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CONTENTS 2 Algebra & Algebraic Geometry 5 Analysis 7 Applications 10 Calculus 13 Differential Equations 13 Discrete Mathematics & Combinatorics 14 General Interest 22 Geometry & Topology 25 Math Education 29 Number Theory 31 Backlist 31 Algebra & Algebraic Geometry AMS 32 Analysis TEXTBOOKS 33 Applications 34 Calculus Find the right textbook for your course! 34 Differential Equations The AMS publishes many high-quality 34 Discrete Mathematics & Combinatorics books for use in the classroom. To view a 35 General Interest comprehensive list of our textbook titles, 39 Geometry & Topology please visit: ams.org/bookstore/textbooks 40 Logic & Foundations 40 Math Education 41 Mathematical Physics 42 Number Theory 42 Probability & Statistics 43 Index 49 Ordering Information

ORDER ONLINE bookstore.ams.org 1 ALGEBRA & ALGEBRAIC GEOMETRY

| Field Theory and Its Classical Problems Charles Robert Hadlock Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular n -gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. Notable topics treated along this route include the transcendence of e and π , cyclotomic polynomials, polynomials over the integers, Hilbert’s irreducibility theorem, and many other gems in classical mathematics. Carus Mathematical Monographs, Volume 19 1975; 323 pp.; softcover; ISBN: 978-0-88385-032-9; List US$41; Institutional member US$32.80; Individual AMS & MAA members US$30.75; Order code: CAR/19

| Elementary Mathematical Models Order Aplenty and a Glimpse of Chaos Dan Kalman The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. With numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences. In a book written for the intelligent and literate non-mathematician, Kalman aims at an understanding of the power and utility of quantitative methods rather than at technical mastery of mathematical operations. AMS/MAA Textbooks, Volume 2 1997; 345 pp.; softcover; ISBN: 978-0-88385-707-6; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: TEXT/2

| Lie Groups A Problem-Oriented Introduction via Matrix Groups Harriet Pollatsek This textbook is a complete introduction to Lie groups for undergraduate students. The only prerequisites are multi-variable calculus and linear algebra. The emphasis is placed on the algebraic ideas, with just enough analysis to define the tangent space and the differential and to make sense of the exponential map. This textbook works on the principle that students learn best when they are actively engaged. To this end nearly 200 problems are included in the text, ranging from the routine to the challenging level. AMS/MAA Textbooks, Volume 13 2009; 177 pp.; hardcover; ISBN: 978-0-88385-759-5; List US$67; Institutional member US$53.60; Individual AMS & MAA members US$50.25; Order code: TEXT/13

| Functions, Data, and Models An Applied Approach to College Algebra Sheldon P. Gordon and Florence S. Gordon This is a college algebra-level textbook written to provide the kind of mathematical knowledge and experiences that students will need for courses in other fields, such as biology, chemistry, business, finance, economics, and other areas that are heavily dependent on data either from laboratory experi- ments or from other studies. The focus is on the fundamental mathematical concepts and the realistic problem-solving via mathematical modeling rather than the development of algebraic skills that might be needed in calculus. The book contains a rich set of exercises, many of which use real data. AMS/MAA Textbooks, Volume 18 2010; 492 pp.; hardcover; ISBN: 978-0-88385-767-0; List US$72; Institutional member US$57.60; Individual AMS & MAA members US$54; Order code: TEXT/18 401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 2 A Guide to Advanced Linear Algebra Steven H. Weintraub Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives. Dolciani Mathematical Expositions, Volume 44 2011; 251 pp.; hardcover; ISBN: 978-0-88385-351-1; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: DOL/44

