James A. Walsh:
  Review: Randomness and Recurrence in Dynamical Systems. The Carus Mathematical Monographs Number 31, Mathematical Association of America, Washington, DC, 2010, xviii + 357 pp., ISBN 978-0-88385-043-5, $52.95. by Rodney Nillsen. 434-438

Volume 119, Number 6, June-July 2012

Articles

• 
  Dimitris Koukoulopoulos, Johann Thiel:
  Arrangements of Stars on the American Flag. 443-450
• 
  Fred Kuczmarski:
  Rolling Sinusoidal Spirals. 451-467
• 
  Robert Mandl, Thomas Pühringer, Maximilian Thaler:
  Analytic Approach to Galileo's Theorem on the Descent Time Along Two-Chord Paths in a Circle. 468-476
• 
  Paul Binding, Hans Volkmer:
  A Prüfer Angle Approach to the Periodic Sturm-Liouville Problem. 477-484
• 
  Raymond Mortini, Rudolf Rupp:
  Mappings into the Euclidean Sphere. 485-494
• 
  Branko Grünbaum:
  Is Napoleon's Theorem Really Napoleon's Theorem? 495-501

Notes

• 
  Michael Dorfling, Johan Meyer:
  On Polynomials and Divisibility. 502-506
• 
  Pedro Roitman:
  Gaussian Curvature, Mirrors, and Maps. 506-509
• 
  Alan J. Aw:
  The Turán Number and Probabilistic Combinatorics. 510-513
• 
  Walter Wyss:
  Perfect Parallelograms. 513-515
• 
  Timothy C. Wallstrom:
  The Equalization Probability of the Pólya Urn. 516-518
• 
  Lars Holst:
  A Proof of Euler's Infinite Product for the Sine. 518-521

Problems and solutions

• 
  Problems and Solutions. 522-529

Reviews

• 
  Jennifer J. Quinn:
  Review: Combinatorics the Rota Way. Cambridge University Press, New York, 2009, xii+396 pp., ISBN 978-0-521-73794-4, $40.99. by Joseph P. S. Kung, Gian-Carlo Rota, and Catherine H. Yan. 530-532

Volume 119, Number 7, August-September 2012

Articles

• 
  David Borwein, Jonathan M. Borwein, Armin Straub:
  A Sinc that Sank. 535-549
• 
  Lionel Levine, Katherine E. Stange:
  How to Make the Most of a Shared Meal: Plan the Last Bite First. 550-565
• 
  Kai F. Kristensen:
  A Nearest Integer Solution to the Longest Run of Randomly Generated Words. 566-572
• 
  Franz Lemmermeyer:
  Parametrization of Algebraic Curves from a Number Theorist's Point of View. 573-583
• 
  Peter B. Borwein, Joe Hobart:
  The Extraordinary Power of Division in Straight Line Programs. 584-592

Notes

• 
  Alin Bostan, Thierry Combot:
  A Binomial-like Matrix Equation. 593-597
• 
  Ezra Brown, Marc Chamberland:
  Generalizing Gauss's Gem. 597-601
• 
  Greg Kuperberg:
  Norms as a Function of p Are Linearly Independent in Finite Dimensions. 601-603
• 
  Cédric De Groote, Mitia Duerinckx:
  Functions with Constant Mean on Similar Countable Subsets of ℝ². 603-605
• 
  Tomasz Tkocz:
  An Upper Bound for Spherical Caps. 606-607

Problems and solutions

• 
  Problems and Solutions. 608-615

Reviews

• 
  Marion Cohen:
  Review: Change Is Possible: Stories of Women and Minorities in Mathematics. American Mathematical Society, Providence, RI, 2005, ix + 211 pp., ISBN 0-8218-3748-6, $32.00 by Patricia Clark Kenschaft. 616-620

