Table of contents for issues of American Mathematical Monthly

Last update: Sat Jan 13 16:08:59 MST 2018                Valid HTML 3.2!

Volume 117, Number 1, January, 2010
Volume 117, Number 10, December, 2010
Volume 117, Number 2, February, 2010
Volume 117, Number 3, March, 2010
Volume 117, Number 4, April, 2010
Volume 117, Number 5, May, 2010
Volume 117, Number 6, June, 2010
Volume 117, Number 7, August, 2010
Volume 117, Number 8, October, 2010
Volume 117, Number 9, November, 2010
Volume 118, Number 1, January, 2011
Volume 118, Number 10, December, 2011
Volume 118, Number 2, February, 2011
Volume 118, Number 3, March, 2011
Volume 118, Number 4, April, 2011
Volume 118, Number 5, May, 2011
Volume 118, Number 6, June, 2011
Volume 118, Number 7, August, 2011
Volume 118, Number 8, October, 2011
Volume 118, Number 9, November, 2011
Volume 119, Number 1, January, 2012
Volume 119, Number 2, February, 2012
Volume 119, Number 3, March, 2012
Volume 119, Number 4, April, 2012
Volume 119, Number 5, May, 2012
Volume 119, Number 6, June, 2012
Volume 119, Number 7, August, 2012
Volume 119, Number 8, October, 2012
Volume 119, Number 9, November, 2012
Volume 119, Number 10, December, 2012
Volume 120, Number 1, January, 2013
Volume 120, Number 2, February, 2013
Volume 120, Number 3, March, 2013
Volume 120, Number 4, April, 2013
Volume 120, Number 5, May, 2013
Volume 120, Number 6, June, 2013
Volume 120, Number 7, August, 2013
Volume 120, Number 8, October, 2013
Volume 120, Number 9, November, 2013
Volume 120, Number 10, December, 2013
Volume 121, Number 1, January, 2014
Volume 121, Number 2, February, 2014
Volume 121, Number 3, March, 2014
Volume 121, Number 4, April, 2014
Volume 121, Number 5, May, 2014
Volume 121, Number 6, June, 2014
Volume 121, Number 7, August, 2014
Volume 121, Number 8, October, 2014
Volume 121, Number 9, November, 2014
Volume 121, Number 10, December, 2014
Volume 122, Number 1, January, 2015
Volume 122, Number 2, February, 2015
Volume 122, Number 3, March, 2015
Volume 122, Number 4, April, 2015
Volume 122, Number 5, May, 2015
Volume 122, Number 6, June, 2015
Volume 122, Number 7, August, 2015
Volume 122, Number 8, October, 2015
Volume 122, Number 9, November, 2015
Volume 122, Number 10, December, 2015
Volume 123, Number 1, January, 2016
Volume 123, Number 2, February, 2016
Volume 123, Number 3, March, 2016
Volume 123, Number 4, April, 2016
Volume 123, Number 5, May, 2016
Volume 123, Number 6, June, 2016
Volume 123, Number 7, August, 2016
Volume 123, Number 8, October, 2016
Volume 123, Number 9, November, 2016
Volume 123, Number 10, December, 2016
Volume 124, Number 1, January, 2017
Volume 124, Number 2, February, 2017
Volume 124, Number 3, March, 2017
Volume 124, Number 4, April, 2017
Volume 124, Number 5, May, 2017
Volume 124, Number 6, June / July, 2017
Volume 124, Number 7, August / September, 2017
Volume 124, Number 8, October, 2017
Volume 124, Number 9, November, 2017
Volume 124, Number 10, December, 2017


American Mathematical Monthly
Volume 117, Number 1, January, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
               Aaron Abrams and   
                 Skip Garibaldi   Finding Good Bets in the Lottery, and
                                  Why You Shouldn't Take Them  . . . . . . 3--26
            Deborah E. Berg and   
             Serguei Norine and   
          Francis Edward Su and   
               Robin Thomas and   
                    Paul Wollan   Voting in Agreeable Societies  . . . . . 27--39
          Christopher S. Hardin   Agreement in Circular Societies  . . . . 40--49
                    Barry Lewis   Revisiting the Pascal Matrix . . . . . . 50--66
             Mircea I. C\^\irnu   Newton's Identities and the Laplace
                                  Transform  . . . . . . . . . . . . . . . 67--71
                 Kurt Girstmair   Farey Sums and Dedekind Sums . . . . . . 72--78
       Friedrich Pillichshammer   Euler's Constant and Averages of
                                  Fractional Parts . . . . . . . . . . . . 78--83
                  Richard Bagby   A Simple Proof that $\Gamma'(1) =
                                  -\gamma$ . . . . . . . . . . . . . . . . 83--85
            Gerald A. Edgar and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 86--93
         Jeffrey Nunemacher and   
                 Amir Alexander   Book Review: \booktitleThe Shape of
                                  Content: Creative Writing in Mathematics
                                  and Science, by Chandler Davis; Marjorie
                                  Wikler Senechal; Jan Zwicky  . . . . . . 94--96
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 10, December, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                Frank A. Farris   The Gini Index and Measures of
                                  Inequality . . . . . . . . . . . . . . . 851--864
                Gary Gordon and   
              Elizabeth McMahon   Moving Faces to Other Places: Facet
                                  Derangements . . . . . . . . . . . . . . 865--880
                 Oleg A. Ivanov   On the Number of Regions into Which $n$
                                  Straight Lines Divide the Plane  . . . . 881--888
             Joel C. Langer and   
                David A. Singer   When Is a Curve an Octahedron? . . . . . 889--902
            Monique Laurent and   
            Alexander Schrijver   On Leonid Gurvits's Proof for Permanents 903--911
            Jonathan Sondow and   
                       Huang Yi   New Wallis- and Catalan-Type Infinite
                                  Products for $\pi$, $e$ and $\sqrt{2 +
                                  \sqrt{2}}$ . . . . . . . . . . . . . . . 912--917
                Nadish de Silva   A Concise, Elementary Proof of
                                  Arzel\`a's Bounded Convergence Theorem   918--920
        Mihály Bessenyei   Functional Equations and Finite Groups
                                  of Substitutions . . . . . . . . . . . . 921--927
                      Shibo Liu   On the Regularity of Operators Near a
                                  Regular Operator . . . . . . . . . . . . 927--928
            Gerald A. Edger and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 929--936
         Jeffrey Nunemacher and   
                     Ethan Akin   Book Review: \booktitle[untitled]  . . . 937--940
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 2, February, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
       Natalie Priebe Frank and   
                   Sean M. Hart   A Dynamical System Using the Voronoï
                                  Tessellation . . . . . . . . . . . . . . 99--112
                  David Sherman   Variations on Kuratowski's $14$-Set
                                  Theorem  . . . . . . . . . . . . . . . . 113--123
        Tamás Keleti and   
                Elliot Paquette   The Trouble with von Koch Curves Built
                                  from $n$ gons  . . . . . . . . . . . . . 124--137
          Lutz Dümbgen and   
        Sara A. van de Geer and   
             Mark C. Veraar and   
                 Jon A. Wellner   Nemirovski's Inequalities Revisited  . . 138--160
             John E. Wetzel and   
                 Ed Scheinerman   An Ancient Elliptic Locus  . . . . . . . 161--167
            Lara K. Pudwell and   
                Eric S. Rowland   Counting Interesting Elections . . . . . 167--174
             Sam B. Nadler, Jr.   A Proof of Darboux's Theorem . . . . . . 174--175
               Emmanuel Lesigne   On the Behavior at Infinity of an
                                  Integrable Function  . . . . . . . . . . 175--181
            Gerald A. Edgar and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 182--189
         Jeffrey Nunemacher and   
               Daniel S. Silver   Book Review: \booktitle[untitled]  . . . 190--192
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 3, March, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                 Barbara Faires   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for 2010 to Kenneth A. Ross for
                                  Distinguished Service to Mathematics . . 195--197
           Marvin Jay Greenberg   Old and New Results in the Foundations
                                  of Elementary Plane Euclidean and
                                  Non-Euclidean Geometries . . . . . . . . 198--219
             David A. Levin and   
                    Yuval Peres   Pólya's Theorem on Random Walks via
                                  Pólya's Urn . . . . . . . . . . . . . . . 220--231
          Alexander Borisov and   
             Mark Dickinson and   
                Stuart Hastings   A Congruence Problem for Polyhedra . . . 232--249
                 Jan Hilmar and   
                    Chris Smyth   Euclid Meets Bézout: Intersecting
                                  Algebraic Plane Curves with the
                                  Euclidean Algorithm  . . . . . . . . . . 250--260
                 Jun Tanaka and   
            Peter F. McLoughlin   A Realization of Measurable Sets as
                                  Limit Points . . . . . . . . . . . . . . 261--266
              Dan McQuillan and   
               R. Bruce Richter   A Parity Theorem for Drawings of
                                  Complete and Complete Bipartite Graphs   267--273
              Sanjay K. Khattri   Three Proofs of the Inequality $e <
                                  {\left( {1 + \frac{1}{n}} \right)^{n +
                                  0.5}}$ . . . . . . . . . . . . . . . . . 273--277
            Gerald A. Edgar and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 278--285
                    Anil Nerode   Book Review: \booktitle[untitled]  . . . 286--288
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 4, April, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                    Adrian Rice   ``To a Factor pr\`es'': Cayley's Partial
                                  Anticipation of the Weierstrass
                                  $\wp$-Function . . . . . . . . . . . . . 291--302
                Geoffrey Pearce   Transitive Decompositions of Graphs and
                                  Their Links with Geometry and Origami    303--310
              Warren P. Johnson   Trigonometric Identities \`a la Hermite  311--327
               David Burton and   
                   John Coleman   Quasi-Cauchy Sequences . . . . . . . . . 328--333
                Grahame Bennett   $p$-Free $\ell^p$ Inequalities . . . . . 334--351
               Timothy Marshall   A Short Proof of $\zeta(2) = \pi^2 / 6$  352--353
                    So Eun Park   The Group of Symmetries of the Tower of
                                  Hanoi Graph  . . . . . . . . . . . . . . 353--360
                    Li Zhou and   
                 Lubomir Markov   Recurrent Proofs of the Irrationality of
                                  Certain Trigonometric Values . . . . . . 360--362
                 M. John Curran   Groups of Cube-Free Odd Order  . . . . . 363--365
                     Mark Kozek   An Asymptotic Formula for Goldbach's
                                  Conjecture with Monic Polynomials in
                                  $\mathbb{Z}[x]$  . . . . . . . . . . . . 365--369
            Gerald A. Edgar and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 370--377
         Jeffrey Nunemacher and   
               Sanford L. Segal   Book Review: \booktitle[untitled]  . . . 378--380
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 5, May, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                 Matthew Richey   The Evolution of Markov Chain Monte
                                  Carlo Methods  . . . . . . . . . . . . . 383--413
        A. B. Kharazishvili and   
            T. Sh. Tetunashvili   On Some Coverings of the Euclidean Plane
                                  with Pairwise Congruent Circles  . . . . 414--423
                  Sherman Stein   Transversals in Rectangular Arrays . . . 424--433
              Cristinel Mortici   Product Approximations via Asymptotic
                                  Integration  . . . . . . . . . . . . . . 434--441
          Francisco J. Freniche   On Riemann's Rearrangement Theorem for
                                  the Alternating Harmonic Series  . . . . 442--448
                Richard Steiner   Modular Divisor Functions and Quadratic
                                  Reciprocity  . . . . . . . . . . . . . . 448--451
                Peter R. Mercer   Another Application of Siebeck's Theorem 452--454
              Alan C. Lazer and   
                  Mark Leckband   The Fundamental Theorem of Algebra via
                                  the Fourier Inversion Formula  . . . . . 455--457
            Gerald A. Edgar and   
              Dough Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 458--465
         Jeffrey Nunemacher and   
            Carol S. Schumacher   Book Review: \booktitle[untitled]  . . . 466--468
             Daniel J. Velleman   Editor's Endnotes  . . . . . . . . . . . 469--470
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 6, June, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
                 James T. Smith   Definitions and Nondefinability in
                                  Geometry . . . . . . . . . . . . . . . . 475--489
           Hartmut Logemann and   
                 Eugene P. Ryan   Volterra Functional Differential
                                  Equations: Existence, Uniqueness, and
                                  Continuation of Solutions  . . . . . . . 490--511
                    Stan Gudder   Finite Quantum Measure Spaces  . . . . . 512--527
              David Borwein and   
        Jonathan M. Borwein and   
               Isaac E. Leonard   $L_p$ Norms and the Sinc Function  . . . 528--539
                  John H. Elton   Indefinite Quadratic Forms and the
                                  Invariance of the Interval in Special
                                  Relativity . . . . . . . . . . . . . . . 540--547
               Brian S. Thomson   Monotone Convergence Theorem for the
                                  Riemann Integral . . . . . . . . . . . . 547--550
                  Marco Manetti   A Proof of a Version of a Theorem of
                                  Hartogs  . . . . . . . . . . . . . . . . 550--552
               Timothy W. Jones   Discovering and Proving that $\pi$ Is
                                  Irrational . . . . . . . . . . . . . . . 553--557
            Gerald A. Edgar and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 558--565
         Charles R. Hampton and   
             Jeffrey Nunemacher   Book Review: \booktitle[untitled]  . . . 566--568
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 7, August, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
          William Cavendish and   
                 John H. Conway   Symmetrically Bordered Surfaces  . . . . 571--580
                Sam Northshield   Stern's Diatomic Sequence $0, 1, 1, 2,
                                  1, 3, 2, 3, 1, 4, \ldots{}$  . . . . . . 581--598
                 Peter J. Olver   Dispersive Quantization  . . . . . . . . 599--610
                   Thomas Stoll   A Fancy Way to Obtain the Binary Digits
                                  of $759250125 \sqrt{2}$  . . . . . . . . 611--617
              T. Amdeberhan and   
                O. Espinosa and   
                 V. H. Moll and   
                      A. Straub   Wallis--Ramanujan--Schur--Feynman  . . . 618--632
                 Mike Krebs and   
                  Thomas Wright   On Cantor's First Uncountability Proof,
                                  Pick's Theorem, and the Irrationality of
                                  the Golden Ratio . . . . . . . . . . . . 633--637
                   Filip Najman   The Diophantine Equation $x^4 \pm y^4 =
                                  i z^2$ in Gaussian Integers  . . . . . . 637--641
         Christopher Frayer and   
               James A. Swenson   Polynomial Root Motion . . . . . . . . . 641--646
            Aviezri S. Fraenkel   From Enmity to Amity . . . . . . . . . . 646--648
            Gerald A. Edgar and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 649--656
         Jeffrey Nunemacher and   
                      Peter Sin   Book Review: \booktitle[untitled]  . . . 657--660
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 8, October, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
              Gerald B. Folland   A Tale of Topology . . . . . . . . . . . 663--672
                 Jack S. Calcut   Grade School Triangles . . . . . . . . . 673--685
             Mark A. Conger and   
                   Jason Howald   A Better Way to Deal the Cards . . . . . 686--700
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Tanvolutes: Generalized Involutes  . . . 701--713
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Loren C. Larson   The Seventieth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 714--721
                Alin Bostan and   
                 Philippe Dumas   Wronskians and Linear Independence . . . 722--727
               Abbas M. Alhakim   A Simple Combinatorial Algorithm for de
                                  Bruijn Sequences . . . . . . . . . . . . 728--732
               Albert Nijenhuis   Short Gamma Products with Simple Values  733--737
                    Miyeon Kwon   Dimension, Linear Functionals, and Norms
                                  in a Vector Space  . . . . . . . . . . . 738--740
                      Anonymous   Problems and Solutions . . . . . . . . . 741--748
          Marion Deutsche Cohen   Book Review: \booktitle[untitled]  . . . 749--753
                      Anonymous   Back matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 117, Number 9, November, 2010