A Guide to Plane Algebraic Curves Keith Kendig This friendly introduction to plane algebraic curves emphasizes geometry and intuition and features a concrete presentation. You’ll find an abundance of pictures and examples to help develop your intuition about the subject, which is so basic to understanding and asking fruitful questions. Highlights of the elementary theory are covered, which for some could be an end in itself, and for others an invitation to investigate further. Proofs, when given, are mostly sketched, some in more detail, but typically with less. References to texts that provide further discussion are often included. Dolciani Mathematical Expositions, Volume 46 2011; 193 pp.; hardcover; ISBN: 978-0-88385-353-5; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: DOL/46

A Guide to Groups, Rings, and Fields Fernando Q. Gouvêa This book offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together and will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. Dolciani Mathematical Expositions, Volume 48 2012; 309 pp.; hardcover; ISBN: 978-0-88385-355-9; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: DOL/48

Beyond the Quadratic Formula Ron Irving The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial’s coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. Classroom Resource Materials, Volume 43 2013; 228 pp.; hardcover; ISBN: 978-0-88385-783-0; List US$55; Institutional member US$44; Individual AMS & MAA members US$41.25; Order code: CLRM/43

ORDER ONLINE bookstore.ams.org 3 ONLY Illustrated Special Relativity through Its Paradoxes A Fusion of Linear Algebra, Graphics, and Reality John dePillis and Jose Wudka Illustrated Special Relativity shows that linear algebra is a natural language for special relativity. It illustrates and resolves several apparent paradoxes of special relativity, including the twin paradox and train-and-tunnel paradox. Assuming a minimum of technical prerequisites, the authors introduce inertial frames and use them to explain a variety of phenomena: the nature of simultaneity, the proper way to add velocities, and why faster-than-light travel is impossible. Most of these explanations are contained in the resolution of apparent paradoxes, including some lesser-known ones: the pea-shooter paradox, the bug-and-rivet paradox, and the accommodating universe paradox. The explanation of time and length contraction is especially clear and illuminating. Spectrum, Volume 78 2013; 464 pp.; ISBN: 978-1-61444-517-3; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: SPEC/78.E

| Learning Modern Algebra From Early Attempts to Prove Fermat’s Last Theorem Al Cuoco and Joseph J. Rotman Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers II recommenda- tions, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems. This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. AMS/MAA Textbooks, Volume 23 2013; 459 pp.; hardcover; ISBN: 978-1-93951-201-7; List US$62; Institutional member US$49.60; Individual AMS & MAA members US$46.50; Order code: TEXT/23

When Life is Linear From Computer Graphics to Bracketology Tim Chartier From simulating complex phenomenon on super- computers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. This book introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on enve- lopes and encrypt sensitive information. Anneli Lax New Mathematical Library, Volume 45 2015; 136 pp.; softcover; ISBN: 978-0-88385-649-9; List US$52; Institutional member US$41.60; Individual AMS & MAA members US$39; Order code: NML/45

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 4 ANALYSIS

A Course in Mathematical Modeling Douglas D. Mooney and Randall J. Swift The emphasis of this book lies in the teaching of mathematical modeling rather than simply presenting models. To this end the book starts with the simple discrete exponential growth model as a building block, and successively refines it. This involves adding variable growth rates, multiple variables, fitting growth rates to data, including random elements, testing exactness of fit, using computer simulations and moving to a continuous setting. Classroom Resource Materials, Volume 13 1999; 431 pp.; softcover; ISBN: 978-0-88385-712-0; List US$68; Institutional member US$54.40; Individual AMS & MAA members US$51; Order code: CLRM/13

Excursions in Classical Analysis Pathways to Advanced Problem Solving and Undergraduate Research Hongwei Chen Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The book will be useful in students’ preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order. Classroom Resource Materials, Volume 35 2010; 301 pp.; hardcover; ISBN: 978-0-88385-768-7; List US$61; Institutional member US$48.80; Individual AMS & MAA members US$45.75; Order code: CLRM/35

Invitation to Complex Analysis Ralph P. Boas Second Edition revised by Harold P. Boas Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. This second edition has been painstakingly revised by the author’s son, himself an award- winning mathematical expositor. AMS/MAA Textbooks, Volume 20 2010; 327 pp.; hardcover; ISBN: 978-0-88385-764-9; List US$63.95; Institutional member US$51.16; Individual AMS & MAA members US$47.96; Order code: TEXT/20