Volume 119, Number 8, October 2012

Articles

• 
  Leonard F. Klosinski, Gerald L. Alexanderson, Mark Krusemeyer:
  The Seventy-Second William Lowell Putnam Mathematical Competition. 623-635
• 
  Yuval Ginosar, Ilan Yona:
  A Model for Pairs of Beatty Sequences. 636-645
• 
  David H. Bailey, Jonathan M. Borwein:
  Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics. 646-657
• 
  Bruce R. Ebanks:
  Looking for a Few Good Means. 658-669
• 
  Paul Pollack:
  Finiteness Theorems for Perfect Numbers and Their Kin. 670-681

Notes

• 
  Akira Sakurai:
  Vector Analysis Proof of Erdős' Inequality for Triangles. 682-684
• 
  Boris M. Makarov:
  Calculation of the Volume of Multidimensional Cones and Balls Using Cavalieris Principle. 685-689
• 
  David Angell:
  Evaluation of Certain Legendre Symbols. 690-693
• 
  Jonathan Groves:
  An Elementary Counterexample in the Compact-Open Topology. 693-694
• 
  Robert Dawson:
  Arithmetic Polygons. 695-698

Problems and solutions

• 
  Problems and Solutions. 699-706

Reviews

• 
  Mark Schwartz:
  Review: Geometry for College Students. American Mathematical Society, The Sally Series, Pure and Applied Undergraduate Texts No 8, Providence, RI, 2001. vii + 222 pp., ISBN 978-0-8218-4794-7. $62 ($49.60 to AMS members). by I. Martin Isaacs. 707-711

Volume 119, Number 9, November 2012

Articles

• 
  Michael Eisermann:
  The Fundamental Theorem of Algebra Made Effective: An Elementary Real-Algebraic Proof via Sturm Chains. 715-752
• 
  Oswaldo Rio Branco de Oliveira:
  The Fundamental Theorem of Algebra: From the Four Basic Operations. 753-758
• 
  John Lorch:
  Magic Squares and Sudoku. 759-770
• 
  Panagiota N. Panagopoulou, Paul G. Spirakis:
  Playing a Game to Bound the Chromatic Number. 771-778
• 
  David Brink:
  The Spiral of Theodorus and Sums of Zeta-values at the Half-integers. 779-786

Notes

• 
  Boris Z. Shapiro, Michael Shapiro:
  A Few Riddles Behind Rolle's Theorem. 787-793
• 
  Boris Alexeev, Jacob Tsimerman:
  Note on a War-like Card Game. 793-795
• 
  Florian Breuer:
  Newton Identities for Weierstrass Products. 796-799

Problems and solutions

• 
  Problems and Solutions. 800-807

Reviews

• 
  Stan Wagon:
  Review: In Pursuit of the Traveling Salesman. Princeton University Press, Princeton, NJ, 2012 xiii + 228 pp., ISBN 978-0-691-15270-7, $27.95. by William J. Cook. 808-811

Volume 119, Number 10, December 2012

Articles

• 
  Tanya Khovanova, Alexey Radul:
  Killer Problems. 815-823
• 
  Robert T. Jantzen, Klaus Volpert:
  On the Mathematics of Income Inequality: Splitting the Gini Index in Two. 824-837
• 
  Carla D. Martin, Mason A. Porter:
  The Extraordinary SVD. 838-851
• 
  William F. Trench:
  An Elementary View of Weyl's Theory of Equal Distribution. 852-861
• 
  Yong-Gao Chen, Min Tang:
  On the Elementary Symmetric Functions of 1, 1⁄2, ..., 1⁄n. 862-867

Notes

• 
  Rolfdieter Frank, Harald Riede:
  Hyperplane Sections of the n-Dimensional Cube. 868-872
• 
  Jacob A. Siehler:
  Tiling Hamiltonian Cycles on the 24-Cell. 872-875
• 
  Witold Sadowski:
  A Toy Forecast Model. 876-879

Problems and solutions

• 
  Problems and Solutions. 880-887

Reviews

• 
  Gerald L. Alexanderson:
  Review: Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture. Springer Verlag, Berlin and Heidelberg, 2012, xi + 289 pp., ISBN 978-3-642-22463-8, $49.95. by Birgit Bergmann, Moritz Epple, and Ruti Ungar, editors. 888-891