People delight in working on problems \"because they are there,\" for the sheer pleasure of meeting a challenge. This is a book full of such delights. In it, Murray S. Klamkin brings together 75 original USA Mathematical Olympiad (USAMO) problems for yearss 1972-1986, with many improvements, extensions, related exercises, open problems, referneces and solutions, often showing alternative approaches. The problems are coded by subject, and solutions are arranged by subject, e.g., algebra, number theory, solid geometry, etc., as an aid to those interested in a particular field. Included is a Glossary of frequently used terms and theorems and a comprehensive bibliography with items numbered and referred to in brackets in the text. This a collection of problemsand solutions of arresting ingenuit, all accessible to secondary school students. The USAMO has been taken annually by about 150 of the nation's best high school mathematics students. This exam helps to find and encourage high school students with superior mathematical talent and creativity and is the culmination of a three-tiered competition that begins with the American High School Mathematics Examination (AHSME) taken by over 400, 000 students. The eight winners of the USAMO are canidates for the US team in the International Mathematical Olympiad. Schools are encouraged to join this large and important enterprise. See page x of the preface for further information. this book includes a list of all of the top contestants in the USAMO and their schools. The problems are intriguing and the solutions elegant and informative. Students and teachers will enjoy working these challenging problems. Indeed, all hose who are mathematically inclined will find many delights and pleasant challenges in this book., Series: Anneli Lax New Mathematical Library, Issue: 2011, Bibliography: p. [120]-127

Often questions about tiling space or a polygon lead to other questions. For instance, tiling by cubes raises questions about finite abelian groups. Tiling by triangles of equal areas soon involves Sperner's lemma from topology and valuations from algebra. The first six chapters of Algebra and Tiling form a self-contained treatment of these topics, beginning with Minkowski's conjecture about lattice tiling of Euclidean space by unit cubes, and concluding with Laczkowicz's recent work on tiling by similar triangles. The concluding chapter presents a simplified version of Rédei's theorem on finite abelian groups: if such a group is factored as a direct product of subsets, each containing the identity element, and each of prime order, than at least one of them is a subgroup. Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers and professional mathematicians will find the book equally appealing., Series: Carus Mathematical Monographs, Issue: 27, Edition: Presentable Ex-Library, Includes bibliographical references and index, Minkowski's conjecture -- Cubical clusters -- Tiling by the semicross and cross -- Packing and covering by the semicross and cross -- Tiling by triangles of equal areas -- Tiling by similar triangles -- Rédei's theorem -- Epilog -- Lattices -- The character group and exact sequences -- Formal sums -- Cyclotomic polynomials

People delight in working on problems \"because they are there,\" for the sheer pleasure of meeting a challenge. This is a book full of such delights. In it, Murray S. Klamkin brings together 75 original USA Mathematical Olympiad (USAMO) problems for yearss 1972-1986, with many improvements, extensions, related exercises, open problems, referneces and solutions, often showing alternative approaches. The problems are coded by subject, and solutions are arranged by subject, e.g., algebra, number theory, solid geometry, etc., as an aid to those interested in a particular field. Included is a Glossary of frequently used terms and theorems and a comprehensive bibliography with items numbered and referred to in brackets in the text. This a collection of problemsand solutions of arresting ingenuit, all accessible to secondary school students. The USAMO has been taken annually by about 150 of the nation's best high school mathematics students. This exam helps to find and encourage high school students with superior mathematical talent and creativity and is the culmination of a three-tiered competition that begins with the American High School Mathematics Examination (AHSME) taken by over 400, 000 students. The eight winners of the USAMO are canidates for the US team in the International Mathematical Olympiad. Schools are encouraged to join this large and important enterprise. See page x of the preface for further information. this book includes a list of all of the top contestants in the USAMO and their schools. The problems are intriguing and the solutions elegant and informative. Students and teachers will enjoy working these challenging problems. Indeed, all hose who are mathematically inclined will find many delights and pleasant challenges in this book., Series: Anneli Lax New Mathematical Library, Edition: First Printing, Bibliography: p. [120]-127

xii, 394 pages : 23 cm "Appendix number 10: papers and talks presented at meetings of the Texas Section ... ": pages 261-360 Includes index

xi, 203 pages 20 cm, Includes bibliographical references (pages 189-190)

iii, 76 pages ; 28 cm Includes index

This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighbouring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the 'Enormous Theorem' - the classification of all simple groups whose entire proof runs to some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those 'sporadic' simple groups, are presented at an undergraduate mathematical level. -- Amazon.com

vii, 212 p. 21 cm Bibliography: p. 208-210

Includes bibliographies

Middle school mathematics teachers occupy a unique place in the mathematical development of students. These teachers need to be proficient in all elementary mathematics topics, together with some secondary mathematics topics. They demand a special kind of preparation that differs from both that of their elementary and secondary colleagues. The Mathematics Education of Teachers (MET) document published by the Conference Board of the Mathematical Sciences set forth criteria for the preparation of mathematics middle school teachers which made it critical that special programs and courses for this group emerge. This collection of articles is in response to the MET document and the result of several gatherings of mathematics educators and mathematicians training middle school teachers. We have chosen the articles that appear in this volume for several purposes: to disseminate various middle school programs structures, to detail methods of teaching specific middle school teachers content courses, and to share materials and resources. While each article describes the unique program or course of its respective institution, each also includes a common core of information to provide some consistency to the volume. In particular, all articles describing middle school programs contain information about the host institution, a history of the program, degree and testing requirements for the program and for state licensure, learning goals and objectives for the program and courses, and any available assessment data. When applicable information is included about particular courses, for example, some articles provide sample activities or syllabi and some have a description of courses in the appendix. Most articles have links to websites containing further information about the program, courses, state requirements, or resources that can be downloaded and used directly.

An Episodic History of Mathematics delivers a series of snapshots of the history of mathematics from ancient times to the twentieth century. The intent is not to provide an encyclopaedic history of mathematics, but to give the reader a sense of mathematical culture and history. The book also acquaints the reader with the nature and techniques of mathematics through its exercises. The book introduces the genesis of many mathematical ideas. For example, while Krantz does not get into the nuts and bolts of Andrew Wiles's solution of Fermat's Last Theorem, he does describe some of the stream of thought that created the problem and led to its solution. The focus in this text is on doing – getting involved with the mathematics and solving problems. Every chapter ends with a detailed problem set that will provide the student with many avenues for exploration and many new entrees into the subject.

https://archive.org/details/indexofamericanm0001mayk

The Contest Problem Book I through IV all in new condition can be sold together. Contact seller for question, please.

Arithmetical Wonderland Is Intended As An Unorthodox Mathematics Textbook For Students In Elementary Education, In A Contents Course Offered By A Mathematics Department. The Scope Is Deliberately Restricted To Cover Only Arithmetic, Even Though Geometric Elements Are Introduced Whenever Warranted. For Example, What The Euclidean Algorithm For Finding The Greatest Common Divisors Of Two Numbers Has To Do With Euclid Is Showcased. Many Students Find Mathematics Somewhat Daunting. It Is The [author];'s Belief That Much Of That Is Caused Not By The Subject Itself, But By The Language Of Mathematics. In This Book, Much Of The Discussion Is In Dialogues Between Alice, Of Wonderland Fame, And The Twins Tweedledum And Tweedledee Who Hailed From Through The Looking Glass. The Boys Are Learning High Arithmetic Or Elementary Number Theory From Alice, And The Reader Is Carried Along In This Academic Exploration. Thus Many Formal Proofs Are Converted To Soothing Everyday Language. Nevertheless, The Book Has Considerable Depth. It Examines Many Arcane Corners Of The Subject, And Raises Rather Unorthodox Questions. For Instance, Alice Tells The Twins That Six Divided By Three Is Two Only Because Of An Implicit Assumption That Division Is Supposed To Be Fair, Whereas Fairness Does Not Come Into Addition, Subtraction Or Multiplication. Some Topics Often Not Covered Are Introduced Rather Early, Such As The Concepts Of Divisibility And Congruence.

viii, 182 p. 21 cm Includes bibliographies Introduction / R.C. Buck -- A theory of limits / E.J. McShane -- A generalized Weierstrass approximation theorem / M.H. Stone -- The spectral theorem / E.R. Lorch -- Preliminaries to functional analysis / C. Goffman

xi, 192 pages : 20 cm, Includes bibliographical references (pages 189-190) and index, Systems of linear equations -- Vector spaces -- Determinants -- Matric polynomials -- Union and intersection -- The rational canonical form -- Elementary divisors -- Orthogonal transformations -- Endomorphisms, Bookplate of Willis H. Ware

Graph Theory Presents A Natural, Reader-friendly Way To Learn Some Of The Essential Ideas Of Graph Theory Starting From First Principles. The Format Is Similar To The Companion Text, Combinatorics: A Problem Oriented Approach Also By Daniel A. Marcus, In That It Combines The Features Of A Textbook With Those Of A Problem Workbook. The Material Is Presented Through A Series Of Approximately 360 Strategically Placed Problems With Connecting Text. This Is Supplemented By 280 Additional Problems That Are Intended To Be Used As Homework Assignments. Concepts Of Graph Theory Are Introduced, Developed, And Reinforced By Working Through Leading Questions Posed In The Problems. This Problem-oriented Format Is Intended To Promote Active Involvement By The Reader While Always Providing Clear Direction. This Approach Figures Prominently On The Presentation Of Proofs, Which Become More Frequent And Elaborate As The Book Progresses. Arguments Are Arranged In Digestible Chunks And Always Appear Along With Concrete Examples To Keep The Readers Firmly Grounded In Their Motivation. Spanning Tree Algorithms, Euler Paths, Hamilton Paths And Cycles, Planar Graphs, Independence And Covering, Connections And Obstructions, And Vertex And Edge Colorings Make Up The Core Of The Book. Hall's Theorem, The Konig-egervary Theorem, Dilworth's Theorem And The Hungarian Algorithm To The Optional Assignment Problem, Matrices, And Latin Squares Are Also Explored.--back Cover. Introduction: Problems Of Graph Theory -- A. Basic Concepts -- B. Isomorphic Graphs -- C. Bipartite Graphs -- D. Trees And Forests -- E. Spanning Tree Algorithms -- F. Euler Paths -- G. Hamilton Paths And Cycles -- H. Planar Graphs -- I. Independence And Covering -- J. Connections And Obstructions -- K. Vertex Coloring -- L. Edge Coloring -- M. Matching Theory For Bipartite Graphs -- N. Applications Of Matching Theory -- O. Cycle-free Digraphs -- P. Network Flow Theory -- Q. Flow Problems With Lower Bounds -- Answers To Selected Problems. Daniel A. Marcus. Includes Index.