A Guide to Functional Analysis Steven G. Krantz This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text, but it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. Dolciani Mathematical Expositions, Volume 49 2013; 137 pp.; hardcover; ISBN: 978-0-88385-357-3; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: DOL/49

ORDER ONLINE bookstore.ams.org 5 | Varieties of Integration C. Ray Rosentrater Varieties of Integration explores the critical contributions by Riemann, Darboux, Lebesgue, Henstock, Kurzweil, and Stieltjes to the theory of integration and provides a glimpse of more recent variations of the integral such as those involving operator-valued measures. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation with little attention paid to the relationships between them or to the historical issues that motivated their definitions. This book redresses this situ- ation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals in a single volume using a common set of examples. Dolciani Mathematical Expositions, Volume 51 2015; 325 pp.; hardcover; ISBN: 978-0-88385-359-7; List US$58; Institutional member US$46.40; Individual AMS & MAA members US$43.50; Order code: DOL/51

| The Lebesgue Integral for Undergraduates William Johnston This text presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Anyone who has mastered single-variable calculus concepts of limits, derivatives, and series can learn the material. The key to this success is the text’s use of a method labeled the “Daniell- Riesz approach.” The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite. Additional curricular options then exist. AMS/MAA Textbooks, Volume 27 2015; 284 pp.; hardcover; ISBN: 978-1-93951-207-9; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: TEXT/27

| An Invitation to Real Analysis Luis F. Moreno An Invitation to Real Analysis is written both as a stepping stone to higher calculus and analysis courses, and as foundation for deeper reasoning in applied mathematics. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers. Over 600 exercises and dozens of figures help the learning process. Several topics (continued fractions, for example), are included in the appendices as enrichment material. AMS/MAA Textbooks, Volume 31 2015; 661 pp.; hardcover; ISBN: 978-1-93951-205-5; List US$75; Institutional member US$60; Individual AMS & MAA members US$56.25; Order code: TEXT/31

Linear Inverse Problems and Tikhonov Regularization Mark S. Gockenbach Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions. Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers. Carus Mathematical Monographs, Volume 32 2016; 320 pp.; hardcover; ISBN: 978-0-88385-141-8; List US$63; Institutional member US$50.40; Individual AMS & MAA members US$47.25; Order code: CAR/32

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 6 Exercises in (Mathematical) Style Stories of Binomial Coefficients John McCleary What does style mean in mathematics? Style is both how one does something and how one commu- nicates what was done. In this book, the author investigates the worlds of the well-known numbers, the binomial coefficients. The author follows the example of Raymond Queneau’s Exercises in Style and offers the reader 99 stories in various styles. The book celebrates the joy of mathematics and the joy of writing mathematics by exploring the rich properties of this familiar collection of numbers. Anneli Lax New Mathematical Library, Volume 48 2017; 275 pp.; softcover; ISBN: 978-0-88385-652-9; List US$48; Institutional member US$38.40; Individual AMS & MAA members US$36; Order code: NML/48

| A Radical Approach to Real Analysis Second Edition David Bressoud In this second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to iden- tify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. AMS/MAA Textbooks, Volume 10 2007; 339 pp.; hardcover; ISBN: 978-0-88385-747-2; List US$65; Institutional member US$52; Individual AMS & MAA members US$48.75; Order code: TEXT/10

APPLICATIONS

| Game Theory and Strategy Philip D. Straffin This book is an introduction to mathematical game theory, which might better be called the mathematical theory of conflict and cooperation. It is applicable whenever two individuals—or companies, or political parties, or nations—confront situations where the outcome for each depends on the behavior of all. Since its creation by John von Neumann and Oskar Morgenstern in 1944, game theory has shed new light on business, politics, economics, social psychology, philosophy, and evolutionary biology. In this book, its fundamental ideas are developed with mathematics at the level of high school algebra and applied to many of these fields (see the table of contents). Anneli Lax New Mathematical Library, Volume 36 1993; 244 pp.; softcover; ISBN: 978-0-88385-637-6; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: NML/36

