Journal: The American Mathematical Monthly

Volume 112, Issue 9

765 -- 785Ibtesam Bajunaid, Joel M. Cohen, Flavia Colonna, David Singman. Function Series, Catalan Numbers, and Random Walks on Trees
786 -- 798Dan Kalman. Virtual Empirical Investigation: Concept Formation and Theory Justification
799 -- 806Nikolai V. Ivanov. A Differential Forms Perspective on the Lax Proof of the Change of Variables Formula
807 -- 816Roger C. Alperin. The Modular Tree of Pythagoras
817 -- 822Ray Redheffer. The Behavior of Solutions near a Stable or Semistable Stationary Point
822 -- 825Michael Nyblom. More Nested Square Roots of 2
825 -- 826A. R. Naghipour. A Simple Proof of Cohen's Theorem
826 -- 829Thierry Coquand, Henri Lombardi. A Short Proof for the Krull Dimension of a Polynomial Ring
829 -- 831Robert Myers. An Elementary Proof of Joris's Theorem
832 -- 838Michael Monastyrsky. Some Remarks on "Mathematics at the Tlirn of the Millennium"
839 -- 0M. N. Deshpande. Problem 11181
839 -- 0David Beckwith. Problem 11183
839 -- 0Suat Namli. Problem 11180
839 -- 0Shahin Amrahov. Problem 11182
840 -- 0Slavko Simic. Problem 11184
840 -- 0Angelo J. Christino Jr., William C. Waterhouse. Problem 11186
840 -- 841Kent Holing, Richard Stong. A Special Set of Integer Points in Space: 11050
840 -- 0Rainer Brück. Problem 11185
841 -- 843Slavko Simic, John H. Lindsey II. Equivalent Asymptotics: 11063
843 -- 844George Lamb, O. P. Lossers. Integral by Mellin Transform: 11067
844 -- 845Herbert S. Wilf, Kenneth Schilling. Think Rationally: 11068
845 -- 846George Lamb, T. K. Callahan. Evaluate an Integral: 11072
847 -- 850J. David Logan. Mathematical Models in Biology by Elizabeth S. Allman; John A. Rhodes
850 -- 851Virginia McShane Warfield. Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition by Steve Olson

Volume 112, Issue 8

673 -- 681Karl Dilcher, Kenneth B. Stolarsky. A Pascal-Type Triangle Characterizing Twin Primes
682 -- 704David A. Cox, Jerry Shurman. Geometry and Number Theory on Clovers
705 -- 712George Leibman. A Nonstandard Proof of the Fundamental Theorem of Algebra
713 -- 725Leonard F. Klosinski, Gerald L. Alexanderson, Loren C. Larson. The Sixty-Fifth William Lowell Putnam Mathematical Competition
726 -- 729N. V. Rao. The Stone-Weierstrass Theorem Revisited
729 -- 734Jonathan Sondow. A Faster Product for and a New Integral for ln
734 -- 740I. M. Isaacs, M. R. Pournaki. Generalizations of Fermat's Little Theorem via Group Theory
740 -- 742Geoffrey Brown. Convexity and Minkowski's Inequality
743 -- 748Boris A. Rosenfeld. The Analytic Principle of Continuity
749 -- 0William Calbeck. Problem 11175
749 -- 0M. N. Deshpande. Problem 11173
749 -- 0Pál Péter Dályay. Problem 11174
749 -- 0Oleg Faynshteyn. Problem 11176
750 -- 0Jon Louis Bentley, Colin Mallows. Problem 11178
750 -- 751Manoj Prakash Singh, Richard Stong. A Prime Summandification of n: 11045
750 -- 0David Beckwith. Problem 11179
750 -- 0Dorin Marghidanu. Problem 11177
751 -- 0Syrous Marivani, O. P. Lossers. Modular Sequences Defined by Polynomials: 11047
751 -- 0Shahin Amrabov, Bernardo M. Ábrego. An Application of Fermat's Little Theorem: 11054
752 -- 0John H. Lindsey II, Omran Kouba. Maximum Compared to Average: 11056
752 -- 753Óscar Ciaurri, O. P. Lossers. A Vanishing Infinite Sum: 11058
753 -- 754Matthew Coppenbarger. "Little Boxes Made of Ticky-Tacky": 11060
754 -- 755Kenneth Schilling. Powered Divergence: 11062
755 -- 0John E. Wetzel, Li Zhou. Lengths of Wrapped Curves: 11064
755 -- 756Douglas B. Tyler, Robin Chapman. A More General Presentation: 11065
757 -- 762Judith V. Grabiner. From Newton to Hawking: A History of Cambridge University's Lucasian Professors of Mathematics by Kevin C. Knox; Richard Noakes