                      Anonymous   Front Matter . . . . . . . . . . . . . . ??
              Francis Edward Su   Teaching Research: Encouraging
                                  Discoveries  . . . . . . . . . . . . . . 759--769
                 Harold P. Boas   Julius and Julia: Mastering the Art of
                                  the Schwarz Lemma  . . . . . . . . . . . 770--785
               Taras Banakh and   
             Oleg Verbitsky and   
              Yaroslav Vorobets   Fermat's Spiral and the Line Between Yin
                                  and Yang . . . . . . . . . . . . . . . . 786--800
              Karel Hrbacek and   
           Olivier Lessmann and   
              Richard O'Donovan   Analysis with Ultrasmall Numbers . . . . 801--816
                Hendrik Lenstra   Irreducible Cubics Modulo Five . . . . . 817--821
              Mateusz Micha\lek   A Short Proof of Combinatorial
                                  Nullstellensatz  . . . . . . . . . . . . 821--823
                Sam H. Creswell   A Continuous Bijection from $\ell^2$
                                  onto a Subset of $\ell^2$ Whose Inverse
                                  Is Everywhere Discontinuous  . . . . . . 823--828
                 Nicolae Anghel   On a Question of Connes and Zagier
                                  Regarding Parallelograms Inscribed in a
                                  Pair of Confocal Ellipses  . . . . . . . 828--831
                Stephen M. Walk   A Streamlined Proof of an Essential
                                  Calculus Fact  . . . . . . . . . . . . . 832--833
            Gerald A. Edger and   
               Doug Hensley and   
                Douglas B. West   Problems and Solutions . . . . . . . . . 834--843
         Jeffrey Nunemacher and   
              Rebecca F. Goldin   Book Review: \booktitle[untitled]  . . . 844--847
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 118, Number 1, January, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 1--2
                   David A. Cox   Why Eisenstein Proved the Eisenstein
                                  Criterion and Why Schönemann Discovered
                                  It First . . . . . . . . . . . . . . . . 3--21
        Jennifer M. Johnson and   
     János Kollár   How Small Can a Polynomial Be Near
                                  Infinity?  . . . . . . . . . . . . . . . 22--40
              Nikolai V. Ivanov   Arnol'd, the Jacobi Identity, and
                                  Orthocenters . . . . . . . . . . . . . . 41--65
             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
                      Anonymous   Problems and Solutions . . . . . . . . . 84--91
      Virginia McShane Warfield   Book Review: \booktitle[untitled]  . . . 92--95
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 96--96

American Mathematical Monthly
Volume 118, Number 10, December, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 861--862
             Henryk Gerlach and   
            Heiko von der Mosel   On Sphere-Filling Ropes  . . . . . . . . 863--876
         Géza Kós   On the Grasshopper Problem with Signed
                                  Jumps  . . . . . . . . . . . . . . . . . 877--886
           Giovanni Falcone and   
                   Marco Pavone   Kirkman's Tetrahedron and the Fifteen
                                  Schoolgirl Problem . . . . . . . . . . . 887--900
              Paul Baginski and   
               Scott T. Chapman   Factorizations of Algebraic Integers,
                                  Block Monoids, and Additive Number
                                  Theory . . . . . . . . . . . . . . . . . 901--920
                Hayri Ardal and   
                  Tom Brown and   
               Veselin Jungi\'c   Chaotic Orderings of the Rationals and
                                  Reals  . . . . . . . . . . . . . . . . . 921--925
          Raphaël Cerf and   
                   Pierre Petit   A Short Proof of Cramér's Theorem in
                                  $\mathbb{R}$ . . . . . . . . . . . . . . 925--931
               Bahman Kalantari   A Geometric Modulus Principle for
                                  Polynomials  . . . . . . . . . . . . . . 931--935
                      Anonymous   Problems and Solutions . . . . . . . . . 936--945
                 Andrew Odlyzko   Book Review: \booktitle[untitled]  . . . 946--951
             Daniel J. Velleman   Book Review: \booktitleEndnotes  . . . . 952--953
                      Anonymous   Index to Volume 118  . . . . . . . . . . 954--964
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 118, Number 2, February, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 97--98
              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 and   
               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
                   Paul Pollack   On Dickson's Theorem Concerning Odd
                                  Perfect Numbers  . . . . . . . . . . . . 161--164
              Eyal Ackerman and   
               Rom Pinchasi and   
             Ludmila Scharf and   
              Marc Scherfenberg   Every Simple Arrangement of n Lines
                                  Contains an Inducing Simple $n$-gon  . . 164--167
José L. Gámez-Merino and   
Gustavo A. Muñoz-Fernández and   
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 and   
                        Chen Xu   Generalization and Probabilistic Proof
                                  of a Combinatorial Identity  . . . . . . 175--177
                      Anonymous   Problems and Solutions . . . . . . . . . 178--185
             Jeffrey Nunemacher   Book Review: \booktitle[untitled]  . . . 186--189
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 190--192

American Mathematical Monthly
Volume 118, Number 3, March, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 193--194
                 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 and   
                   Joseph Stern   Equimodular Polynomials and the
                                  Tritangency Theorems of Euler,
                                  Feuerbach, and Guinand . . . . . . . . . 217--228
                Keith Burns and   
              Boris Hasselblatt   The Sharkovsky Theorem: a Natural Direct
                                  Proof  . . . . . . . . . . . . . . . . . 229--244
            John H. Hubbard and   
            Benjamin E. Lundell   A First Look at Differential Algebra . . 245--261
                    Grant Keady   Lines of Best Fit for the Zeros and for
                                  the Critical Points of a Polynomial  . . 262--264
                Sascha Kurz and   
                   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
                      Anonymous   Problems and Solutions . . . . . . . . . 275--282
           Christopher C. Leary   Book Review: \booktitle[untitled]  . . . 283--286
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 287--288

American Mathematical Monthly
Volume 118, Number 4, April, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 289--290
                   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 and   
                  Ling Long and   
                     YiFan Yang   A Cubic Analogue of the Jacobsthal
                                  Identity . . . . . . . . . . . . . . . . 316--326
               H. M. Hilden and   
           J. M. Montesinos and   
               D. M. Tejada and   
                     M. M. Toro   Artifacts for Stamping Symmetric Designs 327--343
       Jaume Paradís and   
      Pelegrí Viader and   
          Lluís Bibiloni   A New Singular Function  . . . . . . . . 344--354
                    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
                      Anonymous   Problems and Solutions . . . . . . . . . 371--378
              Susan Jane Colley   Book Review: \booktitle[untitled]  . . . 379--382
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 383--384

American Mathematical Monthly
Volume 118, Number 5, May, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 385--386
               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
                   M. Skopenkov   Packing a Cake into a Box  . . . . . . . 424--433
                    Alan Tucker   What Every Mathematician Should Know
                                  about Standards-Based Tests  . . . . . . 434--447
           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 and   
                  Gary L. Walls   On the Group of Automorphisms of a Group 452--455
                    Bogdan Nica   The Unreasonable Slightness of $ E_2 $
                                  over Imaginary Quadratic Rings . . . . . 455--462
                      Anonymous   Problems and Solutions . . . . . . . . . 463--470
          Peggy Aldrich Kidwell   Book Review: \booktitle[untitled]  . . . 471--474
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 475--476

American Mathematical Monthly
Volume 118, Number 6, June, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 477--478
                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 and   
               Elizabeth Skubak   Polynomials, Ellipses, and Matrices: Two
                                  Questions, One Answer  . . . . . . . . . 522--533
          Ronald F. Wotzlaw and   
         Günter M. Ziegler   A Lost Counterexample and a Problem on
                                  Illuminated Polytopes  . . . . . . . . . 534--543
          János Pach and   
                 Ethan Sterling   Conway's Conjecture for Monotone
                                  Thrackles  . . . . . . . . . . . . . . . 544--548
           Kieren MacMillan and   
                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
                      Anonymous   Problems and Solutions . . . . . . . . . 557--564
               Robin Hartshorne   Book Review: \booktitle[untitled]  . . . 565--568
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 118, Number 7, August, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 569--570
                Kenneth A. Ross   Benford's Law, a Growth Industry . . . . 571--583
             Graham Everest and   
                    Thomas Ward   A Repulsion Motif in Diophantine
                                  Equations  . . . . . . . . . . . . . . . 584--598
             Alberto Torchinsky   The Fourier Transform and the Wave
                                  Equation . . . . . . . . . . . . . . . . 599--609
                  W. Aitken and   
                 F. Lemmermeyer   Counterexamples to the Hasse Principle   610--628
              Peyman Eslami and   
              Pawel Góra   On Eventually Expanding Maps of the
                                  Interval . . . . . . . . . . . . . . . . 629--635
    Hichem Ben-El-Mechaiekh and   
               Robert W. Dimand   A Simpler Proof of the von Neumann
                                  Minimax Theorem  . . . . . . . . . . . . 636--641
                     Luigi Pace   Probabilistically Proving that $\zeta(2)
                                  = \pi^2 / 6$ . . . . . . . . . . . . . . 641--643
               M. Ram Murty and   
                 V. Kumar Murty   On a Problem of Ruderman . . . . . . . . 644--650
                Alan F. Beardon   Cyclic Absolute Differences of Integers  650--652
                      Anonymous   Problems and Solutions . . . . . . . . . 653--660
                  Peter Winkler   Book Review: \booktitle[untitled]  . . . 661--664
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 118, Number 8, October, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 665--666
     Murad \HOzaydìn and   
              Charlotte Simmons   The Birthday Trick with Lies . . . . . . 667--679
              Russell A. Gordon   Semiperimeter and Pythagorean Triples    680--692
            A. B. Kharazishvili   Measurability Properties of Vitali Sets  693--703
       Stephan Ramon Garcia and   
     Vincent Selhorst-Jones and   
            Daniel E. Poore and   
                     Noah Simon   Quotient Sets and Diophantine Equations  704--711
               P. J. Giblin and   
                   J. P. Warder   Reconstruction from Medial
                                  Representations  . . . . . . . . . . . . 712--725
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
            Loren C. Larson and   
                Mark Krusemeyer   The Seventy-First William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 726--733
                   R. K. Oliver   On the Parity of a Permutation . . . . . 734--735
                   Wouter Kager   The Hitting Time Theorem Revisited . . . 735--737
             R. Thangadurai and   
                     A. Vatwani   The Least Prime Congruent to One Modulo
                                  $n$  . . . . . . . . . . . . . . . . . . 737--742
                Penghao Cao and   
                    Liping Yuan   A Blichfeldt-type Theorem for $H$-points 743--746
                      Anonymous   Problems and Solutions . . . . . . . . . 747--754
                  Richard Askey   Book Review: \booktitle[untitled]  . . . 755--762
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 118, Number 9, November, 2011

                      Anonymous   Front Matter . . . . . . . . . . . . . . 765--766
                Bruce C. Berndt   The Chief Accountant and Mathematical
                                  Friend of Ramanujan --- S. Narayana
                                  Aiyar  . . . . . . . . . . . . . . . . . 767--776
                      P. Haxell   On Forming Committees  . . . . . . . . . 777--788
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Complete Dissections: Converting Regions
                                  and Their Boundaries . . . . . . . . . . 789--798
              Giacomo Drago and   
     Pier Domenico Lamberti and   
                     Paolo Toni   A ``Bouquet'' of Discontinuous Functions
                                  for Beginners in Mathematical Analysis   799--811
           John B. Cosgrave and   
                   Karl Dilcher   An Introduction to Gauss Factorials  . . 812--829
                   S. 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
                      Anonymous   Problems and Solutions . . . . . . . . . 846--853
                 Matthew Richey   Book Review: \booktitle[untitled]  . . . 854--858
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 119, Number 1, January, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 1--2
                  Scott Chapman   A Letter from the Editor . . . . . . . . 3--3
            Daniel Brinkman and   
                 Peter J. Olver   Invariant Histograms . . . . . . . . . . 4--24
               Thomas Bauer and   
             Mirel Caib\uar and   
                   Gary Kennedy   Zariski Decomposition: a New (Old)
                                  Chapter of Linear Algebra  . . . . . . . 25--41
                 Dan Kalman and   
                  Mark McKinzie   Another Way to Sum a Series: Generating
                                  Functions, Euler, and the Dilog Function 42--51
            Costas J. Efthimiou   A Class of Periodic Continued Radicals   52--58
         Parames Laosinchai and   
                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
                      Anonymous   Problems and Solutions . . . . . . . . . 68--75
                    Alan Durfee   Book Review: \booktitle[untitled]  . . . 76--82
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 83--84

American Mathematical Monthly
Volume 119, Number 2, February, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 85--86
      Boris S. Mordukhovich and   
             Nguyen Mau Nam and   
              Juan Salinas, Jr.   Solving a Generalized Heron Problem by
                                  Means of Convex Analysis . . . . . . . . 87--99
                Sam Vandervelde   Jacobi Sum Matrices  . . . . . . . . . . 100--114
          Donald J. Bindner and   
                Martin Erickson   Alcuin's Sequence  . . . . . . . . . . . 115--121
            Burkard Polster and   
                 Marty Ross and   
                   David Treeby   A Case of Continuous Hangover  . . . . . 122--139
                David A. Herron   Riemann Maps and Diameter Distance . . . 140--147
              Cristinel Mortici   A Power Series Approach to Some
                                  Inequalities . . . . . . . . . . . . . . 147--151
               Julian Rosen and   
             Zachary Scherr and   
             Benjamin Weiss and   
               Michael E. Zieve   Chebyshev Mappings of Finite Fields  . . 151--155
                   Igor Pak and   
                   Rom Pinchasi   Collapsing Walls Theorem . . . . . . . . 156--160
                      Anonymous   Problems and Solutions . . . . . . . . . 161--168
   José Ferreirós   Book Review: \booktitle[untitled]  . . . 169--176
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 119, Number 3, March, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 177--178
                 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
          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
                      Anonymous   Problems and Solutions . . . . . . . . . 247--254
         Gerald L. Alexanderson   Book Review: \booktitleLoving and Hating
                                  Mathematics: Challenging the Myths of
                                  Mathematical Life, by Reuben Hersh and
                                  Vera John-Steiner. Princeton University
                                  Press, Princeton, NJ, 2011, xii + 416
                                  pp. ISBN 978-0-691-14247-0, \$29.95} . . 255--259
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 260--260

American Mathematical Monthly
Volume 119, Number 4, April, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 261--262
          Rachel Wells Hall and   
                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 Cox and   
                     Stan Wagon   Drilling for Polygons  . . . . . . . . . 300--312
              Kenneth Hicks and   
             Xiang-dong Hou and   
                 Gary L. Mullen   Sums of Reciprocals of Polynomials over
                                  Finite Fields  . . . . . . . . . . . . . 313--317
          Evgeny Lakshtanov and   
                 Vera Roshchina   On Finiteness in the Card Game of War    318--323
         Djurdje Cvijovi\'c and   
             Hari M. Srivastava   Limit Representations of Riemann's Zeta
                                  Function . . . . . . . . . . . . . . . . 324--330
             Christian Elsholtz   Prime Divisors of Thin Sequences . . . . 331--333
              I. E. Leonard and   
                   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
                  R. McCutcheon   Monochromatic Permutation Quadruples ---
                                  a Schur Thing in $S_n$ . . . . . . . . . 342--343
                      Anonymous   Problems and Solutions . . . . . . . . . 344--351
                 Bonnie Shulman   Book Review: \booktitlePopulation Games
                                  and Evolutionary Dynamics, by William H.
                                  Sandholm. MIT Press, Cambridge, MA,
                                  2011, xxv + 589 pp., ISBN
                                  978-0-262-19587-4, \$65} . . . . . . . . 352--356
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 119, Number 5, May, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 357--358
                   Tony Gilbert   Lost Mail: The Missing Envelope in the
                                  Problem of the Minimal Surface of
                                  Revolution . . . . . . . . . . . . . . . 359--372
              Frits Beukers and   
               Florian Luca and   
                     Frans Oort   Power Values of Divisor Sums . . . . . . 373--380
             Hassan Boualem and   
                 Robert Brouzet   On What Is the Almost-Near Principle . . 381--397
              Serge Tabachnikov   The (Un)equal Tangents Problem . . . . . 398--405
               Lance Bryant and   
              James Hamblin and   
                    Lenny Jones   A Variation on the Money-Changing
                                  Problem  . . . . . . . . . . . . . . . . 406--414
                   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 and   
                 Morgan Sherman   When Is a Trigonometric Polynomial Not a
                                  Trigonometric Polynomial?  . . . . . . . 422--425
                      Anonymous   Problems and Solutions . . . . . . . . . 426--433
                 James A. Walsh   Book Review: \booktitleRandomness and
                                  Recurrence in Dynamical Systems, by
                                  Rodney Nillsen. The Carus Mathematical
                                  Monographs Number 31, Mathematical
                                  Association of America, Washington, DC,
                                  2010, xviii + 357 pp., ISBN
                                  978-0-88385-043-5, \$52.95}  . . . . . . 434--438
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 439--440