Contained here are solutions to challenging problems from algebra, geometry, combinatorics and number theory featured in the earlier book, together with selected questions (without solutions) from national and regional Olympiads given during the year 2000. Intended for the serious student/problem solver, these books can help to improve performance in the Mathematical Olympiad competition. However, for those not entering the competition, there is much to challenge any mathematician, even those with advanced degrees. Different nations have different mathematical cultures, so you will find that some of the questions are extremely difficult and some rather easy. There are a wide variety of problems especially from those countries that have often done well in the IMO. Anyone interested in mathematical problem solving will encounter some beautiful mathematics in the pages of this book. If you are up to a real challenge, take some of these problems on!

Edited By Lynn Arthur Steen. Bibliography : P. 115-125.

Cover Contents National Science Foundation Budget Request for FY 1985 New Goals for Mathematics Sciences Education The Supply of Mathematical Researchers in the 1990s News and Announcements Queries Letters to the Editor NSF News & Reports 1984 AMS Elections (Nominations by Petition) New Rules Concerning Abstracts Future Meetings of the Society Plymouth, June 29-July 1 Symposium on Mathematical Biology, New York, May 28 Eugene, August 14-19 Synopses, Short Course on Environmental and Natural Resource Mathematics Call for Topics Invited Speakers and Special Sessions New AMS Publications Miscellaneous Personal Items Deaths New Doctorates (Supplement) Special Meetings AMS Reports & Communications Recent Appointments Officers of the Society, 1983 and 1984 Advertisements Registration Forms Summer List of Applicants Eugene Preregistration and Housing Reservation Form

The Combined Membership List (CML) is a comprehensive directory of the membership of the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. There are two lists of individual members.... FROM LONG DESCRIPTION

v, 40 pages ; 22 cm

April 2024 Front Cover Graduate Programs Table of Contents Masthead Letters to the Editor Notices Advertising A Word From...David Manderscheid The Quintic, the Icosahedron, and Elliptic Curves by Bruce Bartlett On the Population Size in Stochastic Differential Games by Dylan Possamai and Ludovic Tangpi Early Career Address Update In Memory of Igor Krichever by Alexander Braverman, PavelEtingof, Andrei Okounkov, Duong Phong, and Paul Wiegmann Mathematicians Confront Political Tests: The American Mathematical Society and the Red Scare in 1954 by Albert C. Lewis and Karen Hunger Parshall Princeton University Press What Is...a Bialynicki-Birula Decomposition? by Alberto Franceschini Bookshelf AMS Bookshelf What Can We Say About "Math/Art"? by George Hart Calls for Nominations & Applications 2024 Prizes AMS Updates Mathematics People Thomas Yizhao Hou won William Bentzer Prize Classified Advertising New Books Offered by the AMS Meetings & Conferences of the AMS April Table of Contents Meetings & Conferences of the AMS Undergraduate Opportunity Awards New AMS Textbook