Volume 112, Issue 7

585 -- 601Kang-Tae Kim, Steven G. Krantz. The Automorphism Groups of Domains
602 -- 611Greg Dresden, Wayne M. Dymàcek. Finding Factors of Factor Rings over the Gaussian Integers
612 -- 630Dov Aharonov, Alan F. Beardon, Kathy Driver. Fibonacci, Chebyshev, and Orthogonal Polynomials
631 -- 638Stephen T. Ahearn. Tolstoy's Integration Metaphor from War and Peace
639 -- 641Mark Finkelstein, Robert Whitley. Eigenvalues, Almost Periodic Functions, and the Derivative of an Integral
641 -- 645João Araújo 0002, James D. Mitchell. An Elementary Proof That Every Singular Matrix Is a Product of Idempotent Matrices
645 -- 651Michael J. Grady. A Group Theoretic Approach to a Famous Partition Formula
651 -- 653David A. Ross. An Elementary Proof of Lyapunov's Theorem
654 -- 0Kent Holing. Problem 11168
654 -- 0Mohammad Hossein Mehrabi. Problem 11169
654 -- 0Vicentiu Radulescu. Problem 11167
654 -- 0Greg Oman. Problem 11166
655 -- 0Heinz-Jürgen Seiffert. Problem 11172
655 -- 657Óscar Ciaurri, Florin Boca. Hyperbolic-Looking Special Functions: 11041
655 -- 0Emeric Deutsch. Problem 11170
655 -- 0Chu Cheng. Problem 11171
657 -- 0Michael Golomb. Don't the Problem Ebitees Read the Monthly? 11043
657 -- 659Michel Bataille, Li Zhou. A Combinatorial Sum Goes on Tangent: 11044
659 -- 660Matthias Beck, Marcin Mazur, Shelemyahu Zacks. "Ordinary" Spherical Triangles: 11048
660 -- 661Vasile Mihai, Zoltán Vörös. One of the Morley Triangles: 11049
661 -- 662Wu Wei Chao. Two Functional Equations: 11053
662 -- 663Razvan A. Satnoianu, Daniele Donini. Medians and Altitudes and the Sum of the Radii: 11055
664 -- 671Kenneth B. Stolarsky. Analytic Theory of Polynomials by Qazi Ibadur Rahman; Gerhard Schmeisser; Complex Polynomials by Terry Sheil-Small

