The American Mathematical Monthly, Volume 118

Volume 118, Number 1, January 2011

Articles

• 
  David A. Cox:
  Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First. 3-21
• 
  Jennifer M. Johnson, János Kollár:
  How Small Can a Polynomial Be Near Infinity? 22-40
• 
  Nikolai V. Ivanov:
  Arnol'd, the Jacobi Identity, and Orthocenters. 41-65

Notes

• 
  Nicholas Pippenger:
  Two Extensions of Results of Archimedes. 66-71
• 
  Paul Pollack:
  On Polynomial Rings with a Goldbach Property. 71-77
• 
  Alfonso Villani:
  Measurable Functions with a Given Set of Integrability Exponents. 77-82
• 
  Alexis Akira Toda:
  Operator Reverse Monotonicity of the Inverse. 82-83

Articles

• 
  Problems and Solutions. 84-91

Reviews

• 
  Virginia McShane Warfield:
  Review: What's Math Got To Do With It? Viking Press, London, England, 2008, xii + 273 pp., ISBN 978-0-670-01952-6, $24.95 by Jo Boaler. 92-95

Volume 118, Number 2, February 2011

Articles

• 
  David M. Bressoud:
  Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus. 99-115
• 
  Ravi Vakil:
  The Mathematics of Doodling. 116-129
• 
  Ian Short:
  Ford Circles, Continued Fractions, and Rational Approximation. 130-135
• 
  Markus Müller, Dierk Schleicher:
  How to Add a Noninteger Number of Terms: From Axioms to New Identities. 136-152
• 
  Lenny Jones:
  When Does Appending the Same Digit Repeatedly on the Right of a Positive Integer Generate a Sequence of Composite Integers? 153-160

Notes

• 
  Paul Pollack:
  On Dickson's Theorem Concerning Odd Perfect Numbers. 161-164
• 
  Eyal Ackerman, Rom Pinchasi, Ludmila Scharf, Marc Scherfenberg:
  Every Simple Arrangement of n Lines Contains an Inducing Simple n-gon. 164-167
• 
  José L. Gámez-Merino, Gustavo A. Muñoz-Fernández, Juan B. Seoane-Sepúlveda:
  A Characterization of Continuity Revisited. 167-170
• 
  Sam Northshield:
  A Short Proof and Generalization of Lagrange's Theorem on Continued Fractions. 171-175
• 
  Guisong Chang, Chen Xu:
  Generalization and Probabilistic Proof of a Combinatorial Identity. 175-177

Problems and solutions

• 
  Problems and Solutions. 178-185

Reviews

• 
  Jeffrey Nunemacher:
  Review: Understanding Analysis. Springer, New York, NY, xii + 257 pp., 2001, ISBN 978-0-367-95060-0, $54.95 by Stephen Abbott; Real Mathematical Analysis. Springer, New York, NY, xi + 437 pp., 2002, ISBN 978-0-387-95297-0, $64.95 by Charles Chapman Pugh. 186-189

Volume 118, Number 3, March 2011

Articles

• 
  Barbara Faires:
  Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2011 to Joseph A. Gallian for Distinguished Service to Mathematics. 195-197
• 
  Fernando Q. Gouvêa:
  Was Cantor Surprised? 198-209
• 
  Steven H. Weintraub:
  On Legendre's Work on the Law of Quadratic Reciprocity. 210-216
• 
  Alexander Ryba, Joseph Stern:
  Equimodular Polynomials and the Tritangency Theorems of Euler, Feuerbach, and Guinand. 217-228
• 
  Keith Burns, Boris Hasselblatt:
  The Sharkovsky Theorem: A Natural Direct Proof. 229-244
• 
  John H. Hubbard, Benjamin E. Lundell:
  A First Look at Differential Algebra. 245-261

Notes

• 
  Grant Keady:
  Lines of Best Fit for the Zeros and for the Critical Points of a Polynomial. 262-264
• 
  Sascha Kurz, Rom Pinchasi:
  Regular Matchstick Graphs. 264-267
• 
  Edward Chlebus:
  A Recursive Scheme for Improving the Original Rate of Convergence to the Euler-Mascheroni Constant. 268-274

Problems and solutions

• 
  Problems and Solutions. 275-282

Reviews

• 
  Christopher C. Leary:
  Review: Logical Labyrinths. A K Peters, Ltd., Wellesley, MA, 2009, vii + 327 pp., ISBN 978-1-56881-443-8, $49.00 by Raymond M. Smullyan. 283-286