American Mathematical Monthly
Volume 119, Number 6, June, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 441--442
    Dimitris Koukoulopoulos and   
                   Johann Thiel   Arrangements of Stars on the American
                                  Flag . . . . . . . . . . . . . . . . . . 443--450
                Fred Kuczmarski   Rolling Sinusoidal Spirals . . . . . . . 451--467
               Robert Mandl and   
      Thomas Pühringer and   
              Maximilian Thaler   Analytic Approach to Galileo's Theorem
                                  on the Descent Time Along Two-Chord
                                  Paths in a Circle  . . . . . . . . . . . 468--476
               Paul Binding and   
                   Hans Volkmer   A Prüfer Angle Approach to the Periodic
                                  Sturm--Liouville Problem . . . . . . . . 477--484
            Raymond Mortini and   
                    Rudolf Rupp   Mappings into the Euclidean Sphere . . . 485--494
           Branko Grünbaum   Is Napoleon's Theorem Really Napoleon's
                                  Theorem? . . . . . . . . . . . . . . . . 495--501
        Michael J. Dorfling and   
                 Johan H. 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
                      Anonymous   Problems and Solutions . . . . . . . . . 522--529
              Jennifer J. Quinn   Book Review: \booktitleCombinatorics the
                                  Rota Way, by Joseph P. S. Kung,
                                  Gian-Carlo Rota, and Catherine H. Yan.
                                  Cambridge University Press, New York,
                                  2009, xii + 396 pp., ISBN
                                  978-0-521-73794-4, \$40.99}  . . . . . . 530--532
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 119, Number 7, August, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 533--534
              David Borwein and   
        Jonathan M. Borwein and   
                   Armin Straub   A Sinc that Sank . . . . . . . . . . . . 535--549
              Lionel Levine and   
            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
                 F. Lemmermeyer   Parametrization of Algebraic Curves from
                                  a Number Theorist's Point of View  . . . 573--583
              Peter Borwein and   
                     Joe Hobart   The Extraordinary Power of Division in
                                  Straight Line Programs . . . . . . . . . 584--592
                Alin Bostan and   
                 Thierry Combot   A Binomial-like Matrix Equation  . . . . 593--597
                 Ezra Brown and   
               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 and   
                Mitia Duerinckx   Functions with Constant Mean on Similar
                                  Countable Subsets of $\mathbb{R}^2$  . . 603--605
                   Tomasz Tkocz   An Upper Bound for Spherical Caps  . . . 606--607
                      Anonymous   Problems and Solutions . . . . . . . . . 608--615
                   Marion Cohen   Book Review: \booktitleChange Is
                                  Possible: Stories of Women and
                                  Minorities in Mathematics, by Patricia
                                  Clark Kenschaft. American Mathematical
                                  Society, Providence, RI, 2005, ix + 211
                                  pp., ISBN 0-8218-3748-6, \$32.00}  . . . 616--620
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 119, Number 8, October, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 621--622
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Mark Krusemeyer   The Seventy-Second William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 623--635
              Yuval Ginosar and   
                      Ilan Yona   A Model for Pairs of Beatty Sequences    636--645
            David H. Bailey and   
            Jonathan M. Borwein   Ancient Indian Square Roots: An Exercise
                                  in Forensic Paleo-Mathematics  . . . . . 646--657
                   Bruce Ebanks   Looking for a Few Good Means . . . . . . 658--669
                   Paul Pollack   Finiteness Theorems for Perfect Numbers
                                  and Their Kin  . . . . . . . . . . . . . 670--681
                  Akira Sakurai   Vector Analysis Proof of Erd\Hos'
                                  Inequality for Triangles . . . . . . . . 682--684
               Boris M. Makarov   Calculation of the Volume of
                                  Multidimensional Cones and Balls Using
                                  Cavalieri's 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
                      Anonymous   Problems and Solutions . . . . . . . . . 699--706
                  Mark Schwartz   Book Review: \booktitleGeometry for
                                  College Students, by I. Martin Isaacs.
                                  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) . . . . . . . . 707--711
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 712--712

American Mathematical Monthly
Volume 119, Number 9, November, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 713--714
              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 and   
               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
                 B. Shapiro and   
                     M. Shapiro   A Few Riddles Behind Rolle's Theorem . . 787--793
              Boris Alexeev and   
                Jacob Tsimerman   Note on a War-like Card Game . . . . . . 793--795
                 Florian Breuer   Newton Identities for Weierstrass
                                  Products . . . . . . . . . . . . . . . . 796--799
                      Anonymous   Problems and Solutions . . . . . . . . . 800--807
                     Stan Wagon   Book Review: \booktitleIn Pursuit of the
                                  Traveling Salesman, by William J. Cook.
                                  Princeton University Press, Princeton,
                                  NJ, 2012 xiii + 228 pp., ISBN
                                  978-0-691-15270-7, \$27.95}  . . . . . . 808--811
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 812--812

American Mathematical Monthly
Volume 119, Number 10, December, 2012

                      Anonymous   Front Matter . . . . . . . . . . . . . . 813--814
            Tanya Khovanova and   
                   Alexey Radul   Killer Problems  . . . . . . . . . . . . 815--823
          Robert T. Jantzen and   
                  Klaus Volpert   On the Mathematics of Income Inequality:
                                  Splitting the Gini Index in Two  . . . . 824--837
            Carla D. Martin and   
                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 and   
                       Min Tang   On the Elementary Symmetric Functions of
                                  $1$, $1/2$, \ldots, $1/n$  . . . . . . . 862--867
           Rolfdieter Frank and   
                   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
                      Anonymous   Problems and Solutions . . . . . . . . . 880--887
         Gerald L. Alexanderson   Book Review: \booktitleTranscending
                                  Tradition: Jewish Mathematicians in
                                  German-Speaking Academic Culture, by
                                  Birgit Bergmann, Moritz Epple, and Ruti
                                  Ungar, editors. Springer Verlag, Berlin
                                  and Heidelberg, 2012, xi + 289 pp., ISBN
                                  978-3-642-22463-8, \$49.95}  . . . . . . 888--891
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 892--894
                      Anonymous   Title Index, Author Index, Problems
                                  Proposed, Problems Solved, Solutions,
                                  Referees . . . . . . . . . . . . . . . . 895--905
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 906--908


American Mathematical Monthly
Volume 120, Number 1, January, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 1--2
          Nicholas R. Baeth and   
                  Roger Wiegand   Factorization Theory and Decompositions
                                  of Modules . . . . . . . . . . . . . . . 3--34
            Steven J. Brams and   
           Michael A. Jones and   
              Christian Klamler   $N$-Person Cake-Cutting: There May Be No
                                  Perfect Division . . . . . . . . . . . . 35--47
               M. Ram Murty and   
             Anastasia Zaytseva   Transcendence of Generalized Euler
                                  Constants  . . . . . . . . . . . . . . . 48--54
Jean-Baptiste Hiriart-Urruty and   
              Patrice Lass\`ere   When Is $ L^r(R) $ Contained in $ L^p(R)
                                  + L^q(R) $?  . . . . . . . . . . . . . . 55--61
  Vinicius Nicolae Petre Anghel   A Use of Symmetry: Generalization of an
                                  Integral Identity Found by M. L. Glasser 62--69
                    Yi Jun Chen   A Proof that Zeilberger Missed: a New
                                  Proof of an Identity by Chaundy and
                                  Bullard Based on the Wilf--Zeilberger
                                  Method . . . . . . . . . . . . . . . . . 69--70
             L. P. Withers, Jr.   Visual Angular Momentum: Mamikon Meets
                                  Kepler . . . . . . . . . . . . . . . . . 71--73
                Wlodzimierz Bak   A Simple Characterization of
                                  Differentiation  . . . . . . . . . . . . 74--75
                      Anonymous   Problems and Solutions . . . . . . . . . 76--83
       Fernando Q. Gouvêa   Book Review: \booktitleElliptic Curves,
                                  Modular Forms, and Their L-functions
                                  (Student Mathematical Library IAS/Park
                                  City Subseries, vol, by Álvaro
                                  Lozano-Robledo. 58), American
                                  Mathematical Society, Providence, RI,
                                  2011, 195 pp., ISBN 978-0-8218-5242-2,
                                  \$29.60} . . . . . . . . . . . . . . . . 84--94
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 95--96

American Mathematical Monthly
Volume 120, Number 2, February, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 97--98
                Holger Teismann   Toward a More Complete List of
                                  Completeness Axioms  . . . . . . . . . . 99--114
           Freeman J. Dyson and   
          Norman E. Frankel and   
            M. Lawrence Glasser   Lehmer's Interesting Series  . . . . . . 116--130
               Dexter Kozen and   
                Alexandra Silva   On Moessner's Theorem  . . . . . . . . . 131--139
          Susan H. Marshall and   
            Alexander R. Perlis   Heronian Tetrahedra Are Lattice
                                  Tetrahedra . . . . . . . . . . . . . . . 140--149
                 Jeremy Alm and   
      Michael Gramelspacher and   
                  Theodore Rice   Rubik's on the Torus . . . . . . . . . . 150--160
               David C. Ullrich   A Simple Elementary Proof of Hilbert's
                                  Inequality . . . . . . . . . . . . . . . 161--164
                   Aaron Melman   The Twin of a Theorem by Cauchy  . . . . 164--168
                    Marco Dalai   How Would Riemann Evaluate $ \zeta (2 n)
                                  $? . . . . . . . . . . . . . . . . . . . 169--171
            Vladimir Dragovi\'c   Polynomial Dynamics and a Proof of the
                                  Fermat Little Theorem  . . . . . . . . . 171--173
                      Anonymous   Problems and Solutions . . . . . . . . . 174--181
              Michael Nathanson   Book Review: \booktitleElements of
                                  Information Theory, by Thomas M. Cover
                                  and Joy A. Thomas. John Wiley and Sons,
                                  Inc., Hoboken, NJ, 2006, xxiv + 748 pp.,
                                  ISBN 0-471-24195-4, \$111.00}  . . . . . 182--187
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 188--188

American Mathematical Monthly
Volume 120, Number 3, March, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 189--190
           Dierk Schleicher and   
              Serge Tabachnikov   Letter from the Guest Editors  . . . . . 191--191
                 John H. Conway   On Unsettleable Arithmetical Problems    192--198
               Robert Foote and   
                  Mark Levi and   
              Serge Tabachnikov   Tractrices, Bicycle Tire Tracks, Hatchet
                                  Planimeters, and a 100-year-old
                                  Conjecture . . . . . . . . . . . . . . . 199--216
                   Dmitry Fuchs   Evolutes and Involutes of Spatial Curves 217--231
            Étienne Ghys   Intersecting Curves (Variation on an
                                  Observation of Maxim Kontsevich) . . . . 232--242
             Aimeric Malter and   
           Dierk Schleicher and   
                     Don Zagier   New Looks at Old Number Theory . . . . . 243--264
                Tadashi Tokieda   Roll Models  . . . . . . . . . . . . . . 265--282
           Rade T. Zivaljevi\'c   Book Review: \booktitleMathematical
                                  Omnibus: Thirty Lectures on Classic
                                  Mathematics, by Dmitry Fuchs and Serge
                                  Tabachnikov. American Mathematical
                                  Society, Providence, RI, 2007, xv + 463
                                  pp., ISBN-13: 978-0-8218-4316-1, \$61}   283--286
                   Pieter Moree   Book Review: \booktitleAn Invitation to
                                  Mathematics: From Competitions to
                                  Research, [edited] by Dierk Schleicher
                                  and Malte Lackmann, editors.
                                  Springer-Verlag, Heidelberg, 2011, xiv +
                                  220 pp. ISBN-13: 978-3-642-19532-7,
                                  \$34.95} . . . . . . . . . . . . . . . . 286--288
           Christoph Pöppe   Book Review: \booktitleDimensions, by
                                  Jos Leys, Étienne Ghys, and Aurélien
                                  Alvarez. A mathematical video.
                                  \urlwww.dimensions-math.org, 117
                                  minutes, no cost . . . . . . . . . . . . 288--290
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 291--292

American Mathematical Monthly
Volume 120, Number 4, April, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 293--294
                 Ann E. Watkins   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for 2013 to William A. Hawkins for
                                  Distinguished Service to Mathematics . . 295--297
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   New Balancing Principles Applied to
                                  Circumsolids of Revolution, and to
                                  $n$-Dimensional Spheres, Cylindroids,
                                  and Cylindrical Wedges . . . . . . . . . 298--321
            Matthew Jenssen and   
         Daniel Montealegre and   
              Vadim Ponomarenko   Irreducible Factorization Lengths and
                                  the Elasticity Problem within $ \mathbb
                                  {N} $  . . . . . . . . . . . . . . . . . 322--328
            Kenneth S. Williams   The Parents of Jacobi's Four Squares
                                  Theorem Are Unique . . . . . . . . . . . 329--345
           Kathryn L. Nyman and   
              Francis Edward Su   A Borsuk--Ulam Equivalent that Directly
                                  Implies Sperner's Lemma  . . . . . . . . 346--354
             Habib Bin Muzaffar   A New Proof of a Classical Formula . . . 355--358
               Steve Alpern and   
                Robbert Fokkink   Illuminating a Network from Its Nodes    358--359
               Orr Moshe Shalit   A Sneaky Proof of the Maximum Modulus
                                  Principle  . . . . . . . . . . . . . . . 359--362
               Olivier Bernardi   A Short Proof of Rayleigh's Theorem with
                                  Extensions . . . . . . . . . . . . . . . 362--364
                      Anonymous   Problems and Solutions . . . . . . . . . 365--372
                   Marie Snipes   Book Review: \booktitleLinear and
                                  Nonlinear Programming, 3rd ed, by David
                                  G. Luenberger and Yinyu Ye., Springer,
                                  New York, 2008, xiv + 546 pp., ISBN
                                  0-387-74502-5, \$109}  . . . . . . . . . 373--379
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 380--380

American Mathematical Monthly
Volume 120, Number 5, May, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 381--382
                  Scott Chapman   A Letter from the Editor . . . . . . . . 383--383
                     Ehud Kalai   Foreword: The High Priest of Game Theory 384--385
                    D. Gale and   
                  L. S. Shapley   College Admissions and the Stability of
                                  Marriage . . . . . . . . . . . . . . . . 386--391
                    James Propp   Real Analysis in Reverse . . . . . . . . 392--408
            Melvyn B. Nathanson   On the Fractional Parts of Roots of
                                  Positive Real Numbers  . . . . . . . . . 409--429
         Stephen M. Buckley and   
                Desmond MacHale   Variations on a Theme: Rings Satisfying
                                  $ x^3 = x $ Are Commutative  . . . . . . 430--440
              Joshua Cooper and   
                    Aaron Dutle   Greedy Galois Games  . . . . . . . . . . 441--451
              Rachid Marsli and   
                  Frank J. Hall   Geometric Multiplicities and Gersgorin
                                  Discs  . . . . . . . . . . . . . . . . . 452--455
                   Jim X. Xiang   A Note on the Cauchy--Schwarz Inequality 456--459
            Costas J. Efthimiou   A Class of Continued Radicals  . . . . . 459--461
                D. Aharonov and   
                       U. Elias   A Binomial Identity via Differential
                                  Equations  . . . . . . . . . . . . . . . 462--466
                F. Galaz-Fontes   Another Proof for Non-Supercyclicity in
                                  Finite Dimensional Complex Banach Spaces 466--468
                      Anonymous   Problems and Solutions . . . . . . . . . 469--476
                    Kevin Woods   Book Review: \booktitleSymmetry: A
                                  Mathematical Exploration, by Kristopher
                                  Tapp. Springer, New York, 2012, xiv +
                                  215pp., ISBN 978-1-4614-0298-5, \$49.95} 477--481
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 482--483
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 484--484