Volume 112, Issue 6

481 -- 492Arthur T. Benjamin, Naiomi T. Cameron. Counting on Determinants
493 -- 501Jonathan M. Borwein, Kwok-Kwong Stephen Choi, Wilfried Pigulla. Continued Fractions of Tails of Hypergeometric Series
502 -- 511Michel Balinski. What Is Just?
512 -- 514Nathaniel Grossman. A Lagrange Inversion Theorem
515 -- 521Mark A. Pinsky. Mean Values and the Maximum Principle: A Proof in Search of More Theorems
521 -- 522Hiroshi Maehara, Tudor Zamfirescu. On the Perimeter of a Triangle in a Minkowski Plane
523 -- 524Daniel Frohn. A (K)-Ring Satisfying the Ascending Chain Condition on Principal Ideals That Is Not a Principal Ideal Ring
524 -- 525Lee Lorch. Continuous Ranking of Zeros of Cylinder Functions
526 -- 566Viktor Blåsjö. The Isoperimetric Problem
567 -- 0Emeric Deutsch. Problem 11161
567 -- 0George Lamb. Problem 11159
567 -- 0Michel Bataille. Problem 11163
567 -- 0Marc Chamberland. Problem 11160
567 -- 0Paolo Perfetti. Problem 11162
568 -- 569William P. Wardlaw, Richard Stong. Adjoint over the Smallest Field: 11034
568 -- 0Yogesh More. Problem 11165
568 -- 0José Luis Díaz-Barrero. Problem 11164
569 -- 572M. L. Glasser, George Lamb. One Easy, One Hard: 11036
572 -- 573Noah Rosenberg, Richard Bagby. Integral over a Simplex: 11039
573 -- 0Yongge Tian, et al.. Range Identities for Hermitian Idempotent Matrices: 11040
573 -- 574M. N. Deshpande, John Henry Steelman. An Invariance of Variance over Expectation: 11042
575 -- 579D. J. H. Garling. The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele
579 -- 581Loukas Grafakos. Constantin Carathéodory: Mathematics and Politics in Turbulent Times by Maria Georgiadou

Volume 112, Issue 5

385 -- 416Arturo Magidin, David McKinnon. Gauss's Lemma for Number Fields
417 -- 425Florian Deloup. The Fundamental Group of the Circle Is Trivial
426 -- 439Antonio Behn, Christopher Kribs-Zaleta, Vadim Ponomarenko. The Convergence of Difference Boxes
440 -- 449Paul E. Becker. Do Normal Subgroups Have Straight Tails?
450 -- 454Raghib M. Abu-Saris, Wajdi Ahmad. Avoiding Eigenvalues in Computing Matrix Powers
454 -- 458Francesc Comellas, José Luis Andres Yebra. Exact Solutions for Minimax Optimization Problems
459 -- 462F. G. Avkhadiev. A Simple Proof of the Gauss-Winckler Inequality
462 -- 466Mowaffaq Hajja. Copositive Symmetric Cubic Forms
467 -- 0Mircea Ivan. Problem 11152
467 -- 0Emmanuel Kowalski. Problem 11155
467 -- 0Paul Bracken. Problem 11153
467 -- 0Kent Holing. Problem 11154
467 -- 468Richard Stanley. Problem 11156
468 -- 0Hillel Gauchman. Problem 11157
468 -- 0Juan-Bosco Romero Márquez, Martin E. Muldoon. Gamma Function Bounds: 11016
468 -- 0David Beckwith. Problem 11158
469 -- 470Mark Pinsky, Nicholas Singer. The Stationary Distribution of a Tridiagonal Row-Stochastic Matrix: 11032
469 -- 0Tim Keller, Doyle Henderson. One Good Factorization Deserves Another: 11029
470 -- 472M. N. Deshpande, R. M. Welukar, Richard Stong. Expansion by Inclusion-Exclusion: 11033
472 -- 473Omer Yayenie, Joe Geiman. Evaluation of an Integral: 11035
473 -- 474M. L. J. Hautus, Julien Grivaux. Shrinking Fréchet Differentiable Maps: 11037
474 -- 0Floor van Lamoen, Michel Bataille. Morley's Triangle and Lemma: 11038
475 -- 478Daniel J. Madden. Abstract Algebra by Ronald Solomon; Integers, Polynomials and Rings by Ronald S. Irving
479 -- 480John Sylvester. Introduction to the Mathematics of Medical Imaging by Charles L. Epstein