Cryptological Mathematics Robert Edward Lewand This is an introduction to the mathematics involved in the intriguing field of cryptology, the science of writing and reading secret messages which are designed to be read only by their intended recipients. It is written at an elementary level, suitable for beginning undergraduates, with careful explanations of all the concepts used. The basic branches of mathematics required, including number theory, abstract algebra and probability, are used to show how to encipher and decipher messages, and why this works, giving a practical as well as theoretical basis to the subject. The book is written in an engaging style which will appeal to all, and also includes challenging computer programming exercises. Classroom Resource Materials, Volume 16 2000; 199 pp.; softcover; ISBN: 978-0-88385-719-9; List US$53; Institutional member US$42.40; Individual AMS & MAA members US$39.75; Order code: CLRM/16

ORDER ONLINE bookstore.ams.org ORDER ONLINE bookstore.ams.org 7 | The Mathematics of Games and Gambling Second Edition Edward Packel This book introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games (roulette, blackjack, keno), some social games (backgammon, poker, bridge) and various other activities (state lotteries, horse racing, etc.) are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory. This second edition includes new material on: sports betting and the mathematics behind it; Game theory applied to bluffing in poker and related to the Texas Holdem phenomenon; The Nash equilibrium concept and its emergence in the popular culture; Internet links to games and to Java applets for practice and classroom use. Anneli Lax New Mathematical Library, Volume 28 2006; 174 pp.; hardcover; ISBN: 978-0-88385-646-8; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: NML/28

| Elementary Cryptanalysis A Mathematical Approach, Second Edition Abraham Sinkov Revised and updated by Todd Feil. Originally published in the New Mathematical Library almost half a century ago, this charming book explains how to solve cryptograms based on elementary mathematical principles, starting with the Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators. Anneli Lax New Mathematical Library, Volume 22 2009; 212 pp.; hardcover; ISBN: 978-0-88385-647-5; List US$61; Institutional member US$48.80; Individual AMS & MAA members US$45.75; Order code: NML/22

| Mathematical Interest Theory Second Edition Leslie Jane Federer Vaaler and James W. Daniel Mathematical Interest Theory gives an introduction of how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. On the other hand, Mathematical Interest Theory is written for anyone who has a strong high- school algebra background and is interested in being an informed borrower or investor. The content is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course. AMS/MAA Textbooks, Volume 14 2009; 475 pp.; hardcover; ISBN: 978-0-88385-754-0; List US$92; Institutional member US$73.60; Individual AMS & MAA members US$69; Order code: TEXT/14

Student Solution Manual for Mathematical Interest Theory Leslie Jane Federer Vaaler This manual is written to accompany Mathematical Interest Theory, by Leslie Jane Federer Vaaler and James Daniel. It includes detailed solutions to the odd-numbered problems. There are solutions to 239 problems, and sometimes more than one way to reach the answer is presented. In keeping with the presentation of the text, calculator discussions for the Texas Instruments BA II Plus or BA II Plus Professional calculator is typeset in a different font from the rest of the text. AMS/MAA Textbooks, Volume 15 2009; 107 pp.; softcover; ISBN: 978-0-88385-755-7; List US$35.95; Institutional member US$28.76; Individual AMS & MAA members US$26.96; Order code: TEXT/15