American Mathematical Monthly
Volume 120, Number 6, June, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 485--486
                Andrew D. Hwang   Paper Surface Geometry . . . . . . . . . 487--499
 Joanna M. Papakonstantinou and   
               Richard A. Tapia   Origin and Evolution of the Secant
                                  Method in One Dimension  . . . . . . . . 500--518
               Nathan Bliss and   
                  Ben Fulan and   
             Stephen Lovett and   
                   Jeff Sommars   Strong Divisibility, Cyclotomic
                                  Polynomials, and Iterated Polynomials    519--536
            Steven H. Weintraub   Several Proofs of the Irreducibility of
                                  the Cyclotomic Polynomials . . . . . . . 537--545
                 Kurt Girstmair   The Equation $ x^2 + \bar{m} y^2 =
                                  \bar{k}$ in $ \mathbb {Z} / p \mathbb
                                  {Z} $  . . . . . . . . . . . . . . . . . 546--552
            Claire-Soizic Henry   Coxeter Friezes and Triangulations of
                                  Polygons . . . . . . . . . . . . . . . . 553--558
              Jonathon Peterson   A Probabilistic Proof of a Binomial
                                  Identity . . . . . . . . . . . . . . . . 558--562
                   S. A. Rankin   The Euclidean Algorithm and the Linear
                                  Diophantine Equation $a x + b y = {\rm
                                  gcd}( a, b )$  . . . . . . . . . . . . . 562--564
                Tadashi Tokieda   A Buoyancy-Driven Perpetual Motion
                                  Machine  . . . . . . . . . . . . . . . . 564--566
                 Manas R. Sahoo   Example of a Monotonic, Everywhere
                                  Differentiable Function on $\mathbb{R}$
                                  Whose Derivative Is not Continuous . . . 566--568
                      Anonymous   Problems and Solutions . . . . . . . . . 569--576
                 David Bressoud   Book Review: \booktitleCalculus, by
                                  Michael Spivak; \booktitleCalculus
                                  Deconstructed: A Second Course in
                                  First-Year Calculus. MAA Textbooks,
                                  Mathematical Association of America,
                                  Washington, DC, 2009, xvi + 491 pp.,
                                  ISBN 978-0-88385-756-4, \$ 59.95. by
                                  Zbigniew Nitecki;
                                  \booktitle{Approximately Calculus}.
                                  American Mathematical Society,
                                  Providence, RI, 2006, xvii + 292 pp.,
                                  ISBN 978-0-8218-3750-4, \$50.00. by
                                  Shahriar Sharhriari; \booktitleGuide to
                                  Cauchy's Calculus: A Translation and
                                  Analysis of Calcul Infinitésimal.
                                  Fairview Academic Press, Walnut Creek,
                                  CA, 2012, viii + 616 pp., ISBN
                                  978-0-9838837-0-8, \$139.00. by Dennis
                                  M. Cates; \booktitle{The Calculus
                                  Integral}. ClassicalRealAnalysis.com,
                                  Charleston, SC, 2010, x + 291, ISBN
                                  978-1442180956, \$14.95. by Brian S.
                                  Thomson. 4th edition. Publish or Perish,
                                  Houston, TX, 2008, xiv + 680 pp., ISBN
                                  978-0-914098-91-1, \$85.00}  . . . . . . 577--580
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 120, Number 7, August, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 581--582
                David J. Aldous   Using Prediction Market Data to
                                  Illustrate Undergraduate Probability . . 583--593
           Stephen D. Casey and   
                Brian M. Sadler   Pi, the Primes, Periodicities, and
                                  Probability  . . . . . . . . . . . . . . 594--608
             Peter Kuchment and   
                    Sergey Lvin   Identities for $ \sin x $ that Came from
                                  Medical Imaging  . . . . . . . . . . . . 609--621
               Steve Butler and   
                     Ron Graham   Subdivision Using Angle Bisectors Is
                                  Dense in the Space of Triangles  . . . . 622--630
            Mikhail G. Katz and   
                 Eric Leichtnam   Commuting and Noncommuting
                                  Infinitesimals . . . . . . . . . . . . . 631--641
                Daniele Ritelli   Another Proof of $ {\zeta (2) = \frac
                                  {\pi^2}{6}} $ Using Double Integrals . . 642--645
            Matthias Arnold and   
              Werner Glaß   Simple Approximation Formulas for the
                                  Birthday Problem . . . . . . . . . . . . 645--648
          Anthony J. Bevelacqua   Another Irreducibility Criterion . . . . 648--650
                Jaban Meher and   
                   M. Ram Murty   Ramanujan's Proof of Bertrand's
                                  Postulate  . . . . . . . . . . . . . . . 650--653
                      T. Samuel   A Simple Proof of Vitali's Theorem for
                                  Signed Measures  . . . . . . . . . . . . 654--659
                      Anonymous   Problems and Solutions . . . . . . . . . 660--669
              Joseph Malkevitch   Book Review: \booktitleThe Mathematical
                                  Coloring Book, by Alexander Soifer.
                                  Springer, New York, xxx + 607 pp., ISBN
                                  978-0-387-74640-1, \$69.95}  . . . . . . 670--674
           Samuel G. Moreno and   
Esther M. García-Caballero   Book Review: \booktitleOn the
                                  Irrationality of $ \surd 2 $ Once Again  674--674
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 675--676

American Mathematical Monthly
Volume 120, Number 8, October, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 677--678
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Mark Krusemeyer   The Seventy-Third William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 679--688
                    Alan Tucker   The History of the Undergraduate Program
                                  in Mathematics in the United States  . . 689--705
                Brant Jones and   
              Laura Taalman and   
                 Anthony Tongen   Solitaire Mancala Games and the Chinese
                                  Remainder Theorem  . . . . . . . . . . . 706--724
                    Paul Monsky   Frobenius' Result on Simple Groups of
                                  Order $ \frac {p^3 - p^2}{2} $ . . . . . 725--732
             Bhaskar Bagchi and   
                  Basudeb Datta   Higher-Dimensional Analogues of the Map
                                  Coloring Problem . . . . . . . . . . . . 733--737
         Dorin Ervin Dutkay and   
    Constantin P. Niculescu and   
                Florin Popovici   Stirling's Formula and Its Extension for
                                  the Gamma Function . . . . . . . . . . . 737--740
           Jean Van Schaftingen   A Direct Proof of the Existence of
                                  Eigenvalues and Eigenvectors by
                                  Weierstrass's Theorem  . . . . . . . . . 741--746
                     A. G. Ramm   A Variational Principle and Its
                                  Application to Estimating the Electrical
                                  Capacitance of a Perfect Conductor . . . 747--751
       Zsolt Lengvárszky   Proving the Pythagorean Theorem via
                                  Infinite Dissections . . . . . . . . . . 751--753
                      Anonymous   Problems and Solutions . . . . . . . . . 754--761
          Takis Konstantopoulos   Book Review: \booktitleAn Introduction
                                  to Measure Theory, by Terence Tao.
                                  American Mathematical Society,
                                  Providence RI, 2011, xvi + 206 pp., ISBN
                                  978-0-8218-6919-2, \$53.00}  . . . . . . 762--768
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 120, Number 9, November, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 769--770
Jacques Lévy Véhel and   
              Franklin Mendivil   Christiane's Hair  . . . . . . . . . . . 771--786
         Daniel J. Velleman and   
          Gregory S. Warrington   What to Expect in a Game of Memory . . . 787--805
   Antonín Slavík   Mixing Problems with Many Tanks  . . . . 806--821
           Jonathan Bayless and   
                  Dominic Klyve   Reciprocal Sums as a Knowledge Metric:
                                  Theory, Computation, and Perfect Numbers 822--831
Jorge Luis Cimadevilla Villacorta   Certain Inequalities Associated with the
                                  Divisor Function . . . . . . . . . . . . 832--837
              Charles S. Kahane   On the Nonexistence of Certain Limits
                                  for the Complex Exponential  . . . . . . 837--840
Árpád Bényi and   
                Branko \'Curgus   A Generalization of Routh's Triangle
                                  Theorem  . . . . . . . . . . . . . . . . 841--846
                      David Pan   A Maximum Principle for High-Order
                                  Derivatives  . . . . . . . . . . . . . . 846--848
           Gerhard J. Woeginger   Nothing New about Equiangular Polygons   849--850
           Stephan Ramon Garcia   Quotients of Gaussian Primes . . . . . . 851--853
                      Anonymous   Problems and Solutions . . . . . . . . . 854--861
                 Betty Mayfield   Book Review: \booktitleCalculus:
                                  Modeling and Application, second
                                  edition, by David A. Smith and Lawrence
                                  C. Moore. Mathematical Association of
                                  America, Washington, D.C., 2010.
                                  http://maa.pinnaclecart.com. Price:
                                  \$35.00. ISBN 978-1-6144-610-1}  . . . . 862--864
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 120, Number 10, December, 2013

                      Anonymous   Front Matter . . . . . . . . . . . . . . 865--866
                David Pengelley   Quick, Does $ 23 / 67 $ Equal $ 33 / 97
                                  $? A Mathematician's Secret from Euclid
                                  to Today . . . . . . . . . . . . . . . . 867--876
      Alexander P. Campbell and   
                  Daniel Daners   Linear Algebra via Complex Analysis  . . 877--892
   Olle Häggström and   
            Johan Wästlund   Rigorous Computer Analysis of the
                                  Chow--Robbins Game . . . . . . . . . . . 893--900
                    Will Traves   From Pascal's Theorem to
                                  $d$-Constructible Curves . . . . . . . . 901--915
                  Roger E. Howe   The Cuoco Configuration  . . . . . . . . 916--923
                    Ulrich Abel   A Generalization of the Leibniz Rule . . 924--928
                Jonathan Sondow   The Parbelos, a Parabolic Analog of the
                                  Arbelos  . . . . . . . . . . . . . . . . 929--935
               G. J. O. Jameson   Inequalities for Gamma Function Ratios   936--940
                      Anonymous   Problems and Solutions . . . . . . . . . 941--948
             James M. Henle and   
               Michael G. Henle   Book Review: \booktitleReal Analysis
                                  Through Modern Infinitesimals, Cambridge
                                  University Press, 2011, xix + 565 pp, by
                                  Nader Vakil., ISBN 978-1-107-00202-9,
                                  \$127.00}  . . . . . . . . . . . . . . . 949--953
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 954--956
                      Anonymous   Title Index, Author Index, Problems
                                  Proposed, Problems Solved, Solutions,
                                  Referees . . . . . . . . . . . . . . . . 957--967
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 968--968


American Mathematical Monthly
Volume 121, Number 1, January, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 1--2
               Scott T. Chapman   A Letter from the Editor: What's In a
                                  Color? . . . . . . . . . . . . . . . . . 3--4
            Melvyn B. Nathanson   Additive Systems and a Theorem of de
                                  Bruijn . . . . . . . . . . . . . . . . . 5--17
                Mario Ponce and   
Patricio Santibáñez   On Equidistant Sets and Generalized
                                  Conics: The Old and the New  . . . . . . 18--32
             Anthony Mendes and   
               Kent E. Morrison   Guessing Games . . . . . . . . . . . . . 33--44
                  Chris D. Lynd   Using Difference Equations to Generalize
                                  Results for Periodic Nested Radicals . . 45--59
             J. A. Conejero and   
P. Jiménez-Rodríguez and   
G. A. Muñoz-Fernández and   
  J. B. Seoane-Sepúlveda   When the Identity Theorem ``Seems'' to
                                  Fail . . . . . . . . . . . . . . . . . . 60--68
    Ádám Besenyei   Peano's Unnoticed Proof of Borel's
                                  Theorem  . . . . . . . . . . . . . . . . 69--72
            Steven H. Weintraub   Values of Polynomials over Integral
                                  Domains  . . . . . . . . . . . . . . . . 73--74
                     Bao Qin Li   A Direct Proof and a Transcendental
                                  Version of the Fundamental Theorem of
                                  Algebra via Cauchy's Theorem . . . . . . 75--77
           Samuel Clowes Huneke   An Inductive Proof of Hex Uniqueness . . 78--80
                Karim Boulabiar   Real-Valued Ring Homomorphisms on $
                                  C(\Omega) $  . . . . . . . . . . . . . . 81--82
                      Anonymous   Problems and Solutions . . . . . . . . . 83--90
                Kenneth A. Ross   Book Review: \booktitleIn the Dark on
                                  the Sunny Side: a Memoir of an
                                  Out-of-Sight Mathematician, Mathematical
                                  Association of America, Washington, DC,
                                  2012, 206 pp, by Larry Baggett., ISBN
                                  978-0-88385-581-2, \$50} . . . . . . . . 91--92
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 121, Number 2, February, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 93--94
                Eric C. Chi and   
                  Kenneth Lange   A Look at the Generalized Heron Problem
                                  through the Lens of
                                  Majorization-Minimization  . . . . . . . 95--108
               Vincent Coll and   
                  Mike Harrison   Two Generalizations of a Property of the
                                  Catenary . . . . . . . . . . . . . . . . 109--119
           Pantelis A. Damianou   A Beautiful Sine Formula . . . . . . . . 120--135
                  Ron Evans and   
                Lihua Huang and   
                    Tuan Nguyen   Keeler's Theorem and Products of
                                  Distinct Transpositions  . . . . . . . . 136--144
                   Jaime Gaspar   Non-recursive Polynomial Formula for the
                                  Sum of the Powers of the Integers  . . . 144--144
                    David Grant   The Quadratic Gauss Sum Redux  . . . . . 145--149
           Miles Dillon Edwards   A Possibly New Proof of the Law of Cos   149--149
                Yuly Billig and   
                  John D. Dixon   An Eigenvalue Theorem for Systems of
                                  Polynomial Equations . . . . . . . . . . 150--153
                    Hongwei Lou   A Short Proof of Stirling's Formula  . . 154--157
              Richard Ehrenborg   Hamiltonian Cycles on Archimedean Solids
                                  Are Twisting Free  . . . . . . . . . . . 158--161
              Chua Cheong Siong   A Simple Proof of Ljunggren's Binomial
                                  Congruence . . . . . . . . . . . . . . . 162--164
             Daniel J. Velleman   Monthly Gems . . . . . . . . . . . . . . 164--164
               Peter J. McGrath   Another Proof of Clairaut's Theorem  . . 165--166
           Hossein Hosseini Giv   Proving the Banach--Alaoglu Theorem via
                                  the Existence of the Stone-\vCech
                                  Compactification . . . . . . . . . . . . 167--169
                      Anonymous   Problems and Solutions . . . . . . . . . 170--177
                 Harold P. Boas   Book Review: \booktitleInvitation to
                                  Classical Analysis, American
                                  Mathematical Society, Providence, RI,
                                  2012, xiii + 392 pp, by Peter Duren.,
                                  ISBN 978-0-8218-6932-1, \$74.00} . . . . 178--182
                   Peter D. Lax   Book Review: \booktitleNumbers and
                                  Functions: From a Classical Experimental
                                  Mathematicians Point of View, American
                                  Mathematical Society, Providence, RI,
                                  2012, 504 pp, by Victor H. Moll., ISBN
                                  978-0-8218-8795-0, \$58} . . . . . . . . 183--183
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 184--184

American Mathematical Monthly
Volume 121, Number 3, March, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 185--186
            Kenneth A. Ross and   
                 Ann E. Watkins   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for 2014 to Joan Leitzel for
                                  Distinguished Service to Mathematics . . 187--190
            David H. Bailey and   
               Jonathan Borwein   Pi Day Is Upon Us Again and We Still Do
                                  Not Know if Pi Is Normal . . . . . . . . 191--206
              Stephan Berendonk   The Length of Spirographic Curves  . . . 207--212
             Alec S. Cooper and   
              Oleg Pikhurko and   
            John R. Schmitt and   
          Gregory S. Warrington   Martin Gardner's Minimum
                                  No-$3$-in-a-Line Problem . . . . . . . . 213--221
     Aleksander Maliszewski and   
             Marcin Szyszkowski   Level Sets on Disks  . . . . . . . . . . 222--228
              Junesang Choi and   
             Hari M. Srivastava   Series Involving the Zeta Functions and
                                  a Family of Generalized Goldbach--Euler
                                  Series . . . . . . . . . . . . . . . . . 229--236
                        B. Sury   A Polynomial Parent to a
                                  Fibonacci--Lucas Relation  . . . . . . . 236--236
                    Trevor Hyde   A Wallis Product on Clovers  . . . . . . 237--243
                   Mircea Merca   On Some Power Sums of Sine or Cosine . . 244--248
               William Johnston   The Weighted Hermite Polynomials Form a
                                  Basis for $ L_2 (\mathbb {R}) $  . . . . 249--253
                    Gerd Herzog   A Proof of Lie's Product Formula . . . . 254--257
                  Kenneth Lange   Hadamard's Determinant Inequality  . . . 258--259
            S. Koçak and   
                     M. Limoncu   Mean of the Mean of the Mean \ldots  . . 259--259
             Justin Tatch Moore   Justin Tatch Moore . . . . . . . . . . . 260--262
           Marc Chamberland and   
               Doron Zeilberger   A Short Proof of McDougall's Circle
                                  Theorem  . . . . . . . . . . . . . . . . 263--265
                      Anonymous   Problems and Solutions . . . . . . . . . 266--273
                     Mark Kozek   Book Review: \booktitleMathematics 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} . . . . . . . . 274--278
                      Anonymous   Back Matter  . . . . . . . . . . . . . . 279--280