Volume 118, Number 4, April 2011

Articles

• 
  Peter Sarnak:
  Integral Apollonian Packings. 291-306
• 
  Thomas C. Hull:
  Solving Cubics With Creases: The Work of Beloch and Lill. 307-315
• 
  Heng Huat Chan, Ling Long, Yifan Yang:
  A Cubic Analogue of the Jacobsthal Identity. 316-326
• 
  Hugh M. Hilden, José M. Montesinos-Amilibia, Débora M. Tejada, Margarita M. Toro:
  Artifacts for Stamping Symmetric Designs. 327-343
• 
  Jaume Paradís, Pelegrí Viader, Lluís Bibiloni:
  A New Singular Function. 344-354

Notes

• 
  Roger Cooke:
  A Remark on Euclid's Theorem on the Infinitude of the Primes. 355-358
• 
  James Rickards:
  When Is a Polynomial a Composition of Other Polynomials? 358-363
• 
  Pieter Moree:
  A Top Hat for Moser's Four Mathemagical Rabbits. 364-370

Problems and solutions

• 
  Problems and Solutions. 371-378

Reviews

• 
  Susan Jane Colley:
  Review: The Mathematics of Sex: How Biology and Society Conspire to Limit Talented Women and Girls. Oxford University Press, Oxford-New York, 2010, xv + 270 pp., ISBN 978-0-19-538939-5, $34.95 by Stephen J. Ceci and Wendy M. Williams. 379-382

Volume 118, Number 5, May 2011

Articles

• 
  David S. Watkins:
  Francis's Algorithm. 387-403
• 
  R. Michael Range:
  Where Are Limits Needed in Calculus? 404-417
• 
  Vincent Vatter:
  Maximal Independent Sets and Separating Covers. 418-423
• 
  Mikhail Skopenkov:
  Packing a Cake into a Box. 424-433
• 
  Alan Tucker:
  What Every Mathematician Should Know about Standards-Based Tests. 434-447

Notes

• 
  Geoffrey R. Robinson:
  Cauchy's Theorem and Sylow's Theorem from the Cyclic Case. 448-449
• 
  Alan D. Sokal:
  A Really Simple Elementary Proof of the Uniform Boundedness Theorem. 450-452
• 
  Marian Deaconescu, Gary L. Walls:
  On the Group of Automorphisms of a Group. 452-455
• 
  Bogdan Nica:
  The Unreasonable Slightness of E₂ over Imaginary Quadratic Rings. 455-462

Problems and solutions

• 
  Problems and Solutions. 463-470

Reviews

• 
  Peggy Aldrich Kidwell:
  Review: Mathematics in Historical Context. Mathematical Association of America, Washington, DC, 2009, x + 409, ISBN: 978-0-88385-570-6, $58.50. by Jeffrey Suzuki. 471-474

Volume 118, Number 6, June-July 2011

Articles

• 
  Fred Kuczmarski:
  Roads and Wheels, Roulettes and Pedals. 479-496
• 
  Martin Griffiths:
  The Golden String, Zeckendorf Representations, and the Sum of a Series. 497-507
• 
  Rafe Jones:
  Achievement Sets of Sequences. 508-521
• 
  Pamela Gorkin, Elizabeth Skubak:
  Polynomials, Ellipses, and Matrices: Two Questions, One Answer. 522-533
• 
  Ronald F. Wotzlaw, Günter M. Ziegler:
  A Lost Counterexample and a Problem on Illuminated Polytopes. 534-543

Notes

• 
  János Pach, Ethan Sterling:
  Conway's Conjecture for Monotone Thrackles. 544-548
• 
  Kieren MacMillan, Jonathan Sondow:
  Proofs of Power Sum and Binomial Coefficient Congruences via Pascal's Identity. 549-551
• 
  Caleb Emmons:
  Meromorphic Continuation of Dirichlet Series via Derivations. 551-556

Problems and solutions

• 
  Problems and Solutions. 557-564

Reviews

• 
  Robin Hartshorne:
  Review: Continuous Symmetry: From Euclid to Klein. American Mathematical Society, Providence, RI, 2007, xxi + 546 pp., ISBN 978-0821839003, $69. by William Barker and Roger Howe. 565-568

Volume 118, Number 7, August-September 2011

Articles

• 
  Kenneth A. Ross:
  Benford's Law, A Growth Industry. 571-583
• 
  Graham Everest, Thomas Ward:
  A Repulsion Motif in Diophantine Equations. 584-598
• 
  Alberto Torchinsky:
  The Fourier Transform and the Wave Equation. 599-609
• 
  Wayne Aitken, Franz Lemmermeyer:
  Counterexamples to the Hasse Principle. 610-628
• 
  Peyman Eslami, Pawel Góra:
  On Eventually Expanding Maps of the Interval. 629-635

Notes

• 
  Hichem Ben-el-Mechaiekh, Robert W. Dimand:
  A Simpler Proof of the Von Neumann Minimax Theorem. 636-641
• 
  Luigi Pace:
  Probabilistically Proving that ζ(2) = π^r/6. 641-643
• 
  M. Ram Murty, V. Kumar Murty:
  On a Problem of Ruderman. 644-650
• 
  Alan F. Beardon:
  Cyclic Absolute Differences of Integers. 650-652