vii, 54 pages : 23 cm

Number 1 / JANUARY 1997......Page 1 Reading the Master: Newton and the Birth of Celestial Mechanics / Bruce Pourciau......Page 3 Applications of linear Algebra in Calculus / Jack W. Rogers, Jr.......Page 22 Periodicity, Quasiperiodicity, and Bieberbach's Theorem on Crystallographic Groups / A. Vince......Page 29 Integration Over Spheres and the Divergence Theorem for Balls / John A. Baker......Page 38 Math Lingo vs. Plain English: Double Entendre / Reuben Hersh......Page 50 Three Secrets About Harmonic Functions / R. B. Burckel......Page 54 A Short Proof of the Erdos-Mordell Theorem / Vilmos Komomik......Page 59 Inverting the Difference of Hilbert Space Projections / Don Buckholtz......Page 62 Glimpses of Algebraic Geometry / I. G. Bashmakova and E. I. Slavutin......Page 64 PROBLEMS AND SOLUTIONS......Page 70 Mathematics and Politics: Voting Power and Proof By Alan D. Taylor / Samuel Merrill, III......Page 84 TELEGRAPHIC REVIEWS......Page 88 THE AUTHORS......Page 92 EDITOR'S ENDNOTES......Page 93 Number 2 / FEBRUARY 1997......Page 101 Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Deborah Tepper Haimo / Carole B. Lacampagne......Page 103 Scheduling Conflict-free Parties for a Dating Service / Bryan L. Shader and Chanyoung Lee Shader......Page 105 An Infinite Set of Heron Triangles with Two Rational Medians / Ralph H. Buchholz and Randall L. Rathbun......Page 113 Connected Sprouts / T. K. Lam......Page 122 Regular Expressions for Program Computations / Ronald E. Prather......Page 126 Relations Between Crossing Numbers of Carsten Thomassen Complete and Complete Bipartite Graphs / R. Bruce Richter......Page 137 Carries, Combinatorics, and an Amazing Matrix / John M. Holte......Page 144 A New Look at Euler's Theorem for Polyhedra: A Comment / Walter Nef......Page 156 The Hopping Hoop / Tadashi F. Tokieda......Page 158 Principal Ideal Domains are Almost Euclidean / John Greene......Page 160 A Colorful Determinantal Identity, a Conjecture of Rota, and Latin Squares / Shmuel Onn......Page 162 Very Semisimple Modules / W. K. Nicholson......Page 165 ApSimon's Diagonal Point Triangle Problem / Richard K. Guy......Page 169 PROBLEMS AND SOLUTIONS......Page 174 The Encyclopedia of Integer Sequences By N. J. A. Sloane and Simon Plouffe / Richard K. Guy......Page 186 TELEGRAPHIC REVIEWS......Page 191 THE AUTHORS......Page 196 Number 3 / MARCH 1997......Page 209 Some probabilistic Aspects of Set Partitions / Jim Pitman......Page 211 Building an International Reputation: The Case of J. J. Sylvester (1814-1897) / Karen Hunger Parshall and Eugene Seneta......Page 220 The Inverse-Similarity Problem for Real Orthogonal Matrices / Geoffrey R. Goodson......Page 233 Rethinking Rigor in Calculus: The Role of the Mean Value Theorem / Thomas W. Tucker......Page 241 Commentary on Rethinking Rigor in Calculus: .The Role of the Mean Value Theorem / Howard Swann......Page 251 Fermat's Last Theorem, The Four Color Conjecture, and Bill Clinton for April Fools' Day / Edward B. Burger and Frank Morgan......Page 256 Euler's \phi Function on Arithmetic Progressions / D. J. Newman......Page 266 A Note on Weyl's Inequality / Steve Fisk......Page 267 Minimal Polynomials Over Cyclotomic Fields / Ming-chang Kang......Page 268 The Significance of Mathematics: The Mathematicians' Share in the General Human Condition / Wilhelm Magnus......Page 271 PROBLEMS AND SOLUTIONS......Page 280 Emblems of Mind: The Inner Life of Music and Mathematics. By Edward Rothstein / Jeffrey Nunemacher......Page 292 A Tour of the Calculus. By David Berlinski / Israel Kleiner......Page 294 TELEGRAPHIC REVIEWS......Page 298 THE AUTHORS......Page 302 Number 4 / APRIL 1997......Page 309 Rectangular Invertible Matrices / A. J. Berrick and M. E. Keating......Page 311 Equal Pay for All Prisoners / Maarten C. Boerlijst, Martin A. Nowak and Karl Sigmund......Page 317 The Long and the Short on Counting Sequences / Jim Sauerberg and Linshsueh Shu......Page 320 Characterizing Continuity / Daniel J. Velleman......Page 332 Probabilistic Pursuits on the Grid / A. M. Bruckstein, C. L. Mallows and I. A. Wagner......Page 337 Hipparchus, Plutarch, Schroder, and Hough / Richard P. Stanley......Page 358 Many Correct Digits of 1T, Revisited / Gert Almkvist......Page 365 A Note on a Cake Cutting Algorithm / Martin L. Jones of Banach and Knaster......Page 367 The Impossibility of Unstable, Globally Attracting Fixed Points for Continuous Mappings of the Line / Hassan Sedaghat......Page 370 Divisors and Desires / Richard K. Guy......Page 373 PROBLEMS AND SOLUTIONS......Page 375 Tables of Integrals, Series and Products: CD-ROM Version. By I. S. Gradshteyn and I. M. Ryzhik / Jet Wimp......Page 387 The Parsimonious Universe. By Stefan Hildebrandt and Anthony Tromba / Frank Morgan......Page 390 TELEGRAPHIC REVIEWS......Page 394 THE AUTHORS......Page 400 EDITOR'S ENDNOTES......Page 402 Number 5 / MAY 1997......Page 409 Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions / Judith V. Grabiner......Page 411 Yet Another Definition of Chaos / Pat Touhey......Page 429 Hereditary Classes of Operators and Matrices / Scott A. McCullough and Leiba Rodman......Page 433 Major Centers of Triangles / Clark Kimberling......Page 449 On lambert's Proof of the Irrationality of \pi / M. Laczkovich......Page 457 A Simple Congruence modulo p / Winfried Kohnen......Page 462 A Geometrical Method for Finding an Explicit Formula for the Greatest Common Divisor / Marcelo Polezzi......Page 463 On the Historical Development of Infinitesimal Mathematics / Detlef Laugwitz......Page 465 PROBLEMS AND SOLUTIONS......Page 474 Mathematical Circles (Russian Experience). By Dmitri Fomin, Sergey Genkin, and Ilia Itenberg / Andre Toom......Page 486 Vita Mathematica: Historical Research and Integration with Teaching. Edited by Ronald Calinger / Hardy Grant......Page 489 TELEGRAPHIC REVIEWS......Page 497 THE AUTHORS......Page 501 EDITOR'S ENDNOTES......Page 502 Number 6 / JUNE-JULY 1997......Page 517 Approximate Isometries on Euclidean Spaces / Rajendra Bhatia and Peter Semrl......Page 519 How To Do MONTHLY Problems With Your Computer / Istvan Nemes, Marko Petkovsek, Herbert S. Wilf and Doran Zeilberger......Page 527 Simultaneously Symmetric Functions. / Lawrence W. Baggett, Herbert A. Medina and Kathy D. Merrill......Page 542 Prime-Producing Quadratics / R. A. Mallin......Page 551 The Poincare-Miranda Theorem / Wladyslaw Kulpa......Page 567 Lecturing at the "Bored" / Melanie Wahlberg......Page 573 A Generalization of Wolstenholme's Theorem / M. Bayat......Page 579 A Note on the Mean Value Theorem for Integrals / Zhang Bao-lin......Page 583 When Is There a Latin Power Set? / J. Denes......Page 585 PROBLEMS AND SOLUTIONS......Page 588 The Life of Stefan Banach. By Roman Kaluza / Sheldon Axler......Page 599 101 Careers in Mathematics. Edited by Andrew Sterrett / J. Kevin Colligan......Page 601 TELEGRAPHIC REVIEWS......Page 605 THE AUTHORS......Page 610 Number 7 / AUGUST-SEPTEMBER 1997......Page 617 The Many Avatars of a Simple Algebra / S. C. Coutinho......Page 619 Multiple Integrals of Symmetric Functions / Tiberiu Trif......Page 631 Some Inequalities for Principal Submatrices / John Chollet......Page 635 Two Applications of Calculus to Triangular Billiards / Eugene Gutkin......Page 644 Early Transcendentals / Steven H. Weintraub......Page 649 The Logical Structure of Computer-Aided Mathematical Reasoning / Keith Devlin......Page 658 The Wallet Paradox / Kent G. Merryfield, Ngo Viet and Saleem Watson......Page 673 The Weierstrass Approximation Theorem and Large Deviations / Henryk Gzyl and Jose Luis Palacios......Page 676 On the Historical Development of Infinitesimal Mathematics: Part 2 / Detlef Laugwitz......Page 680 PROBLEMS AND SOLUTIONS......Page 690 The Sheer Joy of Celestial Mechanics. By Nathaniel Grossman / J. M. Anthony Danby......Page 701 Strength in Numbers: Discovering the Joy and Power of Mathematics in Everyday Life. By Sherman K. Stein / Jennifer R. Galovich......Page 703 TELEGRAPHIC REVIEWS......Page 706 THE AUTHORS......Page 710 LESTER R. FORD AWARDS FOR 1996......Page 712 Number 8 / OCTOBER 1997......Page 725 Areas and Intersections in Convex Domains / Norbert Peyerimhoff......Page 727 Newman's Short Proof of the Prime NumberTheorem / D. Zagier......Page 735 An Exploratory Approach to Kaplansky's Lemma Leads to a Generalized Resultant / David Callan......Page 739 Metric Spaces in Which All Triangles Are Degenerate / Bettina Richmond and Thomas Richmond......Page 743 Partitions of Unity for Countable Covers / Albert Fathi......Page 750 Calculus: A Modern Perspective / Jeff Knisley......Page 754 Pro Choice / Arnold Ostebee and Paul Zorn......Page 758 Rethinking Calculus: Learning and Thinking / James J. Kaput......Page 761 What Do We Do About Calculus? First, Do No Harm / Richard Askey......Page 768 The Fifty-Seventh William Lowell Putnam Mathematical Competition / Leonard F. Klosinski, Gerald L. Alexanderson and Loren C. Larson......Page 774 A Quadratic Trio / Joseph Kupka......Page 785 A Discrete Form of the Beckman-Quarles Theorem / Apoloniusz Tyszka......Page 787 David Gale's Subset Take-Away Game / J. Daniel Christensen and Mark Tilford......Page 792 PROBLEMS AND SOLUTIONS......Page 797 An Introduction to Difference Equations. By Saber Elyadi / Ronald E. Mickens......Page 807 Calculus Lite. By Frank Morgan / Wayne Roberts......Page 810 TELEGRAPHIC REVIEWS......Page 813 THE AUTHORS......Page 819 EDITOR'S ENDNOTES......Page 821 Number 9 / NOVEMBER 1997......Page 833 Mathematics, Statistics, and Teaching / George W. Cobb and David S. Moore......Page 835 When is a Linear Operator Diagonalizable? / Marco Abate......Page 858 Energy Arguments in the Theory of Algorithms / Eric Bach......Page 865 Quine's NF-60 Years On / Thomas Forster......Page 872 Remarks on Sharkovsky's Theorem / Michal Misiurewicz......Page 880 Correction to: Zaphod Beeblebrox's Brain and the Fifty-Ninth Row of Pascal's Triangle / Andrew Granville......Page 882 A Simple Formula for \pi / Victor Adamchik and Stan Wagon......Page 886 Borsuk-Ulam Implies Brouwer: A Direct Construction / Francis Edward Su......Page 889 Does Mathematics Distinguish Certain Dimensions of Spaces / Zdzisfaw pogoda and Leszek M. Sokafowski......Page 894 PROBLEMS AND SOLUTIONS......Page 904 Knots and Surfaces: A Guide to Discovering Mathematics. By David W. Farmer and Theodore B. Stanford; Knots and Surfaces. By N. D. Gilbert and T. Porter / William D. Dunbar......Page 916 The Book of Numbers. By John Horton Conway and Richard K. Guy / Andrew Bremner......Page 918 TELEGRAPHIC REVIEWS......Page 923 THE AUTHORS......Page 927 Number 10 / DECEMBER 1997......Page 941 Ramanujan's Association with Radicals in India / Bruce C Berndt, Heng Huat Chan and Liang-Cheng Zhang......Page 943 Ramanujan, Taxicabs, Birthdates, ZIP Codes, and Twists / Ken Ono......Page 950 Simplicity and Surprise in Ramanujan's "Lost" Notebook / George E. Andrews......Page 956 The Catalan Numbers, The Lebesgue Integral, and 4^{n-2} / Wen-Jin Woan, Lou Shapiro and D. G. Rogers......Page 964 Good Matrices: Matrices that Preserve Ideals / R. Bruce Richter and William P. Wardlaw......Page 970 A Converse of the Mean Value Theorem / Jingcheng Tong and Peter A. Braza......Page 977 Primes at a (Somewhat Lengthy) Glance / Takashi Agoh, Paul Erdos and Andrew Granville......Page 981 The Mathematics Education Reform: Why You Should be Concerned and What You Can Do / H. Wu......Page 984 Confronting Reform / Jeremy Kilpatrick......Page 993 A Shorter Proof of the Ramanujan Congruence Modulo 5 / John L. Drost......Page 1001 An Amusing Representation of x/sin x / Scott Ahlgren, Lars English and Ron Winters......Page 1002 MONTHLY Unsolved Problems, 1969-1997 / Richard K. Guy and Richard J. Nowakowski......Page 1005 PROBLEMS AND SOLUTIONS......Page 1012 Conceptual Mathematics: A First Introduction to Categories. By F. William Lawvere and Steven Schanuel / Saunders Mac Lane......Page 1023 Early Astronomy. By Hugh Thurston / Ezra Brown......Page 1026 TELEGRAPHIC REVIEWS......Page 1030 THE AUTHORS......Page 1036 INDEX TO VOLUME 104......Page 1039

January 2024 Front Cover Current Events Bulletin Contents Masthead Letters to the Editor A Word From...Sergei Gelfand In Search of the Viscosity Operator on Riemannian Manifolds by Magdalena Czubak Running a Minimal Model Program by Joaquin Moraga Graduate Student Chapters Early Career John Coates (1945-2022): Celebration of a Life Metacognition in the Mathematics Classroom by Jo Boaler, Lakeshia Legette Jones, Yvonne Lai, John Nardo, and Jennifer Schultens JMM 2024 Registrations Member Activities What is...a Skew Brace? by Leandro Vendramin Graph Theory in America: The First Hundred Years, Reviewed by Malagorzata Marciniak Bookshelf AMS Bookshelf Abel Interview 2023: Luis Angel Caffarelli by Bjorn Ian Dundas and Christian F. Skau Mathematical Proof Between Generations by Jonas Bayer, Christoph Benzmuller, Kevin Buzzard, Marco David, Leslie Lamport, Yuri Matiyasevich, Lawrence Paulson, Dierk Schleicher, Benedikt Stock, and Efim Zelmanov Using Generative AI for Literature Searches and Scholarly Writing: Is the Integrity of the Scientific Discourse in Jeopardy? by Paul G. Schmidt and Amnon J. Meir On the Importance of Illustration for Mathematical Research by Remi Coulon, Gabriel Dorfsman-Hopkins, Edmund Harriss, Martin Skrodzki, Katherin eE. Stange, and Glen Whitney Fan China Exchange Program Baguenaudy, Baguenaudier, Baguenaudiest by Danny Calegari Calls for Nominations & Applications AMS Updates Mathematics People Classified Advertising Qiuzhen College, Tsinghua New Books Offered by the AMS Meetings & Conferences of the AMS January Table of Contents Meetings & Conferences of the AMS Mathematical Moments Recent Conference Proceedings from the AMS