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 8 ONLY Game Theory through Examples Erich Prisner Game Theory through Examples is a thorough introduction to elementary game theory, covering finite games with complete information. The core philosophy underlying this volume is that abstract concepts are best learned when encountered first (and repeatedly) in concrete settings. Thus, the essential ideas of game theory are here presented in the context of actual games, real games much more complex and rich than the typical toy examples. Classroom Resource Materials, Volume 46 2014; 287 pp.; ISBN: 978-1-61444-115-1; List US$38; Institutional member US$30.40; Individual AMS & MAA members US$28.50; Order code: CLRM/46.E

| The Heart of Calculus Explorations and Applications Philip M. Anselone and John W. Lee This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. The book develops topics from novel and/or unifying perspectives. The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth. A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. The presentation is friendly and accessible to students at various levels of mathematical maturity. Classroom Resource Materials, Volume 50 2015; 228 pp.; hardcover; ISBN: 978-0-88385-787-8; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: CLRM/50

| ONLY Introduction to the Mathematics of Computer Graphics Nathan Carter This text, by an award-winning author, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Classroom Resource Materials, Volume 51 2016; 462 pp.; ISBN: 978-1-61444-122-9; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: CLRM/51.E

| Common Sense Mathematics Ethan D. Bolker and Maura B. Mast Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions. Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we’ve chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics. AMS/MAA Textbooks, Volume 33 2016; 308 pp.; hardcover; ISBN: 978-1-93951-210-9; List US$66; Institutional member US$52.80; Individual AMS & MAA members US$49.50; Order code: TEXT/33

ORDER ONLINE bookstore.ams.org 9 | Discovering Discrete Dynamical Systems Aimee Johnson, Kathleen Madden, and Ays¸e S¸ahin Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. Classroom Resource Materials, Volume 53 2017; 116 pp.; softcover; ISBN: 978-0-88385-793-9; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: CLRM/53

| Teaching Statistics Using Baseball Second Edition Jim Albert Teaching Statistics Using Baseball is a collection of case studies and exercises applying statistical and probabilistic thinking to the game of baseball. Baseball is the most statistical of all sports since players are identified and evaluated by their corresponding hitting and pitching statistics. This book illustrates basic methods of data analysis and probability models by means of baseball statistics collected on players and teams. Students often have difficulty learning statistics ideas since they are explained using examples that are foreign to the students. The idea of the book is to describe statistical thinking in a context (that is, baseball) that will be familiar and interesting to students. The second edition follows the same structure as the first edition, where the case studies and exercises have been replaced by modern players and teams, and the new types of baseball data from the PitchFX system and fangraphs.com are incorporated into the text. AMS/MAA Textbooks, Volume 34 2017; 243 pp.; softcover; ISBN: 978-1-93951-216-1; List US$55; Institutional member US$44; Individual AMS & MAA members US$41.25; Order code: TEXT/34

CALCULUS

| Calculus Deconstructed A Second Course in First-Year Calculus Zbigniew H. Nitecki Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a “bridge course” using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject. AMS/MAA Textbooks, Volume 16 2009; 491 pp.; hardcover; ISBN: 978-0-88385-756-4; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: TEXT/16 401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 10 The Calculus Collection A Resource for AP* and Beyond Caren L. Diefenderfer and Roger B. Nelsen, Editors The Calculus Collection consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus. Classroom Resource Materials, Volume 33 2010; 507 pp.; hardcover; ISBN: 978-0-88385-761-8; List US$77; Institutional member US$61.60; Individual AMS & MAA members US$57.75; Order code: CLRM/33

| Counterexamples in Calculus Sergiy Klymchuk Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus. Classroom Resource Materials, Volume 34 2010; 101 pp.; softcover; ISBN: 978-0-88385-765-6; List US$41; Institutional member US$32.80; Individual AMS & MAA members US$30.75; Order code: CLRM/34

Calculus and Its Origins David Perkins Calculus and Its Origins is primarily a collection of results that show how calculus came to be, beginning in ancient Greece and climaxing with the discovery of calculus. Other books have traveled these paths, but they presuppose knowledge of calculus. This book requires only a basic knowledge of high school geometry and algebra. Exercises introduce further historical figures and their results, and make it possible for a professor to use this book in class. Spectrum, Volume 70 2012; 171 pp.; hardcover; ISBN: 978-0-88385-575-1; List US$62; Institutional member US$49.60; Individual AMS & MAA members US$46.50; Order code: SPEC/70