American Mathematical Monthly
Volume 121, Number 4, April, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 281--282
              Andrew J. Simoson   Periodicity Domains and the Transit of
                                  Venus  . . . . . . . . . . . . . . . . . 283--298
             Daniel J. Velleman   A Drug-Induced Random Walk . . . . . . . 299--317
             Alexei Yu. Uteshev   Analytical Solution for the Generalized
                                  Fermat--Torricelli Problem . . . . . . . 318--331
             Samuel J. Ferguson   A One-Sentence Line-of-Sight Proof of
                                  the Extreme Value Theorem  . . . . . . . 331--331
        Martin Kovár and   
               Alena Chernikava   On the Proof of the Existence of
                                  Undominated Strategies in Normal Form
                                  Games  . . . . . . . . . . . . . . . . . 332--337
             Chao-Ping Chen and   
                  Junesang Choi   An Asymptotic Formula for $ (1 + 1 /
                                  x)^x $ Based on the Partition Function   338--343
                   Steffen Eger   Stirling's Approximation for Central
                                  Extended Binomial Coefficients . . . . . 344--349
              Thorsten Neuschel   A New Proof of Stirling's Formula  . . . 350--352
                Ralph M. Krause   Zeta(2) Once Again . . . . . . . . . . . 353--354
             Andrea M. Hyde and   
                Paul D. Lee and   
              Blair K. Spearman   Polynomials $ (x^3 - n)(x^2 + 3) $
                                  Solvable Modulo Any Integer  . . . . . . 355--358
                        B. Sury   Macaulay Expansion . . . . . . . . . . . 359--360
                   J. J. Koliha   Evaluating Lebesgue Integrals
                                  Efficiently with the FTC . . . . . . . . 361--364
                      Anonymous   Problems and Solutions . . . . . . . . . 365--372
             Jeffrey Nunemacher   Book Review: \booktitleEncounters 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} . . . . 373--376
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 121, Number 5, May, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 377--378
            Allison Henrich and   
              Louis H. Kauffman   Unknotting Unknots . . . . . . . . . . . 379--390
            Alan F. Beardon and   
                      Ian Short   A Geometric Representation of Continued
                                  Fractions  . . . . . . . . . . . . . . . 391--402
                   Tom Leinster   Rethinking Set Theory  . . . . . . . . . 403--415
             Allan J. Kroopnick   An Elementary Application of Brouwer's
                                  Fixed Point Theorem to Transition
                                  Matrices . . . . . . . . . . . . . . . . 415--415
               Jon Grantham and   
            Witold Jarnicki and   
               John Rickert and   
                     Stan Wagon   Repeatedly Appending Any Digit to
                                  Generate Composite Numbers . . . . . . . 416--421
               Iddo Ben-Ari and   
                  Diana Hay and   
         Alexander Roitershtein   On Wallis-type Products and Pólya's Urn
                                  Schemes  . . . . . . . . . . . . . . . . 422--432
               Paul Pollack and   
         Enrique Treviño   The Primes that Euclid Forgot  . . . . . 433--437
             Emmanuel Tsukerman   Solution of Sondow's Problem: A
                                  Synthetic Proof of the Tangency Property
                                  of the Parbelos  . . . . . . . . . . . . 438--443
José Ángel Cid Araújo   A Difference Equation Leading to the
                                  Irrationality of $ \surd 2 $ . . . . . . 443--443
              Nathan A. Carlson   A Connection between Furstenberg's and
                                  Euclid's Proofs of the Infinitude of
                                  Primes . . . . . . . . . . . . . . . . . 444--444
                   Ming-Chia Li   An Elementary Proof of a Generalization
                                  of Banach's Mapping Theorem  . . . . . . 445--446
                  M. L. Glasser   A Technique in Contour Integration . . . 447--448
                   Kyle Luh and   
             Nicholas Pippenger   Large-Deviation Bounds for Sampling
                                  without Replacement  . . . . . . . . . . 449--454
                      Anonymous   Problems and Solutions . . . . . . . . . 455--462
                  Daniel Ullman   Book Review: \booktitleMath 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}  . . . . . . 463--466
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 467--468
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 121, Number 6, June, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 469--470
           Alberto Facchini and   
               Giulia Simonetta   Rational Numbers, Finite Cyclic Monoids,
                                  Divisibility Rules, and Numbers of Type
                                  $ 99 \cdots {} 900 \cdots {} 0 $ . . . . 471--485
              David Borwein and   
        Jonathan M. Borwein and   
                   Brailey Sims   On the Solution of Linear Mean
                                  Recurrences  . . . . . . . . . . . . . . 486--498
                Josef Rukavicka   Rejection of Laplace's Demon . . . . . . 498--498
             C. W. Groetsch and   
                     S. A. Yost   Vertical Projection in a Resisting
                                  Medium: Reflections on Observations of
                                  Mersenne . . . . . . . . . . . . . . . . 499--505
            J. Scott Carter and   
           Daniel S. Silver and   
              Susan G. Williams   Three Dimensions of Knot Coloring  . . . 506--514
                   Harris Kwong   An Alternate Proof of Sury's
                                  Fibonacci--Lucas Relation  . . . . . . . 514--514
                     Jose Pujol   On Hamilton's Nearly-Forgotten Early
                                  Work on the Relation between Rotations
                                  and Quaternions and on the Composition
                                  of Rotations . . . . . . . . . . . . . . 515--522
                        B. Sury   A Heuristic Argument for Hua's Identity
                                  Using Geometric Series . . . . . . . . . 522--522
                   Tommy Wright   Lagrange's Identity and Congressional
                                  Apportionment  . . . . . . . . . . . . . 523--528
                    Chai Wah Wu   Pigeonholes and Repunits . . . . . . . . 529--533
               Kevin K. Ferland   Record Crossword Puzzles . . . . . . . . 534--536
              Michael Z. Spivey   A Combinatorial Proof for the
                                  Alternating Convolution of the Central
                                  Binomial Coefficients  . . . . . . . . . 537--540
            Nikolai Nikolov and   
               Blagovest Sendov   A Converse of the Gauss--Lucas Theorem   541--544
                 Yared Nigussie   Finding Your Seat Versus Tossing a Coin  545--546
              Erich Badertscher   A Simple Direct Proof of Marden's
                                  Theorem  . . . . . . . . . . . . . . . . 547--548
                      Anonymous   Problems and Solutions . . . . . . . . . 549--556
               James A. Swenson   Book Review: \booktitleWhich Numbers Are
                                  Real?, By Michael Henle. Mathematical
                                  Association of America, Washington, DC,
                                  2012, x + 219 pp., ISBN
                                  978-0-88385-777-9, \$53.00}  . . . . . . 557--560
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 121, Number 7, August, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 561--562
      Erwan Brugallé and   
                   Kristin Shaw   A Bit of Tropical Geometry . . . . . . . 563--589
                Marcelo Brafman   Another Algebraic Pythagorean Proof  . . 589--589
                Bryan Brown and   
            Michael Dairyko and   
       Stephan Ramon Garcia and   
                   Bob Lutz and   
                 Michael Someck   Four Quotient Set Gems . . . . . . . . . 590--598
Vinícius G. Pereira de Sá and   
     Celina M. H. de Figueiredo   Blind-friendly von Neumann's Heads or
                                  Tails  . . . . . . . . . . . . . . . . . 600--609
               Richard Katz and   
                 Mike Krebs and   
                Anthony Shaheen   Zero Sums on Unit Square Vertex Sets and
                                  Plane Colorings  . . . . . . . . . . . . 610--618
                      D. Zagier   A Refinement of a Theorem of J. E.
                                  Littlewood . . . . . . . . . . . . . . . 618--618
            Rajendra Bhatia and   
                  Rajesh Sharma   Positive Linear Maps and Spreads of
                                  Matrices . . . . . . . . . . . . . . . . 619--624
               Wen D. Chang and   
              Russell A. Gordon   Trisecting Angles in Pythagorean
                                  Triangles  . . . . . . . . . . . . . . . 625--631
                  Diego Marques   Yet Another Direct Proof of the
                                  Uncountability of the Transcendental
                                  Numbers  . . . . . . . . . . . . . . . . 631--631
                   Rom Pinchasi   Points Covered an Odd Number of Times by
                                  Translates . . . . . . . . . . . . . . . 632--636
                   Meinolf Geck   On the Characterization of Galois
                                  Extensions . . . . . . . . . . . . . . . 637--639
           Samuel G. Moreno and   
Esther M. García-Caballero   Simpson's Rule and Sums of Powers  . . . 639--639
                  F. Dreher and   
                      T. Samuel   Continuous Images of Cantor's Ternary
                                  Set  . . . . . . . . . . . . . . . . . . 640--643
               Robert A. Beezer   Extended Echelon Form and Four Subspaces 644--647
                      Anonymous   Problems and Solutions . . . . . . . . . 648--657
                   Michael Barr   Book Review: \booktitleThe 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} . . . . . . . . . . . . . . . . 658--660
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 121, Number 8, October, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 659--662
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Mark Krusemeyer   The Seventy-Fourth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 663--673
             Persi Diaconis and   
             Xuancheng Shao and   
           Kannan Soundararajan   Carries, Group Theory, and Additive
                                  Combinatorics  . . . . . . . . . . . . . 674--688
      Marc Deléglise and   
                  Andrew Markoe   On the Maximum Arc Length of Monotonic
                                  Functions  . . . . . . . . . . . . . . . 689--699
              David Borwein and   
               Jonathan Borwein   Deriving New Sinc Results from Old . . . 700--705
             Michael Joswig and   
         Günter M. Ziegler   Foldable Triangulations of Lattice
                                  Polygons . . . . . . . . . . . . . . . . 706--710
                 Jonathan Novak   Pólya's Random Walk Theorem . . . . . . . 711--716
            Michael Schramm and   
              John Troutman and   
                Daniel Waterman   Segmentally Alternating Series . . . . . 717--722
                  John Molokach   Law of Cosines --- A Proof Without Words 722--722
                 Mark H. Holmes   Connections Between Cubic Splines and
                                  Quadrature Rules . . . . . . . . . . . . 723--726
               M. Scott Osborne   Hausdorffization and Such  . . . . . . . 727--733
                Donald M. Davis   Binomial Coefficients Involving Infinite
                                  Powers of Primes . . . . . . . . . . . . 734--737
                      Anonymous   Problems and Solutions . . . . . . . . . 738--745
                  Brian M. Loft   Book Review: \booktitleThe 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}    746--748
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 121, Number 9, November, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 747--750
                      Anonymous   Front Matter . . . . . . . . . . . . . . 747--750
                 Fred Adler and   
        Elizabeth S. Allman and   
           Lisette G. de Pillis   A Letter from the Guest Editors  . . . . 751--753
          Jonathan R. Potts and   
                  Mark A. Lewis   A Mathematical Approach to Territorial
                                  Pattern Formation  . . . . . . . . . . . 754--770
                     Mike Steel   Tracing Evolutionary Links between
                                  Species  . . . . . . . . . . . . . . . . 771--792
           Roderick Edwards and   
                     Leon Glass   Dynamics in Genetic Networks . . . . . . 793--809
                 Hoa Nguyen and   
             Ricardo Cortez and   
                     Lisa Fauci   Computing Flows Around Microorganisms:
                                  Slender-Body Theory and Beyond . . . . . 810--823
                   David Terman   Mathematical Neuroscience  . . . . . . . 824--839
          Trachette Jackson and   
           Natalia Komarova and   
                Kristin Swanson   Mathematical Oncology: Using Mathematics
                                  to Enable Cancer Discoveries . . . . . . 840--856
            Laurie J. Heyer and   
                Jeffrey L. Poet   Synthetic Biology: A New Frontier  . . . 857--867
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 121, Number 10, December, 2014