Volume 112, Issue 4

289 -- 310Don Shimamoto, Catherine Vanderwaart. Spaces of Polygons in the Plane and Morse Theory
311 -- 321Edward B. Burger. A Tail of Two Palindromes
322 -- 333Sherman Stein. Remarks on the Gravity Equation
334 -- 341Christopher S. Simons. An Elementary Approach to the Monster
342 -- 350Daniel J. Velleman. The Generalized Simpson's Rule
351 -- 356Boris Mirman. Sufficient Conditions for Poncelet Polygons Not to Close
356 -- 358Jürgen Kindler. A Simple Proof of Sion's Minimax Theorem
358 -- 363John Clifford, David James, Michael A. Lachance, Joan Remski. A Constructive Approach to Singular Value Decomposition and Symmetric Schur Factorization
363 -- 365Marco Dall'Aglio, Fabio Maccheroni. Fair Division without Additivity
366 -- 0M. L. Glasser. Problem 11148
366 -- 0Joel Zinn. Problem 11145
366 -- 0Pamela Gorkin. Problem 11147
366 -- 0Yongge Tian. Problem 11146
367 -- 0Donald E. Knuth. Problem 11151
367 -- 0Emeric Deutsch. Problem 11150
367 -- 0Mircea Ivan, Ioan Rasa. Problem 11149
367 -- 369Jonathan Sondow, Richard Stong, Julien Grivaux. An Identity Involving Harmonic Numbers: 11026
369 -- 370H. Reuvers, Li Zhou, A. Engle. Triangles Inscribed in a Circle: 11027
370 -- 371Götz Trenkler, G. P. Shannon. Hermitian Products of Hermitian Matrices: 11028
371 -- 372Steven Butler, Bruce R. Ebanks. A Functional Equation: 11030
372 -- 373Li Zhou, Robin Chapman. Monster Mean Tamed: 11031
374 -- 381David E. Rowe. Mathematicians under the Nazis by Sanford L. Segal

Volume 112, Issue 3

197 -- 199Robert E. Megginson. Yueh-Gin Gung and Dr. Charles Y. Hu Award to Gerald L. Alexanderson for Distinguished Service to Mathematics
200 -- 211Roger C. Alperin. Trisections and Totally Real Origami
212 -- 232John Bryk, Cesar E. Silva. Measurable Dynamics of Simple p-adic Polynomials
233 -- 250Ivor Grattan-Guinness. The "Ecole Polytechnique", 1794-1850: Differences over Educational Purpose and Teaching Practice
251 -- 256William Duke, Kimberly Hopkins. Quadratic Reciprocity in a Finite Group
257 -- 263Shay Gueron, Itai Shafrir. A Weighted Erdős-Mordell Inequality for Polygons
264 -- 266Luo Xuebo, Zhu-Jun Zheng. An Inequality for Homogeneous Polynomials on
266 -- 268Peter G. Anderson, Arthur T. Benjamin, Jeremy A. Rouse. Combinatorial Proofs of Fermat's, Lucas's, and Wilson's Theorems
269 -- 270Kurt Girstmair. On an Irreducibility Criterion of M. Ram Murty
270 -- 272Robert J. MacG. Dawson. On a "Singular" Integration Technique of Poisson
273 -- 0Roberto Tauraso. Problem 11138
273 -- 0Grahame Bennett. Problem 11139
273 -- 0Walther Janous. Problem 11140
273 -- 0Richard Bagby. Problem 11141
273 -- 274Donald E. Knuth. Problem 11142
274 -- 0Joel Zinn. Problem 11076
274 -- 277Slavko Simic, Richard Stong. Entire Functions of Order Zero: 11018
274 -- 0Alexander Dubinov, Irina Dubinova. Problem 11143
274 -- 0Ernst Schulte-Geers. Problem 11144
274 -- 0Arturas Dubickas. Problem 11123
274 -- 0Bob Berk, Larry Shepp. Problem 11120
277 -- 278Bernardo Recamán Santos, Michail Reid, Kevin Ford. Cycling via Common Divisors: 11019
279 -- 280Donald E. Knuth, Silvia Fernández, Gerry Myerson. A Modular Triple: 11021
280 -- 0Wu Wei Chao, Nadjib Bouzar, Allan K. Swett. A Timely Problem: 11023
280 -- 0Razvan A. Satnoianu, Walther Janous. A Two-Triangle Inequality: 11022
281 -- 288Gerald B. Folland, Jeffrey L. Stuart. Linear Algebra by John B. Fraleigh; Raymond A. Beauregard; Linear Algebra and its Applications by David Lay; Linear Algebra: A Geometric Approach by Theodore Shifrin; Malcolm R. Adams; Introduction to Linear Algebra by Gilbert Strang