April 2021 Front Cover Mathematics and Statistics Awareness Month Table of Contents Masthead A Word From...by Kirsten Bohl, and David Eisenbud The Coupling/Minorization/Drift Approach to Markov Chain Convergence Rates by Yu Hang Jiang, Tong Liu, Zhiya Lou, Jeffrey S. Rosenthal, Shanshan Shangguang, Fei Wang, and Zixuan Wu AMS Graduate Student Chapters The Structure of Homeomorphism and Diffeomorphism Groups by Kathryn Mann On the Mathematics of Swarming--Emergent Behavior in Alignment Dynamics by Eitan Tadmor Enumerative Combinatorics of Lattice Polymers by Nathan Clisby Designing Stable Elections by Steven Heilman Early Career In Memoriam: Peter L. Montgomery (1947-2020) by Joppe W. Bos and Kristin E. Lauter Elias M. Stein (1931-2018) by Lillian B. Piere, William Beckner, Galia Dafni, Charles Fefferman, Alexandru Ionescu, Vickie Kearn, Carlos E. Kenig, Anthony W. Knapp, Steven G. Krantz, Loredana Lanzani, Alexander Nagel, Duong H. Phong, Fulvio Ricci, Linda Rothschild, Rami Shakarchi, Christopher Sogge, Jeremy Stein, Karen Stein, Terence Tao, Stephen Wainger, and Harold Widom Mathematical Moments The Dawning of a New Era in Applied Mathematics by Weinan E What is...the VC-Dimension? by Samuel C. Tenka Hilbert's Tenth Problem, a Review by Alexandra Shlapentokh Bookshelf AMS Bookshelf Heat Flow and Sets of Finite Perimeter by Fabrice Baudoin On Sets and Patterns by Malabika Pramanik Modeling and Forecasting COVID-19 by Li Wang, Guannan Wang, Xinyi Li, Shan Yu, Myungjin Kim, Yueying Wang, Zhiling Gu, and Lei Gao Free AMS Content Geography and MathSciNet/Mathematical Reviews by Edward Dunne Call for Applications and Nominations AMS Associate Secretaries Call for Applications & Nominations Associate Treasurer Calls for Nominations & Applications AMS Prizes and Awards 2021 George David Birkhoff Prize 2021 Frank Nelson Cole Prize in Algebra 2021 Levi L. Conant Prize 2021 Mary P. Dolciani Prize 2021 Ulf Grenander Prize Grad Program sin the Mathematical Sciences 2021 Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student 2021 Bertrand Russell Prize 2021 Ruth Lyttle Satter Prize Thank You 2021 Leroy P. Steele Prizes 2021 Albert Leon Whiteman Memorial Prize 2021 Joint Policy Board for Mathematics Communications Award MathSciNet 2021 Cass of Fellows of the AMS An Interview with Jill Pipher by Evelyn Lamb Mathematics People Community Updates Mathematics Opportunities Classified Advertising New Books Offered by the AMS Meetings & Conferences of the AMS April Table of Contents Meetings & Conferences of the AMS MCA 2021 Call for Submissions

Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors. It is also for students in engineering and the sciences. The mix of ideas offer students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only see geodesics on surfaces, but they will also observe the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

You are probably wondering, 'What exactly are biscuits of number theory?' In this book, the editors have selected easily digested bite-sized articles and notes which aid an understanding of number theory. This is a collection of articles chosen for being exceptionally well written and capable of being appreciated by anyone who has taken (or is taking) a first course in number theory. The list of authors is outstanding, and the chapters cover arithmetic, primes, irrationality, sums of squares and polygonal numbers, Fibonacci numbers, number theoretic functions and elliptic curves, cubes, and Fermat's last theorem. As with any anthology, you don't have to read the chapters in order, you can dive in anywhere, making this book ideal for use as a textbook supplement for a number theory course.