                      Anonymous   Front Matter . . . . . . . . . . . . . . 867--870
                      Anonymous   Front Matter . . . . . . . . . . . . . . 867--870
            Peter J. Giblin and   
                 J. Paul Warder   Evolving Evolutoids  . . . . . . . . . . 871--889
                   Pieter Moree   Numerical Semigroups, Cyclotomic
                                  Polynomials, and Bernoulli Numbers . . . 890--902
                         Lei Ni   A Perron-type Theorem on the Principal
                                  Eigenvalue of Nonsymmetric Elliptic
                                  Operators  . . . . . . . . . . . . . . . 903--908
              Pete L. Clark and   
             Niels J. Diepeveen   Absolute Convergence in Ordered Fields   909--916
              William F. Trench   An Unnoticed Consequence of Szeg\Ho's
                                  Distribution Theorem . . . . . . . . . . 917--921
                Jack Button and   
             Maurice Chiodo and   
     Mariano Zeron-Medina Laris   Coset Intersection Graphs for Groups . . 922--926
                Sam Northshield   Complex Descartes Circle Theorem . . . . 927--931
           Pallab Kanti Dey and   
                 R. Thangadurai   The Length of an Arithmetic Progression
                                  Represented by a Binary Quadratic Form   932--936
               Marshall Hampton   Cosines and Cayley, Triangles and
                                  Tetrahedra . . . . . . . . . . . . . . . 937--941
                   Felipe Acker   A Note on the Spectral Theorem in the
                                  Finite-Dimensional Real Case . . . . . . 942--945
                      Anonymous   Problems and Solutions . . . . . . . . . 946--953
                      Anonymous   Problems and Solutions . . . . . . . . . 946--953
             Genevieve S. Walsh   Book Review: \booktitleMostly Surfaces,
                                  By Richard Evan Schwartz. American
                                  Mathematical Society, Providence, RI,
                                  2010, xiii + 314 pp., ISBN
                                  978-0-8218-5368-9, \$47.00}  . . . . . . 954--956
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 957--959
                      Anonymous   Monthly Referees for 2014  . . . . . . . 960--962
                Jonathan Sondow   From the \booktitleMonthly Over 100
                                  Years Ago \ldots . . . . . . . . . . . . 963--963
                Jonathan Sondow   From the Monthly Over 100 Years
                                  Ago\ldots  . . . . . . . . . . . . . . . 963--963
            Amrik Singh Nimbran   One More Proof of the Irrationality of $
                                  \sqrt 2 $  . . . . . . . . . . . . . . . 964--964
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 122, Number 1, January, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 1--2
               Scott T. Chapman   A Letter from the Editor: 2015 is the
                                  Centennial Year of the MAA . . . . . . . 3--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--23
             Titu Andreescu and   
          Vladimir Georgiev and   
             Oleg Mushkarov and   
          Vladimir Georgiev and   
                 Oleg Mushkarov   Napoleon Polygons  . . . . . . . . . . . 24--29
            Kenneth S. Williams   Historical Remark on Ramanujan's Tau
                                  Function . . . . . . . . . . . . . . . . 30--35
            Branko \'Curgus and   
           Robert I. Jewett and   
               Robert I. Jewett   Somewhat Stochastic Matrices . . . . . . 36--42
                  Michael Hardy   Stereographic Trigonometric Identities   43--47
                     Xianzu Lin   Infinitely Many Primes in the Arithmetic
                                  Progression $ k n - 1 $  . . . . . . . . 48--51
                  P. Mark Kayll   Deranged Matchings: Enumeration by
                                  Integration!!  . . . . . . . . . . . . . 51--51
           Francis C. Motta and   
         Patrick D. Shipman and   
               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--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
                      Anonymous   Problems and Solutions . . . . . . . . . 75--82
             Edward F. Schaefer   Book Review: \booktitleThe Mathematics
                                  of Encryption: An Elementary
                                  Introduction, Reviewed work(s): The
                                  Mathematics of Encryption: An Elementary
                                  Introduction. By Margaret Cozzens and
                                  Steven J. Miller. American Mathematical
                                  Society, Providence, RI, 2013, xviii +
                                  332 pp., ISBN 978-0-8218-8321-1,
                                  \$49.00} . . . . . . . . . . . . . . . . 83--88
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 2, February, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 87--90
                Yves Nievergelt   Backward Analysis Explained with Monthly
                                  Payments . . . . . . . . . . . . . . . . 91--120
        Christopher O'Neill and   
             Roberto Pelayo and   
                 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--137
Carlos A. Catalá de la Torre   A New Proof for a Sharp van der Corput's
                                  Lemma  . . . . . . . . . . . . . . . . . 138--142
                S. Koçak   Dihedral Angles of the Regular
                                  $n$-Simplex  . . . . . . . . . . . . . . 143--143
             Arseniy V. Akopyan   Geometry of the Cardioid . . . . . . . . 144--150
                Marcelo Brafman   Another Algebraic Pythagorean Proof  . . 150--150
                    G. Molinari   Elementary Prime Identities  . . . . . . 151--154
        Joachim Gräter and   
        Karl-Joachim Wirths and   
            Karl-Joachim Wirths   On Elementary Bounds for $ \sum
                                  \nolimits_{k = n}^\infty {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 and   
Esther M. García-Caballero   A Geometric Proof of Morrie's Law  . . . 168--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
                      Anonymous   Problems and Solutions . . . . . . . . . 175--182
              Gerald B. Folland   Book Review: \booktitleHidden
                                  Harmony---Geometric Fantasies: The Rise
                                  of Complex Function Theory, By Umberto
                                  Bottazzini and Jeremy Gray. Springer,
                                  New York, 2013, xvii + 848 pp., ISBN
                                  978-1-4614-5724-4, \$189.00 (hardcover),
                                  ISBN 978-1-4614-5725-1, \$149.00 (eBook) 183--188
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 3, March, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 189--190
              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 and   
               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 and   
Esther M. García-Caballero   A Geometric Proof of Morrie's Law  . . . 233--233
                Jaap Eising and   
            David Radcliffe and   
                       Jaap Top   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 and   
                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 $ \mathbb
                                  {R}^n $ onto $ \mathbb {R}^n $ . . . . . 268--271
              Mizan R. Khan and   
                 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 Horak   Partitioning $ \mathbb {R}^n $ into
                                  Connected Components . . . . . . . . . . 280--283
          Konstantinos Gaitanas   An Explicit Formula for the Prime
                                  Counting Function Which is Valid
                                  Infinitely Often . . . . . . . . . . . . 283--283
                      Anonymous   Problems and Solutions . . . . . . . . . 284--291
                   Reuben Hersh   Book Review: \booktitleHow Humans Learn
                                  to Think Mathematically. Exploring the
                                  Three Worlds of Mathematics  . . . . . . 292--296
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 4, April, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 297--298
             Richard Montgomery   The Three-Body Problem and the Shape
                                  Sphere . . . . . . . . . . . . . . . . . 299--321
            Rebekah Ann Gilbert   A Fine Rediscovery . . . . . . . . . . . 322--331
   Juliá Cufí and   
Agustí Reventó and   
        Carlos J. RodrÍz   Curvature for Polygons . . . . . . . . . 332--337
               Karl Dilcher and   
                 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 and   
                  Brian R. Hunt   Absolute Continuity of a Function and
                                  Uniform Integrability of Its Divided
                                  Differences  . . . . . . . . . . . . . . 362--366
              Vadim Ponomarenko   A Base Conversion Surprise . . . . . . . 366 402--366
               Michal Adamaszek   Face Numbers of Down-Sets  . . . . . . . 367--370
               Dirk Huylebrouck   Generalizing Wallis' Formula . . . . . . 371--372
                   Mehmet Kilic   A New Geometric Proof for Morley's
                                  Theorem  . . . . . . . . . . . . . . . . 373--376
              Hidefumi Katsuura   A New Infinite Series Representation of
                                  $ \ln k $  . . . . . . . . . . . . . . . 376--376
               Maxim Arnold and   
               Vadim Zharnitsky   Cyclic Evasion in the Three Bug Problem  377--380
             \Ethorde Barali\'c   A Short Proof of the Bradley Theorem . . 381--385
                Byron Schmuland   Linear Recurrences via Probability . . . 386--389
                      Anonymous   Problems and Solutions . . . . . . . . . 390--397
                    Will Traves   Book Review: \booktitlePerspectives in
                                  Projective Geometry. A Guided Tour
                                  Through Real and Complex Geometry  . . . 398--402
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 5, May, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 405--406
                Donald G. Saari   Mathematics and the ``Dark Matter''
                                  Puzzle . . . . . . . . . . . . . . . . . 407--423
                  Alex Chin and   
                Gary Gordon and   
             Kellie MacPhee and   
                Charles Vincent   Pick a Tree --- Any Tree . . . . . . . . 424--432
             Christian Aebi and   
                   Grant Cairns   Generalizations of Wilson's Theorem for
                                  Double-, Hyper-, Sub- and
                                  Superfactorials  . . . . . . . . . . . . 433--443
       Óscar Ciaurri and   
              Luis M. Navas and   
          Francisco J. Ruiz and   
                 Juan L. Varona   A Simple Computation of $ \zeta (2 k) $  444--451
                     Nam Gu Heo   A New Proof of the Pythagorean Theorem   451--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--466
                 Ivan Izmestiev   A Porism for Cyclic Quadrilaterals,
                                  Butterfly Theorems, and Hyperbolic
                                  Geometry . . . . . . . . . . . . . . . . 467--475
   Maria Bras-Amorós and   
                    Marta Pujol   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--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--494
    Ádám Besenyei   The Brocard Angle and a Geometrical Gem
                                  from Dmitriev and Dynkin . . . . . . . . 495--499
                      Anonymous   Problems and Solutions . . . . . . . . . 500--507
              Gerald B. Folland   Book Review: \booktitleA History in Sum:
                                  150 Years of Mathematics at Harvard
                                  (1825--1975), By Steve Nadis and
                                  Shing-Tung Yau. Harvard University
                                  Press, Cambridge, 2013, xviii + 249 pp.,
                                  ISBN 978-0-674-72500-3, \$39.95} . . . . 508--510
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 511--512
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 6, June, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 513--514
         Dennis D. A. Epple and   
                  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 and   
      Norbert Hungerbühler   A Simple Proof of Poncelet's Theorem (on
                                  the Occasion of Its Bicentennial)  . . . 537--551
          Aaditya Salgarkar and   
                    Rishi Mehta   Alternate Derivation for the Parity of
                                  the $ n^{\rm th} $ Triangular Number . . 551--551
             Nicholas J. Werner   Covering Numbers of Finite Rings . . . . 552--566
                   J. Rooin and   
                    A. Alikhani   A Geometric Proof of the Beppo--Levi
                                  Inequality . . . . . . . . . . . . . . . 566--566
                Alan Haynes and   
                    Sara Munday   Diophantine Approximation and Coloring   567--580
                 Haryono Tandra   A Proof of the Replacement Theorem by
                                  the Notion of Maximal Elements . . . . . 580--580
            Satomi Murakami and   
                    Hiroki Ohwa   Periodic Points of Some Discontinuous
                                  Mappings . . . . . . . . . . . . . . . . 581--586
              Vadim Ponomarenko   Asymptotic Formula for $ (1 + 1 / x)^x
                                  $, Revisited . . . . . . . . . . . . . . 587--587
                 Virgil Barnard   A Proof of Quadratic Reciprocity . . . . 588--592
                  Daniel Daners   Uniform Continuity of Continuous
                                  Functions on Compact Metric Spaces . . . 592--592
                  Iosif Pinelis   On the Hölder and Cauchy--Schwarz
                                  Inequalities . . . . . . . . . . . . . . 593--595
      José Gascón   Another Proof That the Real Numbers $
                                  \mathbb {R} $ Are Uncountable  . . . . . 596--597
                 Haryono Tandra   A Simple Modified Version for Ferguson's
                                  Proof of the Extreme Value Theorem . . . 598--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
                      Anonymous   Problems and Solutions . . . . . . . . . 604--612
                   Marion Cohen   Book Review: \booktitleMathematicians on
                                  Creativity. Edited by Peter Borwein,
                                  Peter Liljedahl, and Helen Zhai, The
                                  Mathematical Association of America,
                                  Washington DC, 2014, xviii + 199 pp,
                                  ISBN 978-0-88385-574-4, \$30.00} . . . . 613--616
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 7, August, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 616--618
     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 and   
           Ana Berrizbeitia and   
            Michael Dairyko and   
          Claudia Rodriguez and   
                Amanda Ruiz and   
              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--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--689
           James E. McClure and   
                    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--699
                      Anonymous   Problems and Solutions . . . . . . . . . 700--707
              Joseph Malkevitch   Book Review: \booktitleThe Mathematical
                                  Coloring Book  . . . . . . . . . . . . . 708--712
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 8, October, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 713--714
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Mark Krusemeyer   The Seventy-Fifth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 715--725
        California Jack Cassidy   Early Round Bluffing in Poker  . . . . . 726--744
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   Volume/Surface Area Relations for
                                  $n$-Dimensional Spheres, Pseudospheres,
                                  and Catenoids  . . . . . . . . . . . . . 745--756
                 P. Pollack and   
                    J. Vandehey   Besicovitch, Bisection, and the
                                  Normality of $ 0. (1)(4)(9)(16)(25) $    757--765
              Shui-Hung Hou and   
                      Edwin Hou   On a Recursion Formula Related to
                                  Confluent Vandermonde  . . . . . . . . . 766--772
     Syahida Che Dzul-Kifli and   
                     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--780
                Tadashi Tokieda   A Viscosity Proof of the Cauchy--Schwarz
                                  Inequality . . . . . . . . . . . . . . . 781--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 and   
                 Matthias Gorny   An Exponential Inequality for Symmetric
                                  Random Variables . . . . . . . . . . . . 786--789
            Melvyn B. Nathanson   Pairs of Matrices in GL$_2$ (R$_{\geq
                                  0}$ ) That Freely Generate . . . . . . . 790--792
       Zsolt Lengvárszky   Pythagoras by Integral . . . . . . . . . 792--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 Borwein and   
                  Scott Chapman   I Prefer Pi: Addenda . . . . . . . . . . 800--800
                      Anonymous   Problems and Solutions . . . . . . . . . 801--808
                  Ferebee Tunno   Book Review: \booktitleReviews . . . . . 809--812
            Tamás Titkos   How to Make Equivalent Measures? . . . . 812--812
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 9, November, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 813--814
                  Zhiqin Lu and   
                  Julie Rowlett   The Sound of Symmetry  . . . . . . . . . 815--835
        Péter Hajnal and   
László I. Szabó and   
                   Vilmos Totik   Convex Polygons and Common Transversals  836--844
             Titu Andreescu and   
          Vladimir Georgiev and   
                 Oleg Mushkarov   Correction to ''Napoleon Polygons''  . . 844--844
               Qingchun Ren and   
 Jürgen Richter-Gebert and   
                Bernd Sturmfels   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 and   
        Aviezri S. Fraenkel and   
               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--892
                Nguyen S. Hoang   A Limit Comparison Test for General
                                  Series . . . . . . . . . . . . . . . . . 893--896
        Hamid Reza Daneshpajouh   A New Proof of $\aleph_0$-Resolvability
                                  of a Metric Space Without an Isolated
                                  Point  . . . . . . . . . . . . . . . . . 897--898
                      Anonymous   Problems and Solutions . . . . . . . . . 899--906
               Robin Hartshorne   Book Review: \booktitleReviews . . . . . 907--911
                  Michael Henle   Book Review: \booktitleReviews . . . . . 912--915
                      Anonymous   Statement of Ownership . . . . . . . . . 916--916
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 122, Number 10, December, 2015