Paradoxes and Sophisms in Calculus Sergiy Klymchuk and Susan Staples Paradoxes and Sophisms in Calculus offers a delightful supplementary resource to enhance the study of single variable calculus. By the word paradox the authors mean a surprising, unexpected, counter- intuitive statement that looks invalid, but in fact is true. The word sophism describes intentionally invalid reasoning that looks formally correct, but in fact contains a subtle mistake or flaw. In other words, a sophism is a false proof of an incorrect statement. A collection of over fifty paradoxes and sophisms showcases the subtleties of this subject and leads students to contemplate the underlying concepts. A number of the examples treat historically significant issues that arose in the development of calculus, while others more naturally challenge readers to understand common misconceptions. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences, and series are explored. Classroom Resource Materials, Volume 45 2013; 98 pp.; softcover; ISBN: 978-0-88385-781-6; List US$41; Institutional member US$32.80; Individual AMS & MAA members US$30.75; Order code: CLRM/45

ORDER ONLINE bookstore.ams.org 11 | Cameos for Calculus Visualization in the First-Year Course Roger B. Nelsen A thespian or cinematographer might define a cameo as a brief appearance of a known figure, while a gemologist or lapidary might define it as a precious or semiprecious stone. This book presents fifty short enhancements or supplements (the cameos) for the first-year calculus course in which a geometric figure briefly appears. Some of the cameos illustrate mainstream topics such as the derivative, combinatorial formulas used to compute Riemann sums, or the geometry behind many geometric series. Other cameos present topics accessible to students at the calculus level but not usually encountered in the course. Many of the cameos are adapted from articles published in journals of the MAA, such as The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal. Some come from other mathematical journals, and some were created for this book. By gathering the cameos into a book the author hopes that they will be more accessible to teachers of calculus, both for use in the classroom and as supplementary explorations for students. Classroom Resource Materials, Volume 49 2015; 169 pp.; hardcover; ISBN: 978-0-88385-788-5; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: CLRM/49

| College Calculus A One-Term Course for Students With Previous Calculus Experience Michael E. Boardman and Roger B. Nelsen College Calculus: A One-Term Course for Students with Previous Calculus Experience is a textbook for students who have successfully experienced an introductory calculus course in high school. College Calculus begins with a brief review of some of the content of the high school calculus course and proceeds to give students a thorough grounding in the remaining topics in single variable calculus, including integration techniques, applications of the definite integral, separable and linear differential equations, hyperbolic functions, parametric equations and polar coordinates, L’ Hôpital’s rule and improper integrals, continuous probability models, and infinite series. Each chapter concludes with several explorations, extended discovery investigations to supplement that chapter’s material. AMS/MAA Textbooks, Volume 28 2015; 371 pp.; hardcover; ISBN: 978-1-93951-206-2; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: TEXT/28

| ONLY Calculus for the Life Sciences A Modeling Approach James L. Cornette and Ralph A. Ackerman Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text. The students should have studied algebra, geometry, and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses. AMS/MAA Textbooks, Volume 29 2015; 713 pp.; ISBN: 978-1-61444-615-6; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: TEXT/29.E

Φ, Π , e , and i David Perkins Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (Φ , Π , e , and i ), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyam, Newton, Wallis, and Euler. Spectrum, Volume 86 2017; 176 pp.; softcover; ISBN: 978-0-88385-589-8; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: SPEC/86

401-455-4000 (Worldwide)401-455-4000 (Worldwide) ORDER BY PHONE ORDER BY PHONE 800-321-4267 (US and Canada)800-321-4267 (US and Canada) 12 DIFFERENTIAL EQUATIONS

| Ordinary Differential Equations From Calculus to Dynamical Systems Virginia W. Noonburg This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences. The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today’s world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being “flipped.” The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful. AMS/MAA Textbooks, Volume 25 2014; 315 pp.; hardcover; ISBN: 978-1-93951-204-8; List US$65; Institutional member US$52; Individual AMS & MAA members US$48.75; Order code: TEXT/25