Number 1 / JANUARY 1993......Page 1 Finkel Letter......Page 3 COMMENTS......Page 4 The Seventy-Fifth Anniversary Celebration I G. BALEY PRICE......Page 5 An Axiomatic Approach to the Integral/LEONARD GILLMAN......Page 17 Versatile Coins / ISTVAN SZALKAI and DAN VELLEMAN......Page 27 Two-Year Magazine Subscription Rates / UNDERWOOD DUDLEY......Page 35 On Seeing Progressions of Constant Cross Ratio / R. J. DUFFIN......Page 39 100 Years of Monthly Editors / JOHN EWING......Page 49 Quotients of Primes / DAVID HOBBY and D. M. SILBERGER......Page 51 Pathological Functions for Newton's Method / GEORGE C. DONOVAN, ARNOLD R. MILLER, and TIMOTHY J. MORELAND......Page 54 FEATURES......Page NOTES......Page 60 A Short Proof of a Theorem of Erdos and Mordell / ANDRE AVEZ......Page 61 The Computer Solves the Three Tower Problem / ARTHUR ENGEL......Page 63 A Linear Algebra Approach to Cyclic Extensions in Galois Theory / EVAN G. HOUSTON......Page 65 THE AUTHORS......Page 68 LETTERS......Page 70 When Does a Polynomial Over a Finite Field Permute the Elements of Field?, II/RUDOLF LIDL and GARY L. MULLEN......Page 72 PROBLEMS AND SOLUTIONS......Page 76 Iteration of Rational Functions by Alan F. Beardon / ROBERT L. DEVANEY......Page 91 TELEGRAPHIC REVIEWS......Page 95 Number 2 / FEBRUARY 1993......Page 103 CONTENTS......Page 105 COMMENTS......Page 106 Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Henry O. Pollak / RAMANATHAN GNANADESIKAN and HENRY J. LANDAU......Page 107 John Marvin Colaw: and The American Mathematical Monthly / JOHN D. MAXWELL......Page 109 Newton and the Transmutation of Force / TRISTAN NEEDHAM......Page 111 A Note on Diophantine Representations / CHRISTOPH BAXA......Page 130 Recurrence of Simple Random Walk in the Plane / TERENCE R. SHORE and DOUGLAS B. TYLER......Page 136 Pick's Theorem / BRANKO GRUNBAUM AND G. C. SHEPHARD......Page 142 Mathematics for Liberal Arts Students / ALBERT W. BRIGGS, JR.......Page 154 Sequences with Large Numbers of Prime Value / Ulrich Abel, Hartmut Siebert......Page 159 Regular Simplices in Spaces of Constant Curvature / Horst Martini......Page 161 A Simple Example of Little Big Set / John K. Williams......Page 164 PICTURE PUZZLE......Page 167 THE AUTHORS......Page 168 LETTERS......Page 170 A mod-n Ackermann Function, or What's So Special About 1969? / JON FROEMKE AND JERROLD W. GROSSMAN......Page 172 PROBLEMS AND SOLUTIONS......Page 176 How to Read and Do Proofs, by Daniel Solow / M. F. JANOWITZ......Page 189 TELEGRAPHIC REVIEWS......Page 192 Number 3 / MARCH 1993......Page 200 CONTENTS......Page 202 COMMENTS......Page 203 Szeged in 1934/ EDGAR R. LORCH......Page 204 Tarski's High School Identities / STANLEY BURRIS and SIMON LEE......Page 216 Aperiodic Chaotic Orbits / STEVEN N. MACEACHERN and L. MARK BERLINER......Page 222 Bricklaying and the Hermite Normal Form / WILLIAM J. GILBERT......Page 227 A Characterization of Inner Product Spaces / NEIL FALKNER......Page 231 Polar Area Is the Average of Strip Areas / GILBERT STRANG......Page 235 Counting Critical Points of Real Polynomials in Two Variables / ALAN DURFEE, NATHAN KRONENFELD, HEIDI MUNSON, JEFF ROY, and INA WESTBY......Page 240 Separation of the Zeros of Polynomials / Peter Walker......Page 257 A Short Proof of Jacobi's Formula for the Number of Representations of an Integer as a Sum of Four Squares / George E. Andrews, Shalosh B. Ekhad, Doron Zeilberger......Page 259 An Elementary Proof of Hilbert's Inequality / Krzysztof Oleszkiewicz......Page 261 A Note on Fubini's Theorem / Camille Debieve......Page 266 PICTURE PUZZLE......Page 267 THE AUTHORS......Page 268 LETTERS......Page 270 Parker's Permutation Problem Involves the Catalan Numbers......Page 272 PROBLEMS AND SOLUTIONS......Page 275 Ethnomathematics: A Multicultural View of Mathematical Ideas by Marcia Ascher / JUDITH V. GRABINER......Page 289 TELEGRAPHIC REVIEWS......Page 294 Number 4 / APRIL 1993......Page 302 CONTENTS......Page 304 COMMENTS......Page 305 Taxicabs and Sums of Two Cubes / JOSEPH H. SILVERMAN......Page 306 The Evil Twin Strategy for a Football Pool/JOSEPH DESTEFANO, PETER DOYLE, and J. LAURIE SNELL......Page 316 Six, Lies, and Calculators / R. M. CORLESS......Page 319 What Is a Napierian Logarithm? / RAYMOND AYOUB......Page 326 The Tyranny of Tests / PETER HILTON......Page 340 A Really Trivial Proof of the Lucas-Lehmer Test / J. W. BRUCE......Page 345 Pascal's Matrices / GREGORY S. CALL and DANIEL J. VELLEMAN......Page 347 Symmetries of the Cube and Outer Automorphisms of S_6 / THOMAS A. FOURNELLE......Page 352 Isogonal Configurations / TIMOTHY A. MURDOCH......Page 356 PSL2(Z) = Z2 * Z3 / Roger C. Alperin......Page 360 Generators for the Algebra of Symmetric Polynomials / D. G. Mead......Page 361 A Formula and a Proof of the Infinitude of the Primes / Michael Rubinstein......Page 363 PICTURE PUZZLE......Page 368 THE AUTHORS......Page 369 LETTERS......Page 371 Are There only Finitely Many Binomial Coefficients with Positive Deficiency?......Page 373 PROBLEMS AND SOLUTIONS......Page 375 Journey into Geometries by Marta Sved; Roads to Geometry by Edward C. Wallace and Stephen F. West / WILLIAM E. FENTON......Page 386 Polyominoes: A Guide to Puzzles and Problems in Tiling by George Martin / VICTOR G. FESER......Page 387 TELEGRAPHIC REVIEWS......Page 392 Number 5 / MAY 1993......Page 400 CONTENTS......Page 402 COMMENTS......Page 403 Thomas Archer Hirst-Mathematician Xtravagant I. A Yorkshire Surveyor / J. HELEN GARDNER and ROBIN J. WILSON......Page 404 Hyperbolic Geometry on a Hyperboloid / WILLIAM F. REYNOLDS......Page 411 A Simple Heuristic Proof of Hardy and Littlewood's Conjecture B / MICHAEL RUBINSTEIN......Page 425 The Pompeiu Problem / H. TURNER LAQUER......Page 430 A Quicker Convergence to Euler's Constant / DUANE W. DETEMPLE......Page 437 The Minimal Polynomial of COS(2\pi/n) / WILLIAM WATKINS and JOEL ZEITLIN......Page 440 The Equal Area Zones Property / B. RICHMOND and T. RICHMOND......Page 444 Graph Theory and the Game of Sprouts / MARK COPPER......Page 447 Elementary Proof of the Remez Inequality / Borislav Bojanov......Page 452 A Note on an Identity of Ramanujan / T. S. Nanjundiah......Page 454 On an Identity of Daubechies / Doron Zeilberger......Page 456 PICTURE PUZZLE......Page 457 THE AUTHORS......Page 458 LETTERS......Page 460 Data Compression / CATHERINE C. McGEOCH......Page 462 PROBLEMS AND SOLUTIONS......Page 467 Linear Algebra Through Geometry by Thomas Banchoff and John Wermer / JAMES KUZMANOVICH......Page 475 TELEGRAPHIC REVIEWS......Page 478 Number 6/ JUNE-JULY 1993......Page 486 CONTENTS......Page 488 COMMENTS......Page 489 Thomas Archer Hirst-Mathematician Xtravagent II. Student Days in Germany / J. HELEN GARDNER and ROBIN J. WILSON......Page 490 How to Make Wavelets / ROBERT S. STRICHARTZ......Page 498 A Matrix Maximum / WILLIAM C. WATERHOUSE......Page 516 Chaotic Motion of a Pendulum with Oscillatory Forcing / S. P. HASTINGS and J. B. MCLEOD......Page 522 An Application for the Curiosity (log_x N)' / DAVID A. WAGSTAFF, THEODORE A. NORMAN, and DOUGLAS M. CAMPBELL......Page 532 Vandermonde Strikes Again / MIRIAM SCHAPIRO GROSOF and GERALDINE TAIANI......Page 534 Embedding Countable Groups in 2-Generator Groups / Fred Galvin......Page 537 Abelian Forcing Sets / Joseph A. Gallian, Michael Reid......Page 539 PICTURE PUZZLE......Page 497 THE AUTHORS......Page 542 Is There a k-Anisohedral Tile for k > 5? / JOHN BERGLUND......Page 544 PROBLEMS AND SOLUTIONS......Page 548 Mathematics in Industrial Problems. Parts 1-4. Edited by Avner Friedman / ELLIS CUMBERBATCH......Page 556 TELEGRAPHIC REVIEWS......Page 559 Number 7 / AUGUST-SEPTEMBER 1993......Page 567 CONTENTS......Page 569 COMMENTS......Page 570 Thomas Archer Hirst-Mathematician Xtravagant III. Gottingen and Berlin / J. HELEN GARDNER and ROBIN J. WILSON......Page 571 Bisectors of Triangles and Tetrahedra / W. A. BEYER and BLAIR SWARTZ......Page 578 More on Rectangles Tiled by Rectangles / D. G. MEAD and S. K. STEIN......Page 593 Ramanujan-For Lowbrows I BRUCE C. BERNDT and S. BHARGA VA......Page 596 Chebychev Polynomials and Regular Polygons / D. Y. SAVIO and E. R. SURYANARAYAN......Page 609 Small-Group Learning / JULIAN WEISSGLASS......Page 614 A Fast Pick-Type Approximation for Areas of H-Polygons / DING REN, KRZYSZTOF KOODZIEJCZYK, GRATTAN MURPHY, and JOHN REAY......Page 621 PICTURE PUZZLE......Page 613 A Simple Example on Non-Sequentialness in Topological Spaces / Heinz Konig......Page 626 The Secant Method and the Golden Mean / Melvin J. Maron, Robert J. Lopez......Page 628 Rn Contains a Division Ring Does / Ayman Badawi......Page 631 A Further Simplification of Dixon's Proof of Cauchy's Integral Theorem / Peter A. Loeb......Page 632 Zero-Knowledge Proofs / CATHERINE C. McGEOCH......Page 634 THE AUTHORS......Page 638 PROBLEMS AND SOLUTIONS......Page 640 A First Course in Noncommutative Rings. By T.-Y. Lam / LANCE SMALL......Page 650 TELEGRAPHIC REVIEWS......Page 652 Number 8 / OCTOBER 1993......Page 660 CONTENTS......Page 662 COMMENTS......Page 663 Thomas Archer Hirst-Mathematician Xtravagant IV. Queenwood, France and Italy / J. HELEN GARDNER and ROBIN J. WILSON......Page 664 Thoughts on Innumeracy: Mathematics Versus the World? / PETER L. RENZ John Allen Paulos Replies......Page 673 Reflections on Rippling Water / MICHEL MENDES FRANCE......Page 684 The Principal Axis Theorem over Arbitrary Fields / DAVID MORNHINWEG, DANIEL B. SHAPIRO, and K. G. VALENTE......Page 690 The Fifty-Third William Lowell Mathematical Competition / LEONARD F. KLOSINSKI, GERALD L. ALEXANDERSON, and LOREN C. LARSON......Page 699 A Visual Explanation of Jensen's Inequality / TRISTAN NEEDHAM......Page 709 The Index of a Constrained Critical Point / CATHERINE HASSELL and ELMER REES......Page 713 On Some Irrational Decimal Fractions / NORBERT HEGYVARI......Page 720 PICTURE PUZZLE......Page 689 The Symmetry Principle for Mobius Transformations / Louis Brickman......Page 722 A Short Proof for Romberg Integration / T. von Petersdorff......Page 724 An Elementary Proof that the Borromean Rings are Non-Splittable / Ollie Nanyes......Page 727 LETTER TO THE EDITOR......Page 730 Open Problems in Pattern Avoidance / JAMES CURRIE......Page 731 THE AUTHORS......Page 735 PROBLEMS AND SOLUTIONS......Page 737 Ordinary Differential Equations. By Vladimir I. Arnol'd / FRED BRAUER......Page 751 TELEGRAPHIC REVIEWS......Page 753 Number 9 / NOVEMBER 1993......Page 759 CONTENTS......Page 761 COMMENTS......Page 762 Thomas Archer Hirst-Mathematician Xtravagant V. London in the 1860s / J. HELEN GARDNER and ROBIN J. WILSON......Page 763 From the Post-Markov Theorem Through Decision Problems to Public-Key Cryptography / IRIS LEE ANSHEL and MICHAEL ANSHEL......Page 771 Famous Nonmathematicians / STEVEN G. BUYSKE......Page 781 The Fundamental Theorem of Linear Algebra / GILBERT STRANG......Page 784 A Simple Proof of the Jordan-Alexander Complement Theorem / ALBRECHT DOLD......Page 792 Squaring the Circle with Holes / HANSKLAUS RUMMLER......Page 794 PICTURE PUZZLE......Page 783 Simplifying the Proof of Dirichlet's Theorem / Paul Monsky......Page 797 Why is P2 Not Embeddable in R3? / Hiroshi Maehara......Page 798 Polynomial Root Dragging / Bruce Anderson......Page 800 Parallel Addition / CATHERINE C. MCGEOCH......Page 804 THE AUTHORS......Page 808 PROBLEMS AND SOLUTIONS......Page 811 Second Year Calculus: From Celestial Mechanics to Special Relativity. By David M. Bressoud / WILLIAM FARIS......Page 820 TELEGRAPHIC REVIEWS......Page 825 Number 10 / DECEMBER 1993......Page 831 CONTENTS......Page 833 COMMENTS......Page 834 Thomas Archer Hirst-Mathematician Xtravagant VI. Years of Decline / J. HELEN GARDNER and ROBIN J. WILSON......Page 835 Densest Pac kings of Congruent Circles in an Equilateral Triangle / HANS (J. B. M.) MELISSEN......Page 844 Partnerships / ALAN H. SCHOENFELD......Page 854 A Simple Proof of Pascal's Hexagon Theorem / JAN VAN YZEREN......Page 858 The Mathematical Relationship between Kepler's Laws and Newton's Laws / Andrew T. Hyman......Page 860 A Short Proof of a Result on Polynomials / Razvan Gelca......Page 864 Two Amusing Dynkin Diagram Graph Classifications / Robert A. Proctor......Page 865 POSTCARDS FROM MAX / PAUL HALMOS......Page 870 A Quarter Century of Monthly Unsolved Problems, 1969-1993 / RICHARD K. GUY......Page 873 THE AUTHORS......Page 878 PROBLEMS AND SOLUTIONS......Page 879 A First Course in Chaotic Dynamical Systems: Theory and Experiment. By Robert Devaney. A First Course in Chaotic Dynamical Systems: Labs 1-6. By James Georges, Del Johnson and Robert Devaney / PHILIP D. STRAFFIN......Page 889 TELEGRAPHIC REVIEWS......Page 892 INDEX TO VOLUME 100......Page 898