Problems and solutions

• 
  Problems and Solutions. 653-660

Reviews

• 
  Peter Winkler:
  Review: Famous Puzzles of Great Mathematicians. American Mathematical Society, Providence, RI, 2009, xviii + 325 pp., ISBN 978-0-8218-4814-2, $36. by Miodrag S. Petkovič. 661-664

Volume 118, Number 8, October 2011

Articles

• 
  Murad Özaydin, Charlotte Simmons:
  The Birthday Trick with Lies. 667-679
• 
  Russell A. Gordon:
  Semiperimeter and Pythagorean Triples. 680-692
• 
  Alexander B. Kharazishvili:
  Measurability Properties of Vitali Sets. 693-703
• 
  Stephan Ramon Garcia, Vincent Selhorst-Jones, Daniel E. Poore, Noah Simon:
  Quotient Sets and Diophantine Equations. 704-711
• 
  Peter J. Giblin, John P. Warder:
  Reconstruction from Medial Representations. 712-725
• 
  Leonard F. Klosinski, Gerald L. Alexanderson, Loren C. Larson, Mark Krusemeyer:
  The Seventy-First William Lowell Putnam Mathematical Competition. 726-733

Notes

• 
  R. K. Oliver:
  On the Parity of a Permutation. 734-735
• 
  Wouter Kager:
  The Hitting Time Theorem Revisited. 735-737
• 
  R. Thangadurai, A. Vatwani:
  The Least Prime Congruent to One Modulo n. 737-742
• 
  Penghao Cao, Liping Yuan:
  A Blichfeldt-type Theorem for H-points. 743-746

Problems and solutions

• 
  Problems and Solutions. 747-754

Reviews

• 
  Richard Askey:
  Review: The Mathematics that Every Secondary School Math Teacher Needs to Know. Routledge, New York and London, 2010, xxvii + 732 pp., ISBN 978-0-415-99413-2 (pbk), $89.95. by Alan Sultan and Alice F. Artzt. 755-762

Volume 118, Number 9, November 2011

Articles

• 
  Bruce C. Berndt:
  The Chief Accountant and Mathematical Friend of Ramanujan - S. Narayana Aiyar. 767-776
• 
  Penny Haxell:
  On Forming Committees. 777-788
• 
  Tom M. Apostol, Mamikon A. Mnatsakanian:
  Complete Dissections: Converting Regions and Their Boundaries. 789-798
• 
  Giacomo Drago, Pier Domenico Lamberti, Paolo Toni:
  A "Bouquet" of Discontinuous Functions for Beginners in Mathematical Analysis. 799-811
• 
  John B. Cosgrave, Karl Dilcher:
  An Introduction to Gauss Factorials. 812-829

Notes

• 
  Stephen P. Glasby:
  Enumerating the Rationals from Left to Right. 830-835
• 
  Semyon N. Litvinov:
  On the Banach-Steinhaus Theorem for Topological Groups. 836-838
• 
  Michael D. Hirschhorn:
  Ramanujan's "Most Beautiful Identity". 839-845

Problems and solutions

• 
  Problems and Solutions. 846-853

Reviews

• 
  Matthew Richey:
  Review: Elementary Probability for Applications. Cambridge University Press, Cambridge, 2009, ix + 243 pp., ISBN 978-0-521-86756-6, $52.98. by Rick Durrett. 854-858

Volume 118, Number 10, December 2011

Articles

• 
  Henryk Gerlach, Heiko von der Mosel:
  On Sphere-Filling Ropes. 863-876
• 
  Géza Kós:
  On the Grasshopper Problem with Signed Jumps. 877-886
• 
  Giovanni Falcone, Marco Pavone:
  Kirkman's Tetrahedron and the Fifteen Schoolgirl Problem. 887-900
• 
  Paul Baginski, Scott T. Chapman:
  Factorizations of Algebraic Integers, Block Monoids, and Additive Number Theory. 901-920

Notes

• 
  Hayri Ardal, Tom C. Brown, Veselin Jungic:
  Chaotic Orderings of the Rationals and Reals. 921-925
• 
  Raphaël Cerf, Pierre Petit:
  A Short Proof of Cramér's Theorem in ℝ. 925-931
• 
  Bahman Kalantari:
  A Geometric Modulus Principle for Polynomials. 931-935

Problems and solutions

• 
  Problems and Solutions. 936-945

Reviews

• 
  Andrew M. Odlyzko:
  Review: Experimental Mathematics in Action. A K Peters, Wellesley, MA, 2007. xii + 322 pp., ISBN 978-1-56881-271-7. $65. by D. H. Bailey, J. M. Borwein, N. J. Calkin, R. Girgensohn, D. R. Luke, and V. H. Moll. 946-951