DISCRETE MATHEMATICS & COMBINATORICS

| Combinatorics A Problem Oriented Approach Daniel A. Marcus The format of this book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems, about 250 in all, with connecting text; this is supplemented by 250 additional problems suitable for homework assignment. The problems are structured in order to introduce concepts in a logical order and in a thought- provoking way. The first four sections of the book deal with basic combinatorial entities; the last four cover special counting methods. Many applications to probability are included along the way. Students from a wide range of backgrounds—mathematics, computer science, or engineering—will appreciate this appealing introduction. Classroom Resource Materials, Volume 8 1998; 136 pp.; softcover; ISBN: 978-0-88385-710-6; List US$45; Institutional member US$36; Individual AMS & MAA members US$33.75; Order code: CLRM/8

| Proofs that Really Count The Art of Combinatorial Proof Arthur T. Benjamin and Jennifer J. Quinn Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians. Dolciani Mathematical Expositions, Volume 27 2003; 194 pp.; hardcover; ISBN: 978-0-88385-333-7; List US$58; Institutional member US$46.40; Individual AMS & MAA members US$43.50; Order code: DOL/27

ORDER ONLINE bookstore.ams.org 13 | Combinatorics A Guided Tour David R. Mazur Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. AMS/MAA Textbooks, Volume 17 2010; 391 pp.; hardcover; ISBN: 978-0-88385-762-5; List US$68; Institutional member US$54.40; Individual AMS & MAA members US$51; Order code: TEXT/17

| Graph Theory A Problem Oriented Approach Daniel A. Marcus 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. AMS/MAA Textbooks, Volume 11 2011; 205 pp.; softcover; ISBN: 978-0-88385-772-4; List US$59; Institutional member US$47.20; Individual AMS & MAA members US$44.25; Order code: TEXT/11

GENERAL INTEREST Euler The Master of Us All William Dunham Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler’s work. Dolciani Mathematical Expositions, Volume 22 1999; 185 pp.; softcover; ISBN: 978-0-88385-328-3; List US$43; Institutional member US$34.40; Individual AMS & MAA members US$32.25; Order code: DOL/22

The Contest Problem Book VI American High School Mathematics Examinations 1989-1994 Leo J. Schneider The Contest Problem Book VI contains 180 challenging problems from the six years of the American High School Mathematics Examinations (AHSME), 1989 through 1994, as well as a selection of other problems. A Problems Index classifies the 180 problems in the book into subject areas: algebra, complex numbers, discrete mathematics, number theory, statistics, and trigonometry. Anneli Lax New Mathematical Library, Volume 40 2000; 212 pp.; softcover; ISBN: 978-0-88385-642-0; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: NML/40 401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 14 Calculus Gems Brief Lives and Memorable Moments George F. Simmons Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices (“Biographical Notes” and “Variety of Additional Topics”) found in Simmons’ 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The overall aim is bound up in the question, “What is mathematics for?” and in Simmons’ answer, “To delight the mind and help us understand the world”. The essays are independent of one another, allowing the instructor to pick and choose among them. Part A, “Brief Lives”, is a biographical history of mathematics from earliest times (Thales, 625–547 BC) through the late 19th century (Weierstrass, 1815–1897) that serves to connect mathematics to the broader intellectual and social history of Western civilization. Part B, “Memorable Mathematics”, is a collection of interesting topics from number theory, geometry, and science arranged in an order roughly corresponding to the order of most calculus courses. Spectrum, Volume 55 2007; 355 pp.; hardcover; ISBN: 978-0-88385-561-4; List US$55; Institutional member US$44; Individual AMS & MAA members US$41.25; Order code: SPEC/55