Volume 112, Issue 2

105 -- 118Gregory S. Warrington. Juggling Probabilities
119 -- 130Alex D. D. Craik. Prehistory of Faà di Bruno's Formula
131 -- 140Paolo Codecà, Mohan Nair. The Lesser-Known Δ-Function in Number Theory
141 -- 154Juan Carlos Álvarez Paiva, Anthony Thompson. On the Perimeter and Area of the Unit Disc
155 -- 164Ian Doust, Michael D. Hirschhorn, Jocelyn Ho. Trigonometric Identities, Linear Algebra, and Computer Algebra
165 -- 167Connie Maude Campbell, William Staton. A Square-Packing Problem of Erdős
168 -- 171Laurentiu Panaitopol. On the Representation of Natural Numbers as Sums of Squares
171 -- 175Jiu Ding, Temple H. Fay. The Perron-Frobenius Theorem and Limits in Geometry
176 -- 179Piotr Hajlasz, Pawel Strzelecki. How to Measure Volume with a Thread
180 -- 0Kent D. Boklan. Problem 11134
180 -- 0N. G. de Bruijn. Problem 11131
180 -- 0Paul Bracken. Problem 11133
180 -- 0Jonathan Sondow. Problem 11132
181 -- 0Ray Redheffer. Problem 11135
181 -- 182Donald P. Minassian. Baire Class One: 10999
181 -- 0Vicentiu Radulescu. Problem 11137
181 -- 0Raymond Mortini. Problem 11136
182 -- 183George Lamb, Zafar Ahmed. An Application of the Gaussian Integral: 11011
183 -- 184Calin Popescu, Chu Wenchang. Cube Sum Inequalities: 11012
184 -- 185Achilleas Sinefakopoulos, Knut Dale. A Recursively Defined Series: 11014
184 -- 0David Callan, Marc Renault. Dyck Paths Skipping Every Fourth Point: 11013
185 -- 186Ovidiu Furdui, Li Zhou. Sines in a Triangle: 11015
186 -- 187C. R. Pranesachar, Saïd Amghibech. When the Brocard Points Are Collinear with a Vertex: 11017
188 -- 191Eric S. Weber. An Introduction to Frames and Riesz Bases by Ole Christensen
191 -- 194Jeffrey Nunemacher. Geometry by David A. Brannan; Matthew F. Esplen; Jeremy J. Gray