                      Anonymous   Front Matter . . . . . . . . . . . . . . 917--918
              Zhaiming Shen and   
             Lasse Rempe-Gillen   The Exponential Map Is Chaotic: An
                                  Invitation to Transcendental Dynamics    919--940
            Fred Kuczmarski and   
               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 and   
               Peter J. Cameron   A Graph Partition Problem  . . . . . . . 972--982
                   Jaime Gaspar   All Triangles at Once  . . . . . . . . . 982--982
        Guram Bezhanishvili and   
                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--989
        Mehmet Kiliç and   
             Sahin Koçak   On Products of Uniquely Geodesic Spaces  990--994
            Sadi Abu-Saymeh and   
             Mowaffaq Hajja and   
               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--1007
                   Jun-Ming Zhu   A Semi-Finite Proof of Jacobi's Triple
                                  Product Identity . . . . . . . . . . . . 1008--1009
                      Anonymous   Problems and Solutions . . . . . . . . . 1010--1017
                 Michael Harris   Book Review: \booktitleReviews . . . . . 1018--1022
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 1023--1025
                      Anonymous   Monthly Referees for 2015  . . . . . . . 1026--1028
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 123, Number 1, January, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 1--2
           Richard D. Neidinger   A Fair-Bold Gambling Function Is Simply
                                  Singular . . . . . . . . . . . . . . . . 3--18
              Adrien Kassel and   
                David B. Wilson   The Looping Rate and Sandpile Density of
                                  Planar Graphs  . . . . . . . . . . . . . 19--39
        J. Ángel Cid and   
     Rodrigo López Pouso   Integration by Parts and by Substitution
                                  Unified with Applications to Green's
                                  Theorem and Uniqueness for ODEs  . . . . 40--52
               M. Ram Murty and   
              Chester Weatherby   A Generalization of Euler's Theorem for
                                  $ \zeta (2 k) $  . . . . . . . . . . . . 53--65
                  Shivarajkumar   Beyond Schur's Conjecture  . . . . . . . 66--70
                Yaroslav Shitov   The Diameter of Chess Grows
                                  Exponentially  . . . . . . . . . . . . . 71--77
             Daniel J. Velleman   Monthly Gems . . . . . . . . . . . . . . 77--77
            Michael C. Slattery   On a Property Motivated by Groups with a
                                  Specified Number of Subgroups  . . . . . 78--81
                      Oleg Viro   Pictorial Calculus for Isometries  . . . 82--87
          Konstantinos Gaitanas   A Partial Solution of Representing $1$
                                  as a Sum of $n$ Distinct Unit Fractions  87--87
             David G. Radcliffe   A Function That Is Surjective on Every
                                  Interval . . . . . . . . . . . . . . . . 88--89
                   Thomas Osler   Iterations for the Lemniscate Constant
                                  Resembling the Archimedean Algorithm for
                                  Pi . . . . . . . . . . . . . . . . . . . 90--93
          Kuldeep Kumar Kataria   A Probabilistic Proof of the Multinomial
                                  Theorem  . . . . . . . . . . . . . . . . 94--96
                     Xiaoxue Li   A Synthetic Approach to a USAMO Problem  96--96
                      Anonymous   Problems and Solutions . . . . . . . . . 97--105
                Darren B. Glass   Book Review: \booktitleReviews . . . . . 106--112
    József Sándor   A Note on the Logarithmic Mean . . . . . 112--112
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 2, February, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 113--114
           Francis C. Motta and   
         Patrick D. Shipman and   
            Bethany D. Springer   Optimally Topologically Transitive
                                  Orbits in Discrete Dynamical Systems . . 115--135
               Ian Morrison and   
                David Swinarski   Can You Play a Fair Game of Craps with a
                                  Loaded Pair of Dice? . . . . . . . . . . 136--148
            Deborah A. Kent and   
                David J. Muraki   A Geometric Solution of a Cubic by Omar
                                  Khayyam \ldots in Which Colored Diagrams
                                  Are Used Instead of Letters for the
                                  Greater Ease of Learners . . . . . . . . 149--160
Mariano Suárez-Álvarez   Cyclic Extensions Are Radical  . . . . . 160--160
                    Josh Hiller   Old Friends in Unexpected Places: Pascal
                                  (and Other) Matrices in $ {\rm GL}_n(C)
                                  $  . . . . . . . . . . . . . . . . . . . 161--167
             John Brillhart and   
         Richard Blecksmith and   
                    Mike Decaro   Using Conic Sections to Factor Integers  168--174
              Michael Z. Spivey   Probabilistic Proofs of a Binomial
                                  Identity, Its Inverse, and
                                  Generalizations  . . . . . . . . . . . . 175--180
              E. W. Dekking and   
                  F. M. Dekking   Helge von Koch's Snowflake Curve
                                  Revisited  . . . . . . . . . . . . . . . 181--184
                 Jonathan Baker   Strong Convexity Does Not Imply Radial
                                  Unboundedness  . . . . . . . . . . . . . 185--188
                    Xin-Jie Sun   On Sums of Three Pentagonal Numbers  . . 189--191
                 Jeffrey Lutgen   A Combinatorial Proof of an Alternating
                                  Convolution Identity for Multichoose
                                  Numbers  . . . . . . . . . . . . . . . . 192--196
                      Anonymous   Problems and Solutions . . . . . . . . . 197--204
             Jeffrey Nunemacher   Book Review: \booktitleReviews . . . . . 205--208
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 3, March, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 209--210
              Jennifer J. Quinn   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for 2016 to George Berzsenyi for
                                  Distinguished Service to Mathematics . . 211--213
          Karen Hunger Parshall   Mathematics and the Politics of Race:
                                  The Case of William Claytor (Ph.D.,
                                  University of Pennsylvania, 1933)  . . . 214--240
                   John P. Boyd   Correcting Three Errors in Kantorovich &
                                  Krylov's Approximate Methods of Higher
                                  Analysis . . . . . . . . . . . . . . . . 241--257
            Boris M. Bekker and   
             Oleg A. Ivanov and   
         Alexander S. Merkurjev   Milnor's Lemma, Newton's Method, and
                                  Continued Fractions  . . . . . . . . . . 258--266
           Clark Kimberling and   
           Kenneth B. Stolarsky   Slow Beatty Sequences, Devious
                                  Convergence, and Partitional Divergence  267--273
               Steve Butler and   
                 Ron Graham and   
                  Richard Stong   Inserting Plus Signs and Adding  . . . . 274--279
                Tom Mertens and   
                     Jeff Weeks   Electromagnetism in a Multiconnected
                                  Universe . . . . . . . . . . . . . . . . 280--286
               Jeffrey S. Ovall   The Laplacian and Mean and Extreme
                                  Values . . . . . . . . . . . . . . . . . 287--291
                  Peter McGrath   On the Smooth Jordan Brouwer Separation
                                  Theorem  . . . . . . . . . . . . . . . . 292--295
  José L. Ramírez   An Identity of Carlitz and Its
                                  Generalization . . . . . . . . . . . . . 295--295
                      Anonymous   Problems and Solutions . . . . . . . . . 296--303
               Craig H. Jackson   Book Review: \booktitleReviews . . . . . 304--308
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 4, April, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 309--310
            Paul-Jean Cahen and   
               Jean-Luc Chabert   What You Should Know About
                                  Integer-Valued Polynomials . . . . . . . 311--337
              Keith Johnson and   
               Kira Scheibelhut   Rational Polynomials That Take Integer
                                  Values at the Fibonacci Numbers  . . . . 338--346
                Gary Brookfield   Factoring Forms  . . . . . . . . . . . . 347--362
               Grant Cairns and   
          Yuri Nikolayevsky and   
                 Gavin Rossiter   Conewise Linear Periodic Maps of the
                                  Plane with Integer Coefficients  . . . . 363--375
               Mohamed Ayad and   
                 Omar Kihel and   
                   Jesse Larone   When Does a Given Polynomial with
                                  Integer Coefficients Divide Another? . . 376--381
             Neil J. Calkin and   
                Beth Novick and   
       Hayato Ushijima-Mwesigwa   What Moser Could Have Asked: Counting
                                  Hamilton Cycles in Tournaments . . . . . 382--386
                     Nuno Luzia   A Proof of The Pythagorean Theorem After
                                  Descartes  . . . . . . . . . . . . . . . 386--386
              Ovidiu Costin and   
               Neil Falkner and   
              Jeffery D. McNeal   Some Generalizations of the
                                  Riemann--Lebesgue Lemma  . . . . . . . . 387--391
         Peter S. Landweber and   
           Emanuel A. Lazar and   
                     Neel Patel   On Fiber Diameters of Continuous Maps    392--397
     Daniel López-Aguayo   Irrationality via Maximality . . . . . . 397--397
        Dennis S. Bernstein and   
       Khaled F. Aljanaideh and   
               Arthur E. Frazho   Laurent Series and $ l^p $ Sequences . . 398--398
                      Anonymous   Problems and Solutions . . . . . . . . . 399--406
                 Thomas Garrity   Book Review: \booktitleReviews . . . . . 407--412
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 5, May, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 413--414
            Sòren Eilers   The LEGO Counting Problem  . . . . . . . 415--426
                 Harold P. Boas   Mocposite Functions  . . . . . . . . . . 427--438
             Tom M. Apostol and   
        Mamikon A. Mnatsakanian   A New Look at Surfaces of Constant
                                  Curvature  . . . . . . . . . . . . . . . 439--447
        Jaime Cruz-Sampedro and   
  Margarita Tetlalmatzi-Montiel   Hardy's Reduction for a Class of
                                  Liouville Integrals of Elementary
                                  Functions  . . . . . . . . . . . . . . . 448--470
                 Piotr Josevich   An Alternative Approach to the Product
                                  Rule . . . . . . . . . . . . . . . . . . 470--470
               G. L. Mullen and   
                 D. Panario and   
                     D. Thomson   Fast and Simple Modular Interpolation
                                  Using Factorial Representation . . . . . 471--480
                  Iosif Pinelis   On Measurable Semigroups in $R$  . . . . 481--481
            Arseniy Sheydvasser   A Corrigendum to Unreasonable Slightness 482--485
               Karl Dilcher and   
              Christophe Vignat   Euler and the Strong Law of Small
                                  Numbers  . . . . . . . . . . . . . . . . 486--490
                    Tim Hsu and   
                San José   Rational Nonaxis Points on the Unit
                                  Circle Have Irrational Angles  . . . . . 490--490
                  Iosif Pinelis   Explicit Additive Decomposition of Norms
                                  on $ R^2 $ . . . . . . . . . . . . . . . 491--496
               Michael Gaul and   
                Fred Kuczmarski   Parabolas and Archimedes' $ 2 /
                                  3$-Property  . . . . . . . . . . . . . . 497--501
                  Peter McGrath   An Extremely Short Proof of the Hairy
                                  Ball Theorem . . . . . . . . . . . . . . 502--503
                      Anonymous   Problems and Solutions . . . . . . . . . 504--511
         Gerald L. Alexanderson   Book Review: \booktitleReviews . . . . . 512--514
                      Anonymous   Editor's End Notes . . . . . . . . . . . 515--516
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 6, June, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 517--518
        Jennifer M. Johnson and   
     János Kollár   Arcology . . . . . . . . . . . . . . . . 519--541
               Steve Butler and   
             Persi Diaconis and   
                     Ron Graham   The Mathematics of the Flip and
                                  Horseshoe Shuffles . . . . . . . . . . . 542--556
         Valerio De Angelis and   
               Dominic Marcello   Wilf's Conjecture  . . . . . . . . . . . 557--573
       F. Adrián F. Tojo   A Hyperbolic Analog of the Phasor
                                  Addition Formula . . . . . . . . . . . . 574--582
               Pablo A. Panzone   Tiling the Plane with Different Hexagons
                                  and Triangles  . . . . . . . . . . . . . 583--591
          Franklin H. J. Kenter   How to Win Your Betting Pool with
                                  Jensen's Inequality and the Law of Large
                                  Numbers  . . . . . . . . . . . . . . . . 592--596
               Erhan Gürel   On the Occurrence of Perfect Squares
                                  Among Values of Certain Polynomial
                                  Products . . . . . . . . . . . . . . . . 597--599
                    Hunter Swan   Expected Number of Vertices of a
                                  Hypercube Slice  . . . . . . . . . . . . 600--604
                 Peter McCauley   Proofs Without Using Limits of Both
                                  Calculus Power Rules . . . . . . . . . . 604--604
             Pham Duy Khanh and   
                  Marc Lassonde   Quasiconvex Linear Perturbations and
                                  Convexity  . . . . . . . . . . . . . . . 605--608
                 Ariel Amir and   
           Mikhail Lemeshko and   
                Tadashi Tokieda   Surprises in Numerical Expressions of
                                  Physical Constants . . . . . . . . . . . 609--612
                      Anonymous   Problems and Solutions . . . . . . . . . 613--620
              Leslie Hogben and   
                   Mark Hunacek   Book Review: \booktitleReviews . . . . . 621--624
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 7, August, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 625--626
             Laura Florescu and   
              Lionel Levine and   
                    Yuval Peres   The Range of a Rotor Walk  . . . . . . . 627--642
               Lawrence Zalcman   A Tale of Three Theorems . . . . . . . . 643--656
Márton Balázs and   
              Áron Folly   An Electric Network for Nonreversible
                                  Markov Chains  . . . . . . . . . . . . . 657--682
            Vincent E. Coll and   
                      Jeff Dodd   A Characteristic Averaging Property of
                                  the Catenary . . . . . . . . . . . . . . 683--688
              Dennis Ivanov and   
              Serge Tabachnikov   The Six Circles Theorem Revisited  . . . 689--698
                Arnon Avron and   
              Nachum Dershowitz   Cayley's Formula: A Page From The Book   699--700
                  Michael Hardy   On Tangents and Secants of Infinite Sums 701--703
                    Alex Kasman   Factorization of a Matrix Differential
                                  Operator Using Functions in Its Kernel   704--709
             Brian D. Sittinger   Computing $ \zeta (2 m) $ by using
                                  Telescoping Sums . . . . . . . . . . . . 710--715
               Yuanyuan Yao and   
                      Wenxia Li   Generating Iterated Function Systems for
                                  the Vicsek Snowflake and the Koch Curve  716--721
                      Anonymous   Problems and Solutions . . . . . . . . . 722--730
                 Matthew Richey   Book Review  . . . . . . . . . . . . . . 731--736
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 8, October, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 737--738
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Mark Krusemeyer   The Seventy-Sixth William Lowell Putnam
                                  Mathematical Competition . . . . . . . . 739--752
            Jeffrey C. Lagarias   Erd\Hos, Klarner, and the $ 3 x + 1 $
                                  Problem  . . . . . . . . . . . . . . . . 753--776
                Dvij Bajpai and   
             Daniel J. Velleman   Anonymity in Predicting the Future . . . 777--788
           Philippe Caldero and   
    Jérôme Germoni   Equilateral Triangles and the Fano Plane 789--801
              T. S. Michael and   
                     Val Pinciu   The Art Gallery Theorem, Revisited . . . 802--807
               Lon Mitchell and   
           Michael A. Jones and   
               Brittany Shelton   Abelian and Non-Abelian Triangle
                                  Mysteries  . . . . . . . . . . . . . . . 808--813
                  Yong Kong and   
                  Shaowei Zhang   The Adventitious Angles Problem: The
                                  Lonely Fractional Derived Angle  . . . . 814--816
  J. Jerónimo-Castro and   
                  C. Yee-Romero   Maximal Isoptic Chords of Convex Curves  817--820
       Olivier de La Grandville   An Alternate Derivation of the
                                  Euler--Poisson Equation  . . . . . . . . 821--824
                  J. A. Grzesik   Yet Another Analytic Proof of Napoleon's
                                  Theorem  . . . . . . . . . . . . . . . . 824--824
       Bálint Farkas and   
                Sven-Ake Wegner   Variations on Barbalat's Lemma . . . . . 825--830
                      Anonymous   Problems and Solutions . . . . . . . . . 831--839
                   Mark Kidwell   Book Review  . . . . . . . . . . . . . . 840--843
                    Halil Mutuk   A Physical Proof for Cauchy's Inequality 843--843
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 9, November, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 845--846
               Scott T. Chapman   A Letter From the Editor: Jonathan M.
                                  Borwein (1951--2016) . . . . . . . . . . 847--848
              Paul Baginski and   
             Ryan Rodriguez and   
        George J. Schaeffer and   
                      Yiwei She   Finding Elements With Given
                                  Factorization Lengths and Multiplicities 849--870
                   Lyle Ramshaw   Stråhle's Equal-Tempered Triumph  . . . . 871--883
              Jean C. Cortissoz   A Note on Harmonic Functions on Surfaces 884--893
            Uuganbaatar Ninjbat   Another Memorable Mongolian Olympiad
                                  Problem: A Two-Colored Rectangular
                                  Lattice  . . . . . . . . . . . . . . . . 894--899
          Josh Brown Kramer and   
            Jonathan Cutler and   
                A. J. Radcliffe   The Multistep Friendship Paradox . . . . 900--908
               Sean Eastman and   
              Selwyn Hollis and   
         Kawee Numpacharoen and   
                Jared Schlieper   The Volume of the Spatial Region
                                  Corresponding to $ n \times n $
                                  Correlation Matrices . . . . . . . . . . 909--918
                Ivica Martinjak   Two Extensions of the Sury's Identity    919--919
                Bernd Schomburg   Primitivity and Orbit Decomposition  . . 920--923
                Adrian W. Dudek   On the Success of Mishandling Euclid's
                                  Lemma  . . . . . . . . . . . . . . . . . 924--927
            Alan J. Hoffman and   
                    Chai Wah Wu   A Simple Proof of a Generalized
                                  Cauchy--Binet Theorem  . . . . . . . . . 928--930
                 Nicolae Anghel   Optimal Bounds for the Roots of
                                  Polynomials  . . . . . . . . . . . . . . 931--935
          Anthony J. Bevelacqua   A Family of Non-Euclidean PIDs . . . . . 936--939
          Kuldeep Kumar Kataria   An Alternate Proof of the Binomial
                                  Theorem  . . . . . . . . . . . . . . . . 940--940
                      Anonymous   Problems and Solutions . . . . . . . . . 941--948
              Gerald B. Folland   Book Review  . . . . . . . . . . . . . . 949--952
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 123, Number 10, December, 2016

                      Anonymous   Front Matter . . . . . . . . . . . . . . 953--954
               Scott T. Chapman   A Letter from the Editor: The Long and
                                  Winding Road . . . . . . . . . . . . . . 955--958
                Franco Bradshaw   Single Digit NFL Scores  . . . . . . . . 959--959
             Alfred Geroldinger   Sets of Lengths  . . . . . . . . . . . . 960--988
          Anton A. Klyachko and   
             Anton N. Vassilyev   Balanced Factorizations  . . . . . . . . 989--1000
            Melvyn B. Nathanson   Cantor Polynomials and the Fueter--Pólya
                                  Theorem  . . . . . . . . . . . . . . . . 1001--1012
         Aaron M. Broussard and   
         Martin E. Malandro and   
               Abagayle Serreyn   Optimizing the Video Game Multi-Jump:
                                  Player Strategy, AI, and Level Design    1013--1032
        Jeffrey C. Lagarias and   
            Takumi Murayama and   
               D. Harry Richman   Dilated Floor Functions That Commute . . 1033--1038
       Stephan Ramon Garcia and   
                   Florian Luca   Quotients of Fibonacci Numbers . . . . . 1039--1044
          Richard Ehrenborg and   
                      Alex Happ   Parking Cars of Different Sizes  . . . . 1045--1048
                      Anonymous   Corrigendum to ''A New Proof of the
                                  Change of Variable Theorem for the
                                  Riemann Integral'' . . . . . . . . . . . 1049--1049
                      Anonymous   Problems and Solutions . . . . . . . . . 1050--1057
                  Chris A. Marx   Book Review: \booktitleA First Course in
                                  the Calculus of Variations. By Mark Kot.
                                  Student Mathematical Library Vol 72,
                                  American Mathematical Society,
                                  Providence, Rhode Island, 2014, x + 298
                                  pp., ISBN 978-1-4704-1495-5, \$50} . . . 1058--1061
                      Anonymous   Monthly Referees for 2016  . . . . . . . 1062--1066
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??