s1......Page 1 s2......Page 5 s3......Page 24 s4......Page 43 s5......Page 68 s6......Page 74 s7......Page 81 s8......Page 87 s9......Page 89 s10......Page 97

May 2021 Front Cover Research Resources Call for Nominations William Benter Prize Table of Contents Masthead Letters to the Editor A Word From...Freeman A. Hrabowski III On the Gonality of Metric Graphs by Jan Draisma and Alejandro Vargas MathJobs.Org Contact and Symplectic Topology: Mastering the Art of Front Cooking by Roger Casals Mathematical Modeling of the Vascular System by Ju Liu, Ingrid S. Lan, and Alison L. Marsden Rigidity of Transformation Groups in Differential Geometry by Karin Melnick Data on the Community Sums of Squares: A Real Projective Story by Grigoriy Blekhman, Rainer Sinn, Gregory G. Smith, and Mauricio Velasco Earlyl Career Mathematical Imagery Mithcell Feigenbaum by Konstantin Khanin, Mikhail Lyubich, Eric Siggia, and Yakov Sinai Memorial Article for John Tate, Edited by Barry Mazur and Kenneth A. Ribet, with Karen Acquista, Joe Buhler, Dustin Clausen, John H. Coates, Benedict H. Gross, Stephen Lichtenbaum, Jonathan Lubin, Barry Mazur, V. Kumar Murty, Bernadette Perrin-Riou, Cristian D. Popescu, Kenneth A. Ribet, Joseph H. Silverman, Karen Uhlenbeck, and Jose Felipe Voloch Erdos 100 Plus, Reviewed by Dan Goldston Bookshelf AMS Bookshelf Counting Books and Beyond: Some Mathematical Books for Children by Edmund Harriss London Mathematical Society Cibercoloquio Latinoamericano de Matematicas by Daniel Campos, Manuel Rivera, Maria Amelia Salazar, Jose Alejandro Samper, Jose Simental, and Soledad Villar Problems That Feel Like Play: Sidewalk Math as Pandemic-Era Diversion by Sophia D. Merow The Brownian Map by John C. Baez Call for Applications & Nominations AMS Associate Secretaries Calls for Nominations & Applications AMS Prizes & Awards 2021 Award for Impact on the Teaching and Learning of Mathematics by Solomon Friedberg Call for Applicatinos & Nominations Associate Treasurer of the AMS 2021 Award for an Exemplary Program or Achievement in a Mathematics Department 2021 Mathematics Programs That Make a Difference Award AMS Membership MSRI-UP: Using Community and Connectedness to Increase Diversity in Mathematics by Elizabeth Platt Hamblin Mathematics People Community Updates Feature Column Mathematics Opportunities Classified Advertising New Books Offered by the AMS Math in the Media Meetings & Conferences of the AMS May Table of Contents Meetings & conferences of the AMS Undergraduate Opportunity Awards Open Math Notes

Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors. It is also for students in engineering and the sciences. The mix of ideas offer students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only see geodesics on surfaces, but they will also observe the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