Volume 112, Issue 10

0 -- 0. Volume Information
861 -- 875Lisa D. Humphreys, P. Joseph McKenna. When a Mechanical Model Goes Nonlinear: Unexpected Responses to Low-Periodic Shaking
876 -- 890Eric Driver, Philip A. Leonard, Kenneth S. Williams. Irreducible Quartic Polynomials with Factorizations modulo p
891 -- 909Stephen M. Zemyan. On the Zeroes of the Nth Partial Sum of the Exponential Series
910 -- 912Jan J. Dijkstra. On Homeomorphism Groups and the Compact-Open Topology
913 -- 919Zhibo Chen, Gary L. Mullen. Transpositions and Representability
919 -- 921Oleg Pikhurko. Generating Edge-Labeled Trees
921 -- 924Adrian Dumitrescu. A Remark on the Erdős-Szekeres Theorem
924 -- 925Seon-Hong Kim. On the Moduli of the Zeros of a Polynomial
926 -- 928Leif Arkeryd. Nonstandard Analysis
929 -- 930Barthel Wayne Huff. Problem 11191
929 -- 0Lajos Csete. Problem 11189
929 -- 0José Luis Díaz-Barrero. Problem 11190
929 -- 0David Bailey. Problem 11188
929 -- 0Li Zhou. Problem 11187
930 -- 0Marian Tetiva. Problem 11193
930 -- 0Brett Stevens. Problem 11192
930 -- 932Floor van Lamoen. Six Surprises from Four Lines: 11025
932 -- 933Sebastian M. Cioaba, Tim LeSaulnier, Dan Saracino. A Sufficient Condition for Commutativity: 11066
933 -- 0Götz Trenkler, Lawrence J. Baker. An Easy Complex Inequality: 11075
933 -- 0Péter Ivády, Richard Stong. Sine Bound: 11069
934 -- 0Gheorge Costovici, Uros Milutinovic. An Oscillating Sequence: 11077
934 -- 935Razvan A. Satnoianu, Li Zhou. A Majorization Consequence: 11080
935 -- 0Stephen Morse, Robin Chapman. Harmonious Trios Are the Vertices of a Regular Icosahedron: 11081
936 -- 0Marty Getz, Dixon Jones. Errata: Partitioning by Arithmetic Progressions
936 -- 0Michael Golomb, Kit Hanes. The Orthocenter of a Simplex: 11087
936 -- 0Wu Wei Chao. Errata: Continuous Additive Functions
937 -- 940Gerald B. Folland. Functional Analysis by Peter D. Lax; John Wiley; Functional Analysis: An Introduction by Yuli Eidelman; Vitaly Milman; Antonis Tsolomitis
941 -- 946Bruce P. Palka. Editor's Endnotes

Volume 112, Issue 1

1 -- 19William Dunham. Touring the Calculus Gallery
20 -- 31Marcel Wild. The Groups of Order Sixteen Made Easy
32 -- 41Shif Berhanu, Ahmed Mohammed. A Harnack Inequality for Ordinary Differential Equations
42 -- 50Janko Hernández, Leonel Robert. Figures of Constant Width on a Chessboard
51 -- 60H. S. Bear, Dale Myers. A Simpler Approach to Integration and the Fubini Theorem
61 -- 65Jonathan Sondow. Double Integrals for Euler's Constant and in and an Analog of Hadjicostas's Formula
66 -- 69Dan Romik. Roots of the Derivative of a Polynomial
69 -- 76Joel L. Weiner, George R. Wilkens. Quaternions and Rotations in
76 -- 78José Carlos de Sousa, Oliveira-Santos. Another Proof of the Fundamental Theorem of Algebra
79 -- 86V. F. Kagan. Riemann's Geometric Ideas
87 -- 0Bogdan Nica. Problem 11124
87 -- 0Li Zhou. Problem 11127
87 -- 0Shahin Amrahov. Problem 11125
87 -- 0James S. Weber. Problem 11126
88 -- 0Paul Bateman. Problem 11130
88 -- 0Tom Apostol. Problem 11128
88 -- 0Yongge Tian. Problem 11129
88 -- 89Victor Pambuccian, Michael Wolterman. Saccheri Quadrilateral: 11004
88 -- 0Wu Wei Chao, O. P. Lossers. Point Causing Equal Angles: 10996
89 -- 90Marty Getz, Dixon Jones, Ken Dutch. Partitioning by Arithmetic Progressions: 11005
90 -- 91Bogdan Suceava, Daniele Donini. A Circle Centered on the Euler Circle: 11006
91 -- 92José Luis Díaz-Barrero, Juan José Egozcue, Arturas Dubickas. Zero and Coefficient Inequality: 11008
92 -- 93David Borwein, Julien Grivaux. Convex and Concave Functions: 11009
93 -- 94Erwin Just, Norman Schaumberger, et al.. Regular Polygon Inscription: 11010
95 -- 98Steve Kennedy. Turing: A Novel About Computation by Christos H. Papadimitriou
98 -- 101Marion Deutsche Cohen. The Magic of Numbers by Benedict Gross; Joe Harris