American Mathematical Monthly
Volume 124, Number 1, January, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 1--2
              Susan Jane Colley   Letter from the Editor . . . . . . . . . 3--3
                 Ryan Blair and   
             Marion Campisi and   
              Jesse Johnson and   
            Scott A. Taylor and   
                   Maggy Tomova   Neighbors of Knots in the Gordian Graph  4--23
            Robert J. Vanderbei   The Falling Slinky . . . . . . . . . . . 24--36
             Antonio Cafure and   
                  Eda Cesaratto   Irreducibility Criteria for Reciprocal
                                  Polynomials and Applications . . . . . . 37--53
              Joseph A. Gallian   Seventy-Five Years of the Putnam
                                  Mathematical Competition*  . . . . . . . 54--59
             Saveliy Ustuzhanin   A Novel Way to Prove the Irrationality
                                  of $ \sqrt 2 $ . . . . . . . . . . . . . 59--59
                 Nicolae Anghel   On a 2015 Putnam Problem Related to a
                                  Double Recursion . . . . . . . . . . . . 60--69
                    Ian Stewart   Why Do All Triangles Form a Triangle?    70--73
                     Cezar Lupu   A New Proof of the Finsler--Hadwiger
                                  Inequality . . . . . . . . . . . . . . . 73--73
           Yusuf Z. Gürtas   Chebyshev Polynomials and the Minimal
                                  Polynomial of $ \cos (2 \pi / n) $ . . . 74--78
                 Eli Shamir and   
                  Benny Sudakov   Two-Sided, Unbiased Version of Hall's
                                  Marriage Theorem . . . . . . . . . . . . 79--80
               Bart van Munster   Hausdorffization and Homotopy  . . . . . 81--82
                      Anonymous   Problems and Solutions . . . . . . . . . 83--91
               Jason Rosenhouse   Reviews  . . . . . . . . . . . . . . . . 92--95
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 2, February, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 98--98
          Annalisa Crannell and   
                Marc Frantz and   
                Fumiko Futamura   The Image of a Square  . . . . . . . . . 99--115
                  Allen Stenger   Experimental Math for Math Monthly
                                  Problems . . . . . . . . . . . . . . . . 116--131
             Michael Maltenfort   Characterizing Additive Systems  . . . . 132--148
            Bisharah Libbus and   
              Gordon Simons and   
                   Yi-Ching Yao   Rotating Multiple Sets of Labeled Points
                                  to Bring Them Into Close Coincidence: A
                                  Generalized Wahba Problem  . . . . . . . 149--160
                Scott Ginebaugh   Generalized Infinite Products for Powers
                                  of $ e^{1 / k} $ . . . . . . . . . . . . 161--165
             Christian Aebi and   
                   Grant Cairns   Sums of Quadratic Residues and
                                  Nonresidues  . . . . . . . . . . . . . . 166--169
                   Idris Mercer   Another Proof That There Are Infinitely
                                  Many Primes  . . . . . . . . . . . . . . 169--169
        Chatchawan Panraksa and   
               Pornrat Ruengrot   A Note on Average of Roots of Unity  . . 170--174
                  Charles Audet   Maximal Area of Equilateral Small
                                  Polygons . . . . . . . . . . . . . . . . 175--178
                      Anonymous   Problems and Solutions . . . . . . . . . 179--187
                     Alan Baker   The Philosophies of Mathematics  . . . . 188--192
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 3, March, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 194--194
          Annalisa Crannell and   
                    Doug Ensley   Yueh-Gin Gung and Dr. Charles Y. Hu
                                  Award for 2017 to Martha Siegel for
                                  Distinguished Service to Mathematics . . 195--197
                  Pete L. Clark   The Euclidean Criterion for Irreducibles 198--216
                 Joseph Bak and   
      Strashimir G. Popvassilev   The Evolution of Cauchy's Closed Curve
                                  Theorem and Newman's Simple Proof  . . . 217--231
            Jonathan Sondow and   
               Kieren MacMillan   Primary Pseudoperfect Numbers,
                                  Arithmetic Progressions, and the
                                  Erd\Hos--Moser Equation  . . . . . . . . 232--240
              Koji Momihara and   
              Masashi Shinohara   Distance Sets on Circles . . . . . . . . 241--254
                  Michael Weiss   Where Are the Rational Squares?  . . . . 255--259
               Shubhodip Mondal   Surjectivity of Maps Induced on Matrices
                                  by Polynomials and Entire Functions  . . 260--264
               Dirk Huylebrouck   A New Regular (Compound) Polyhedron (of
                                  Infinite Kepler--Poinsot Type) . . . . . 265--268
                  Joseph Plante   A Proof of Bonnet's Version of the Mean
                                  Value Theorem by Methods of Cauchy . . . 269--273
                      Anonymous   Problems and Solutions . . . . . . . . . 274--281
               Dominic Lanphier   Book Review: \booktitleSumming it Up:
                                  From One Plus One to Modern Number
                                  Theory . . . . . . . . . . . . . . . . . 282--288
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 4, April, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 290--290
             Paul E. Becker and   
               Martin Derka and   
          Sheridan Houghten and   
                Jennifer Ulrich   Build a Sporadic Group in Your Basement  291--305
               John P. Boyd and   
                    Houjun Wang   Convergent Power Series for Boundary
                                  Value Problems and Eigenproblems with
                                  Application to Atmospheric and Oceanic
                                  Tides  . . . . . . . . . . . . . . . . . 306--323
                    Arno Berger   More Grade School Triangles  . . . . . . 324--336
            Hiroshi Maehara and   
                  Horst Martini   On Lexell's Theorem  . . . . . . . . . . 337--344
      Antonio Avilés and   
              Grzegorz Plebanek   A Little Ado about Rectangles  . . . . . 345--350
               Trevor D. Wooley   A Superpowered Euclidean Prime Generator 351--352
                   Carl McTague   On the Greatest Common Divisor of
                                  Binomial Coefficients  . . . . . . . . . 353--356
             Mehtaab S. Sawhney   A Telescoping Proof of the AM--GM
                                  Inequality . . . . . . . . . . . . . . . 356--356
                David E. Speyer   A Counting Proof of a Theorem of
                                  Frobenius  . . . . . . . . . . . . . . . 357--359
          Evelyn R. Easdale and   
          Jolene E. Fleming and   
              Bogdan D. Suceava   Convergence for Series With Terms
                                  Defined by a Recurrence Relation . . . . 360--364
             Christian Elsholtz   Golomb's Conjecture on Prime Gaps  . . . 365--368
                      Anonymous   Problems and Solutions . . . . . . . . . 369--378
                   Marion Cohen   Book Review: \booktitleMom the Chemistry
                                  Professor: Personal Accounts and Advice
                                  from Chemistry Professors Who Are
                                  Mothers  . . . . . . . . . . . . . . . . 379--383
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 5, May, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 386--386
              Maria Deijfen and   
       Alexander E. Holroyd and   
                James B. Martin   Friendly Frogs, Stable Marriage, and the
                                  Magic of Invariance  . . . . . . . . . . 387--402
              Juan Monterde and   
                  David Rochera   Holditch's Ellipse Unveiled  . . . . . . 403--421
            Frantisek Marko and   
                Semyon Litvinov   On the Steiner--Routh Theorem for
                                  Simplices  . . . . . . . . . . . . . . . 422--435
            Marek Balcerzak and   
           Michal Poplawski and   
             Julia Wódka   Local Extrema and Nonopenness Points of
                                  Continuous Functions . . . . . . . . . . 436--443
           Jeremiah Farrell and   
               William Johnston   Mathematical Evolution . . . . . . . . . 444--444
    Péter E. Frenkel and   
   József Pelikán   On the Greatest Common Divisor of the
                                  Value of Two Polynomials . . . . . . . . 446--450
             Valerio De Angelis   The Stern Diatomic Sequence via
                                  Generalized Chebyshev Polynomials  . . . 451--455
            Melvyn B. Nathanson   Subalgebras of a Polynomial Ring That
                                  Are Not Finitely Generated . . . . . . . 456--458
               Beniamin Bogosel   A Geometric Proof of the Siebeck--Marden
                                  Theorem  . . . . . . . . . . . . . . . . 459--463
                 Haryono Tandra   A More Direct Proof of the Extreme Value
                                  Theorem  . . . . . . . . . . . . . . . . 464--464
                      Anonymous   Problems and Solutions . . . . . . . . . 465--474
                   Reuben Hersh   Book Review: \booktitleElements of
                                  Mathematics: From Euclid to Gödel . . . . 475--478
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 480--480
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 6, June / July, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 481--482
              Francis Edward Su   Mathematics for Human Flourishing  . . . 483--493
           Andrey Kupavskii and   
              János Pach   From Tarski's Plank Problem to
                                  Simultaneous Approximation . . . . . . . 494--505
               David Aldous and   
                    Weijian Han   Introducing Nash Equilibria via an
                                  Online Casual Game That People Actually
                                  Play . . . . . . . . . . . . . . . . . . 506--517
                   Grant Cairns   Equitable Candy Sharing  . . . . . . . . 518--526
                Finbarr Holland   On the Limiting Behavior of Solutions of
                                  Linear Difference Equations  . . . . . . 527--534
                Paul Carter and   
               David Lowry-Duda   On Functions Whose Mean Value Abscissas
                                  Are Midpoints, with Connections to
                                  Harmonic Functions . . . . . . . . . . . 535--542
                Darren B. Glass   Klein Four Actions on Graphs and Sets    543--547
           Mikhail A. Patrakeev   Dissection of an Equilateral Triangle
                                  into Five Congruent Open Sets  . . . . . 547--547
             Heinrich Steinlein   Fermat's Little Theorem and Gauss
                                  Congruence: Matrix Versions and Cyclic
                                  Permutations . . . . . . . . . . . . . . 548--553
                   Mircea Merca   The Riemann Zeta Function With Even
                                  Arguments as Sums Over Integer
                                  Partitions . . . . . . . . . . . . . . . 554--557
                   Lee K. Jones   An Elementary Derivation of the
                                  Numerical Integration Bounds in
                                  Beginning Calculus . . . . . . . . . . . 558--561
              Romeo Mestrovi\'c   A Very Short Proof of the Infinitude of
                                  Primes . . . . . . . . . . . . . . . . . 562--562
                      Anonymous   Problems and Solutions . . . . . . . . . 563--571
             Jeffrey Nunemacher   Book Review: \booktitleVector Calculus,
                                  Linear Algebra, and Differential Forms:
                                  A Unified Approach (5th Edition) . . . . 572--575
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 7, August / September, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 577--578
                  Peter Winkler   The Sleeping Beauty Controversy  . . . . 579--587
            Arseniy Akopyan and   
             Vladislav Vysotsky   On the Lengths of Curves Passing Through
                                  Boundary Points of a Planar Convex Shape 588--596
                Moa Apagodu and   
               Doron Zeilberger   Using the ``Freshman's Dream'' to Prove
                                  Combinatorial Congruences  . . . . . . . 597--608
             Philip P. West and   
             Brian D. Sittinger   A Further Stroll into the Eisenstein
                                  Primes . . . . . . . . . . . . . . . . . 609--620
             John C. Bowers and   
               Philip L. Bowers   A Menger Redux: Embedding Metric Spaces
                                  Isometrically in Euclidean Space . . . . 621--636
             David A. Levin and   
                    Yuval Peres   Counting Walks and Graph Homomorphisms
                                  via Markov Chains and Importance
                                  Sampling . . . . . . . . . . . . . . . . 637--641
                      Anonymous   The Other Moore Method . . . . . . . . . 641--641
            Christian Axler and   
           Thomas Leßmann   On the First $k$-Ramanujan Prime . . . . 642--646
            Amrik Singh Nimbran   An Infinite Product for the Square Root
                                  of an Integer  . . . . . . . . . . . . . 647--650
                   Tomasz Kania   On Bases That Are Closed Under
                                  Multiplication . . . . . . . . . . . . . 651--653
           Óscar Ciaurri   Maria Gaetana Agnesi Meets Johannes
                                  Kepler . . . . . . . . . . . . . . . . . 654--658
                 Jitender Singh   Another Proof of the Binomial Theorem    658--658
                      Anonymous   Problems and Solutions . . . . . . . . . 659--666
                 Calvin Jongsma   Book Review: \booktitleSourcebook in the
                                  Mathematics of Medieval Europe and North
                                  Africa . . . . . . . . . . . . . . . . . 667--672
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 8, October, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 673--674
       Leonard F. Klosinski and   
     Gerald L. Alexanderson and   
                Mark Krusemeyer   The Seventy-Seventh William Lowell
                                  Putnam Mathematical Competition  . . . . 675--687
                 Soham Basu and   
             Daniel J. Velleman   On Gauss's First Proof of the
                                  Fundamental Theorem of Algebra . . . . . 688--694
           Bernd C. Kellner and   
                Jonathan Sondow   Power-Sum Denominators . . . . . . . . . 695--709
               Hugo Parlier and   
                   Samuel Zappa   Distances in Domino Flip Graphs  . . . . 710--722
           Stephan Ramon Garcia   Linearly Independent Spanning Sets . . . 722--722
                Ulrich Abel and   
            Linda Beukemann and   
           Vitaliy Kushnirevych   Rolling Curves: An Old Proof of the
                                  Roulette Lemma . . . . . . . . . . . . . 723--736
             David J. Platt and   
            Timothy S. Trudgian   On the Sum of Two Squares and At Most
                                  Two Powers of 2  . . . . . . . . . . . . 737--740
               Jens Marklof and   
     Andreas Strömbergsson   The Three Gap Theorem and the Space of
                                  Lattices . . . . . . . . . . . . . . . . 741--745
    Zoltán Kánnai   A One-to-One Popcorn Function  . . . . . 746--748
                   Stasys Jukna   Minkowski Complexity of Sets: An Easy
                                  Lower Bound  . . . . . . . . . . . . . . 749--753
                      Anonymous   Problems and Solutions . . . . . . . . . 754--762
                      Anonymous   Problems for Metagrobologists: A
                                  Collection of Puzzles with Real
                                  Mathematical, Logical, or Scientific
                                  Content; One Hundred Prisoners and A
                                  Light Bulb . . . . . . . . . . . . . . . 763--768
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 9, November, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 769--770
           Scott T. Chapman and   
              Joseph A. Gallian   From the Guest Editors . . . . . . . . . 771--771
                      Anonymous   About the Cover  . . . . . . . . . . . . 772--772
            Paul-Jean Cahen and   
           Jean-Luc Chabert and   
               Kiran S. Kedlaya   Bhargava's Early Work: The Genesis of
                                  $P$-Orderings  . . . . . . . . . . . . . 773--790
                    Colin Adams   Turning Knots into Flowers and Related
                                  Undergraduate Research . . . . . . . . . 791--806
                 Cesar E. Silva   On Mixing-Like Notions in Infinite
                                  Measure  . . . . . . . . . . . . . . . . 807--825
           Adrian Chun Pong Chu   Dihedral Angle of the Regular
                                  $n$-Simplex via Menelaus' Theorem  . . . 826--826
                     Yufei Zhao   Extremal Regular Graphs: Independent
                                  Sets and Graph Homomorphisms . . . . . . 827--843
                     Rishi Nath   Advances in the Theory of Cores and
                                  Simultaneous Core Partitions . . . . . . 844--861
                  Nathan Kaplan   Counting Numerical Semigroups  . . . . . 862--875
     Carlos Castillo-Chavez and   
          Christopher Kribs and   
                 Benjamin Morin   Student-Driven Research at the
                                  Mathematical and Theoretical Biology
                                  Institute  . . . . . . . . . . . . . . . 876--892
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??

American Mathematical Monthly
Volume 124, Number 10, December, 2017

                      Anonymous   Front Matter . . . . . . . . . . . . . . 893--894
               Peter Frankl and   
                 Amram Meir and   
              János Pach   Decomposition of a Cube into Nearly
                                  Equal Smaller Cubes  . . . . . . . . . . 895--904
           Michael Barnsley and   
                   Andrew Vince   Self-Similar Polygonal Tiling  . . . . . 905--921
         Emmanuel Tsukerman and   
                  Ellen Veomett   Brunn--Minkowski Theory and Cauchy's
                                  Surface Area Formula . . . . . . . . . . 922--929
               Yann Bugeaud and   
             Andrej Dujella and   
        Tomislav Pejkovi\'c and   
                    Bruno Salvy   Absolute Real Root Separation  . . . . . 930--936
                    Martin Kreh   ``Lights Out'' and Variants  . . . . . . 937--950
               Andrew Granville   Squares in Arithmetic Progressions and
                                  Infinitely Many Primes . . . . . . . . . 951--954
              Joshua Cooper and   
                  Anton Swifton   Throwing a Ball as Far as Possible,
                                  Revisited  . . . . . . . . . . . . . . . 955--959
           Sunil K. Chebolu and   
                 Keir Lockridge   How Many Units Can a Commutative Ring
                                  Have?  . . . . . . . . . . . . . . . . . 960--965
             Jen\Ho Szigeti and   
                    Leon vanWyk   A Constructive Elementary Proof of the
                                  Skolem--Noether Theorem for Matrix
                                  Algebras . . . . . . . . . . . . . . . . 966--968
            Umberto Cerruti and   
                    Nadir Murru   If the Primes are Finite, Then All of
                                  Them Divide the Number One . . . . . . . 969--969
                      Anonymous   Problems and Solutions . . . . . . . . . 970--978
                      Anonymous   Book Review: \booktitleFrom Music to
                                  Mathematics: Exploring the Connections,
                                  Gareth E. Roberts. Johns Hopkins
                                  University Press, Baltimore, MD, 2016.
                                  Price: \$49.95 ISBN: 978-1-4214-1918-3}  979--982
                      Anonymous   Editor's Endnotes  . . . . . . . . . . . 983--985
                      Anonymous   Monthly Referees For 2017  . . . . . . . 986--988
                      Anonymous   Back Matter  . . . . . . . . . . . . . . ??