Number 1 / JANUARY 1994......Page 1 CONTENTS......Page 3 COMMENTS......Page 4 Introduction to Fermat's Last Theorem / DAVID COX......Page 5 Future Elementary Teachers: The Neglected Constituency / THOMAS W. HUNGERFORD......Page 17 Galois Theory for Beginners / JOHN STILLWELL......Page 24 Into the Hourglass: Reflections on the Forces Acting on a Granular Material/ E. BRUCE PITMAN......Page 30 Orderly Currencies / JOHN DEWEY JONES......Page 38 An Interior Fixed Point Property of the Disc / ROBERT F. BROWN and ROBERT E. GREENE......Page 41 Le Cam's Inequality and Poisson Approximations / J. MICHAEL STEELE......Page 50 PICTURE PUZZLE......Page 29 A Generalization of a Theorem of Euler / DORINA MITREA AND MARIUS MITREA......Page 57 The Existence of a Triangle with Prescribed Angle Bisector Lengths / PETRU MIRONESCU and LAURENTIU PANAITOPOL......Page 60 Turing Machines and Computational Complexity / BILL MARION......Page 63 The Evolution of Integration / A. SHENITZER and J. STEPRANS......Page 68 THE AUTHORS......Page 75 PROBLEMS AND SOLUTIONS......Page 77 Mathematical Cranks, by Underwood Dudley / IAN STEWART......Page 89 Complex Analysis: The Geometric Viewpoint, by Steven G. Krantz / JOHN POLKING......Page 93 TELEGRAPHIC REVIEWS......Page 97 Number 2 / FEBRUARY 1994......Page 109 CONTENTS......Page 111 COMMENTS......Page 112 Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to J. Sutherland Frame / DAVID W. BALLEW......Page 113 A New Look at Euler's Theorem for Polyhedra / BRANKO GRUNBAUM and G. C. SHEPHARD......Page 115 Otto Neugebauer: Reminiscences and Appreciation / PHILIP J. DAVIS......Page 135 From the Buffon Needle Problem to the Kreiss Matrix Theorem / ELIAS WEGERT and LLOYD N. TREFETHEN......Page 138 A Counterexample for Germain /WILLIAM C. WATERHOUSE......Page 146 Cubic Equations, or Where Did the Examination Question Come From? / H. B. GRIFFITHS and A. E. HIRST......Page 157 PICTURE PUZZLE......Page 145 On the Identity of Polyhedra / HELLMUTH STACHEL......Page 168 More on the Pompeiu Problem / DAVID C. ULLRICH......Page 171 Every Number Is Expressible as the Sum of How Many Polygonal Numbers? / RICHARD K. GUY......Page 175 THE AUTHORS......Page 179 PROBLEMS AND SOLUTIONS......Page 181 Reality Rules 1. The Fundamentals; 11. The Frontier. By John Casti / RUTHERFORD ARIS......Page 192 Geometry of Surfaces. By John Stillwell / DAVID L. WEBB......Page 194 TELEGRAPHIC REVIEWS......Page 197 Number 3 / MARCH 1994......Page 209 CONTENTS......Page 211 COMMENTS......Page 212 A Marvelous Proof / FERNANDO Q. GOUVEA......Page 213 Triangulating the Circle, at Random / DAVID ALDOUS......Page 233 Hypatia and Her Mathematics / MICHAEL A. B. DEAKIN......Page 244 Calculus II and Euler Also (with a Nod to Series Integral Remainder Bounds) / RICHARD BARSHINGER......Page 254 A Focusing Property of the Ellipse / MARC FRANTZ......Page 260 Reflections Can Be Trapped / ROBERTO PEIRONE......Page 269 Euler's Theorem / KATHERINE HEINRICH and PETER HORAK......Page 270 PICTURE PUZZLE......Page 271 Universal Traversal Sequences / JOAN FEIGENBAUM and NICK REINGOLD......Page 272 What Are Algebraic Integers and What Are They For? / JOHN STILLWELL......Page 276 THE AUTHORS......Page 281 PROBLEMS AND SOLUTIONS......Page 283 Revolutions in Mathematics. Edited by Donald Gillies / MICHAEL MAHONEY......Page 293 TELEGRAPHIC REVIEWS......Page 298 Number 4 / APRIL 1994......Page 317 CONTENTS......Page 319 COMMENTS......Page 320 Pizza Slicing, Phi's and the Riemann Hypothesis / EDWARD A. BENDER, OREN PATASHNIK, and HOWARD RUMSEY, JR.......Page 321 Rational Periodic Points of the Quadratic Function Qc(x) = x 2 + c / RALPH WALDE and PAULA RUSSO......Page 332 Frechet vs. Caratheodory / ERNESTO ACOSTA G. and CESAR DELGADO G.......Page 346 Odd Magic Powers / A. C. THOMPSON......Page 353 Mathematicians, Including Undergraduates, Look at Soap Bubbles / FRANK MORGAN......Page 357 A Proof of Dilworth's Chain Decomposition Theorem / FRED GALVIN......Page 366 On Intervals, Transitivity = Chaos / MICHEL VELLEKOOP and RAOUL BERGLUND......Page 367 Proof of a Mixed Arithmetic-Mean, Geometric-Mean Inequality / KIRAN KEDLAYA......Page 369 ApSimon's Mints Problem......Page 372 THE AUTHORS......Page 374 PROBLEMS AND SOLUTIONS......Page 376 Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory, edited by A. N. Kolmogorov and A. P. Yushkevich / KAREN HUNGER PARSHALL......Page 383 Calculus Gems: Brief Lives and Memorable Mathematics. By George F. Simmons / DAVID J. PENGELLEY......Page 388 TELEGRAPHIC REVIEWS......Page 395 Number 5 / MAY 1994......Page 417 CONTENTS......Page 419 COMMENTS......Page 420 On the Geometry of Piecewise Circular Curves / THOMAS BANCHOFF and PETER GIBLIN......Page 421 The Two Envelope Paradox / ELLIOT LINZER......Page 435 Fourier Series of Polygons / ALAIN ROBERT......Page 438 The Paradox of Nontransitive Dice / RICHARD P. SAVAGE, JR.......Page 447 Squares Expressible as Sum of Consecutive Squares / LAURENT BEECKMANS......Page 455 Square Roots mod p / STEPHEN M. TURNER......Page 461 Kummer's Test Gives Characterizations for Convergence or Divergence of all Positive Series / JINGCHENG TONG......Page 468 Isometries of \ell_p-norm / CHI-KWONG LI and WASIN SO......Page 470 A Trace Inequality for Unitary Matrices / BOYING WANG and FUZHEN ZHANG......Page 471 An Elementary Proof of the Square Summability of the Discrete Hilbert Transform / LOUKAS GRAFAKOS......Page 474 Does Anybody Really Know What Time It Is? / CATHERINE C. McGEOCH......Page 477 How Hyperbolic Geometry Became Respectable / ABE SHENITZER......Page 482 THE AUTHORS......Page 489 PROBLEMS AND SOLUTIONS......Page 491 The Lure of the Integers. By Joe Roberts / PAUL T. BATEMAN and HAROLD G. DIAMOND......Page 498 Excursions in Calculus: An Interplay of the Continuous and the Discrete. By Robert M. Young / ANITA E. SOLOW......Page 500 TELEGRAPHIC REVIEWS......Page 503 Number 6 / JUNE-JULY 1994......Page 525 CONTENTS......Page 527 COMMENTS......Page 528 Juggling Drops and Descents / JOE BUHLER, DAVID EISENBUD, RON GRAHAM, and COLIN WRIGHT......Page 529 Teaching Integration by Substitution / DAVID GALE......Page 542 Workable Gears, Archimedian Solids and Planar Bipartite Graphs / GARY GORDON......Page 549 On the Kummer Solutions of the Hypergeometric Equation / REESE T. PROSSER......Page 557 Reflections on a Mira / JOHN W. EMERT, KAY I. MEEKS, and ROGER B. NELSON......Page 566 Buffon Noodles / ED WAYMIRE......Page 572 PICTURE PUZZLE......Page 581 On a Curious Property of Counting Sequences / VICTOR BRONSTEIN and A VIEZRI S. FRAENKEL......Page 582 Chaos Without Nonperiodicity / CARSTEN KNUDSEN......Page 585 A Reverse Stolarsky's Inequality / JOSIP PECARIC......Page 587 A Note on Some Irrational Decimal Fractions / A. MCD. MERCER......Page 589 THE AUTHORS......Page 591 A Possible Permanent Formula / DAVID CALLAN......Page 593 PROBLEMS AND SOLUTIONS......Page 596 Ideals, Varieties, and Algorithms. By David Cox, John Little, and Donal O'Shea / MOSS SWEEDLER......Page 604 TELEGRAPHIC REVIEWS......Page 609 Number 7 / AUGUST-SEPTEMBER 1994......Page 625 CONTENTS......Page 627 COMMENTS......Page 628 A Tale of Two CD's / DAN KENNEDY......Page 629 Three Problems in Search of a Measure / JONATHAN L. KING......Page 635 The n-Queens Problem / IGOR RIVIN, ILAN VARDI, and PAUL ZIMMERMANN......Page 655 What's the Difference Between Cantor Sets? / ROGER L. KRAFT......Page 666 Morphisms, Squarefree Strings, and the Tower of Hanoi Puzzle / JEAN-PAUL ALLOUCHE, DAN ASTOORIAN, JIM RANDALL, and JEFFREY SHALLIT......Page 677 Sierpinski's Theorem Is Deducible from Euler and Dirichlet / A. A. AGEEV......Page 685 On Nonnegativity of Symmetric Polynomials / F. MATUS......Page 687 New Tricks for Old Trees: Maps and the Pigeonhole Principle / N. GRAHAM, R. C. ENTRINGER, AND L. A. SZEKELY......Page 690 Do You Know the Way to Vertex A? / JEFF ONDICH......Page 694 On the Calculus of Variations and Its Major Influences on the Mathematics of the First Half of Our Century. Part I / ERWIN EREYSZIG......Page 700 THE AUTHORS......Page 705 PROBLEMS AND SOLUTIONS......Page 707 How to Teach Mathematics, By Steven G. Krantz / MEYER JERISON......Page 718 TELEGRAPHIC REVIEWS......Page 721 Number 8 / OCTOBER 1994......Page 741 CONTENTS......Page 743 COMMENTS......Page 744 Behind the Scenes of a Random Dot Stereogram / MARIA S. TERRELL and ROBERT E. TERRELL......Page 745 The Fifty-Fourth William Lowell Putnam Mathematical Competition / LEONARD F. KLOSINSKI, GERALD L. ALEXANDERSON, and LOREN C. LARSON......Page 755 Literacy in the Language of Mathematics / JAMES O. BULLOCK......Page 765 Fractional and Trigonometric Expressions for Matrices / GORO SHIMURA......Page 774 Noether Lasker Primary Decomposition Revisited / BARBARA L. OSOFSKY......Page 789 Elementary Infinite Sources of Non-Unique Factorization Rings / S. STEIN and S. SZABO......Page 799 Apropos Two Notes on Notation / ANTAL E. FEKETE......Page 801 The Coin Exchange Problem for Arithmetic Progressions / AMITABHA TRIPATHI......Page 809 Congruence of Triangles / LEONARD GILLMAN......Page 812 A Short Elementary Proof of the Mohr-Mascheroni Theorem / NORBERT HUNGERBUHLER......Page 814 Which Triangles Are Plane Sections of Regular Tetrahedra? / FOLKE ERIKSSON......Page 818 THE AUTHORS......Page 820 PROBLEMS AND SOLUTIONS......Page 822 Brouwer's Intuitionism. By Walter P. van Stigt / C. SMORYNSKI......Page 829 TELEGRAPHIC REVIEWS......Page 833 RESPONSE TO COMMENT On PAGE 714......Page 839 Number 9 / NOVEMBER 1994......Page 849 CONTENTS......Page 851 COMMENTS......Page 852 Georg Cantor and Transcendental Numbers / ROBERT GRAY......Page 853 The SOOth Anniversary of the Sharing Problem (The Oldest Problem in the Theory of Probability) / MILTON SOBEL and KRZYSZTOF FRANKOWSKI......Page 867 What Is Teaching?/ PAUL R. HALMOS......Page 882 What Is Wrong with the Definition of dy / dx? / HUGH THURSTON......Page 889 A Stochastic Approach to the Gamma Function / LOUIS GORDON......Page 892 Arrangements and Topological Planes / JACOB E. GOODMAN, RICHARD POLLACK, RAPHAEL WENGER, and TUDOR ZAMFIRESCU......Page 900 An Application of Fourier Series to the Most Significant Digit Problem / JEFF BOYLE......Page 913 Cross Product Identities in Arbitrary Dimension / ANDREW DITTMER......Page 921 A Non-Constant, Continuous Function on the Plane Whose Integral on Every Line Is Zero / D. H. ARMITAGE......Page 926 Chu's 1303 Identity Implies Bombieri's 1990 Norm-Inequality (Via an Identity of Beauzamy and Degot) / DO RON ZEILBERGER......Page 928 How to Stay Competitive / CATHERINE C. McGEOCH......Page 931 On the Calculus of Variations and Its Major Influences on the Mathematics of the First Half of Our Century. Part II / ERWIN KREYSZIG......Page 936 THE AUTHORS......Page 943 PROBLEMS AND SOLUTIONS......Page 945 Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China. By Lam Lay Yong and Ang Tian Se / FRANK SWETZ......Page 955 TELEGRAPHIC REVIEWS......Page 958 Number 10 / DECEMBER 1994......Page 973 CONTENTS......Page 975 COMMENTS......Page 976 The Rectilinear Crossing Number of a Complete Graph and Sylvester's "Four Point Problem" of Geometric Probability / EDWARD R. SCHEINERMAN and HERBERT S. WILF......Page 977 String Matching for the Novice / ORA E. PERCUS and JEROME K. PERCUS......Page 982 Bernoulli Trials and Number Theory / DON RAWLINGS......Page 986 What Is the Shape of a Mylar Balloon? / WILLIAM H. PAULSEN......Page 991 Euler's Theorem for Polyhedra: A Topologist and Geometer Respond / PETER HILTON and JEAN PEDERSEN......Page 997 The Role of Paradoxes in the Evolution of Mathematics / I. KLEINER and N. MOVSHOVITZ-HADAR......Page 1001 Regions in the Complex Plane Containing the Eigenvalues of a Matrix / RICHARD A. BRUALDI and STEPHEN MELLENDORF......Page 1013 Characterization of Solvable Quintics x^5 + ax + b / BLAIR K. SPEARMAN and KENNETH S. WILLIAMS......Page 1024 A Halmos Problem and a Related Problem / JOHN B. COSGRAVE......Page 1031 A "Popular" Class Number Formula / KURT GIRSTMAIR......Page 1035 Variations on Wolstenholme's Theorem / EMRE ALKAN......Page 1039 The Second-Partials Test for Local Extrema of f(x, y) / LEONARD GILLMAN......Page 1042 Mousetrap / RICHARD K. GUY and RICHARD J. NOWAKOWSKI......Page 1045 THE AUTHORS......Page 1049 PROBLEMS AND SOLUTIONS......Page 1051 Linear Programs and Related Problems, by Evar D. Nering and Albert W. Tucker / STEPHEN B. MAURER......Page 1060 TELEGRAPHIC REVIEWS......Page 1065 INDEX TO VOLUME 101......Page 1071

This is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid s first book and a high school axiomatic system as well as Hilbert s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematics-both classical and modern. Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincaré, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists. This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practical-getting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on. This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process.

A resource for discrete mathematics teachers at all levels. Resources for Teaching Discrete Mathematics presents nineteen classroom tested projects complete with student handouts, solutions, and notes to the instructor. Topics range from a first day activity that motivates proofs to applications of discrete mathematics to chemistry, biology, and data storage. Other projects provide: supplementary material on classic topics such as the towers of Hanoi and the Josephus problem, how to use a calculator to explore various course topics, how to employ Cuisenaire rods to examine the Fibonacci numbers and other sequences, and how you can use plastic pipes to create a geodesic dome. The book contains eleven history modules that allow students to explore topics in their original context. Sources range from eleventh century Chinese figures that prompted Leibniz to write on binary arithmetic, to a 1959 article on automata theory. Excerpts include: Pascal's'Treatise on the Arithmetical Triangle,'Hamilton's'Account of the Icosian Game,'and Cantor's (translated)'Contributions to the Founding of the Theory of Transfinite Numbers.'Five articles complete the book. Three address extensions of standard discrete mathematics content: an exploration of historical counting problems with attention to discovering formulas, a discussion of how computers store graphs, and a survey connecting the principle of inclusion-exclusion to Möbius inversion. Finally, there are two articles on pedagogy specifically related to discrete mathematics courses: a summary of adapting a group discovery method to larger classes, and a discussion of using logic in encouraging students to construct proofs.

Archimedes is one of the greatest mathematicians to have lived. He worked in geometry, physics, and ballistics. His work has spanned the ages. What's more, he did his work without the tools we have today. With tools I don't mean calculators, or computers. I mean without the descriptive mathematical language of equations and the number systems of today. Archimedes held his ideas in total within his mind and was able to solve problems that would take calculus today. And he didn't have calculus either.r r This book describes many of the problems Archimedes solved and how he approached the problems. We find center of gravity and buoyancy, for example. Each chapter is a thorough discussion of the problems, Archimedes's solution, and, at times, the importance of the problem. The book is slim and handy to take with you for reading whenever you find a few minutes. In that sense, the chapters are short enough to read quickly (although you'll want to spend time going through the equations) so that you get a good view of the approach taken.r r Finally, the author takes you on a few tangents to explain how Archimedes viewed mathematics and here, too, you see the greatness of Archimedes. He was meticulous and precise in his work. He didn't publish his methods until he was certain of them and he corresponded with other mathematicians to work out problems and discuss various topics. What a good insight into the past and, for us, a good place to draw lessons for our own work.r, Series: Classroom Resource Material Classroom Resource Materials, Issue: 0, Edition: 1, Includes bibliographical references (p. 149-152) and index

Edited By Rick Gillman. Includes Bibliographical References.

Preparing middle grades mathematics teachers at Georgia College and State University / Angel R. Abney, Nancy B. Mizelle, and Janet Shiver -- The mathematics for middle school teachers program at Western Oregon University / Cheryl Beaver, Rachel Harrington, and Klay Kruczek -- Connecting middle school mathematics with college mathematics: a core of mathematics courses for middle grade mathematics teachers / Ira J. Papick -- The middle school program at the University of Wisconsin Oshkosh / Jennifer Szydlik, John Beam, Eric Kuennen, and Carol Seaman -- The master of arts in middle school mathematics program at Salem (MA) State University / Julie A. Belock -- The math in the middle institute: strengthening middle level teachers' mathematical and pedagogical capacities / Ruth M. Heaton, W. James Lewis, and Wendy M. Smith -- A professional development program for middle school math teachers in Maryland / M. Elizabeth Mayfield and Christy Danko Graybeal -- Discrete mathematics: a course in problem solving in 21st century middle school teachers / Tanya Cofer, Valerie A. DeBellis, Cathy Liebars, Joseph G. Rosenstein, Bonnie Saunders, and Margaret Wirth -- Guided discovery in a discrete mathematics course for middle school teachers / Mary Flahive and Reva Kasman -- Geometry for middle school teachers at Northern Kentucky University / Bethany Noblitt -- A number and algebra course for middle school math teachers / Michael Mays and David Miller -- Verically connecting precalculus and calculus with middle school mathematics / Theresa Jorgensen -- Visual college algebra for teachers / Laurie J. Burton and Klay T. Kruczek -- Probability and statistics for prospective middle grade teachers / Jennifer Szydlik, John Beam, Eric Kuennen, and Carol Seaman -- Vermont middle level mathematics initiative: courses and materials for mathematical educators / George Ashline and Marny Frantz -- Challenging yet accessible mathematics courses for middle level teachers / Ruth M. Heaton, W. James Lewis, Michelle R. Homp, Steven R. Dunbar, and Wendy M. Smith.

Back Matter......Page 0 [unnumbered]......Page 1 [unnumbered]......Page 2 p. 105......Page 3 p. 106......Page 4 p. 107......Page 5 p. 108......Page 6 p. 109......Page 7 p. 110......Page 8 p. 111......Page 9 p. 112......Page 10 p. 113......Page 11 p. 114......Page 12 p. 115......Page 13 p. 116......Page 14 p. 117......Page 15 p. 118......Page 16 p. 119......Page 17 p. 120......Page 18 p. 121......Page 19 p. 122......Page 20 p. 123......Page 21 p. 124......Page 22 p. 125......Page 23 p. 126......Page 24 p. 127......Page 25 p. 128......Page 26 p. 129......Page 27 p. 130......Page 28 p. 131......Page 29 p. 132......Page 30 p. 133......Page 31 p. 134......Page 32 p. 135......Page 33 p. 136......Page 34 p. 137......Page 35 p. 138......Page 36 p. 139......Page 37 p. 140......Page 38 p. 141......Page 39 p. 142......Page 40 p. 143......Page 41 p. 144......Page 42 p. 145......Page 43 p. 146......Page 44 p. 147......Page 45 p. 148......Page 46 p. 149......Page 47 p. 150......Page 48 p. 151......Page 49 p. 152......Page 50 p. 153......Page 51 p. 154......Page 52 p. 155......Page 53 p. 156......Page 54 p. 157......Page 55 p. 158......Page 56 p. 159......Page 57 p. 160......Page 58 p. 161......Page 59 p. 162......Page 60 p. 163......Page 61 p. 164......Page 62 p. 165......Page 63 p. 166......Page 64 p. 167......Page 65 p. 168......Page 66 p. 169......Page 67 p. 170......Page 68 p. 171......Page 69 p. 172......Page 70 p. 173......Page 71 p. 174......Page 72 0001......Page 73 0002......Page 74 0003......Page 75 0004......Page 76 0005......Page 77 0006......Page 78 0007......Page 79 0008......Page 80 0009......Page 81 0010......Page 82 0011......Page 83 p. 186......Page 84 p. 187......Page 85 p. 188......Page 86 p. 189......Page 87 p. 190......Page 88 p. 191......Page 89 p. 192......Page 90 p. 193......Page 91 p. 194......Page 92 p. 195......Page 93 p. 196......Page 94 p. 197......Page 95 p. 198......Page 96 p. 199......Page 97

Where did maths come from? Who thought up all those algebra symbols, and why? What's the story behind ... negative numbers? ... the metric system? ... quadratic equations? ... sine and cosine? The 25 independent sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that's accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. Reading suggestions after each sketch provide starting points for readers who want to pursue a topic further.

Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors. It is also for students in engineering and the sciences. The mix of ideas offer students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only see geodesics on surfaces, but they will also observe the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

December 2023 Front Cover AMS Young Scholars Contents Masthead A Word From...Karen Saxe JMM 2024 Presbyopia Correction, Differential Geometry, and Free Boundary PDEs by Sergio Barbero and Maria del Mar Gonzalez Differentiating by Prime Numbers by Jack Jeffries The Next Generation On Bernoulli-Type Elliptic Free Boundary Problems by Daniela De Silva AMS Employment Center at JMM 2024 Some Arithmetic Properties of Complex Local Systems by Helene Esnault Crossed Modules by Johannes Huebschmann AMS Congressional Fellowship 2024-2025 Early Career MRCs Memorial Article for Yuri Manin, Edited by Fedor Bogomolov and Yuri Tschinkel MCA 2025 What is...an Inductive Mean? by Frank Nielsen The Discrete Mathematical Charms of Paul Erdos: A Simple Introduction, a Review by Ranjan Rohatgi Bookshelf AMS Bookshelf Support Area of Greatest Need The Heidelberg Laureate Forum: Bringing Together Some of the Brightest Minds in Mathematics by marianne Freiberger and Rachel Thomas Calls for Nominations & Applications Catching Up with AMS Congressional Fellows by Elaine Beebe AMS Updates Mathematics People Classified Advertising Section Editors New Books Offered by the AMS Math Imagery Meetings & Conferences of the AMS December Table of Contents Meetings & Conferences AMS Donors 2024 Epsilon of Math Wall Calendar