Mathematics in Historical Context Jeff Suzuki What would Newton see if he looked out his bedroom window? Mathematics in Historical Context describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course. Spectrum, Volume 62 2009; 409 pp.; hardcover; ISBN: 978-0-88385-570-6; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: SPEC/62

Voltaire’s Riddle Micromégas and the Measure of All Things Andrew J. Simoson Did you know that Voltaire was the first to publish the legend of Isaac Newton discovering gravity upon seeing an apple fall? That he tried for about eight years to be a mathematician? That in 1752 he wrote Micromégas, a story about a French expedition to the arctic (1736-7) whose purpose was to test Newton’s controversial theories about gravity? This book is about that story and its underlying mathematics. All in all, this book is a case study in how mathematical and scientific knowledge becomes common knowledge. Dolciani Mathematical Expositions, Volume 39 2010; 382 pp.; hardcover; ISBN: 978-0-88385-345-0; List US$64; Institutional member US$51.20; Individual AMS & MAA members US$48; Order code: DOL/39

Mathematics and Sports Joseph A. Gallian, Editor This book is an eclectic compendium of the essays solicited for the 2010 Mathematics Awareness Month web page on the theme of Mathematics and Sports. In keeping with the goal of promoting mathematics awareness to a broad audience, all of the articles are accessible to college level mathematics students and many are accessible to the general public. The book is divided into sections by the kind of sports. The articles provide source material for classroom use and student projects. Many students will find mathematical ideas motivated by examples taken from sports more interesting than the examples selected from traditional sources. Dolciani Mathematical Expositions, Volume 43 2010; 329 pp.; softcover; ISBN: 978-0-88385-349-8; List US$41; Institutional member US$32.80; Individual AMS & MAA members US$30.75; Order code: DOL/43

ORDER ONLINE bookstore.ams.orgORDER ONLINE bookstore.ams.org 15 A Historian Looks Back The Calculus as Algebra and Selected Writings Judith V. Grabiner Judith Grabiner, the author of A Historian Looks Back, has long been interested in investigating what mathematicians actually do, and how mathematics actually has developed. She addresses the results of her investigations not principally to other historians, but to mathematicians and teachers of mathematics. This book brings together much of what she has had to say to this audience. The centerpiece of the book is The Calculus as Algebra: J.-L. Lagrange, 1736–1813. The book describes the achieve- ments, setbacks, and influence of Lagrange’s pioneering attempt to reduce the calculus to algebra. Nine additional articles round out the book describing the history of the derivative. The development of mathematics cannot be programmed or predicted. Appreciating its cultural background can humanize mathematics for students, and famous mathematicians struggles and successes should interest—and perhaps inspire—researchers. Spectrum, Volume 64 2010; 287 pp.; hardcover; ISBN: 978-0-88385-572-0; List US$64; Institutional member US$51.20; Individual AMS & MAA members US$48; Order code: SPEC/64

| An Episodic History of Mathematics Mathematical Culture Through Problem Solving Steven G. Krantz 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 be an encyclopedic history of mathematics, but to give the reader a sense of mathematical culture and history. The book abounds with stories, and personalities play a strong role. The book will introduce readers to some of the genesis of mathematical ideas. The focus in this text is on getting involved with 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. AMS/MAA Textbooks, Volume 19 2010; 381 pp.; hardcover; ISBN: 978-0-88385-766-3; List US$72; Institutional member US$57.60; Individual AMS & MAA members US$54; Order code: TEXT/19

Rediscovering Mathematics You Do the Math Shai Simonson Rediscovering Mathematics is an eclectic collection of mathematical topics and puzzles aimed at talented youngsters and inquisitive adults who want to expand their view of mathematics. By focusing on problem solving, and discouraging rote memorization, the book shows how to learn and teach mathematics through investigation, experimentation, and discovery. Topics range in difficulty and cover a wide range of historical periods, with some examples demonstrating how to uncover mathematics in everyday life. Rediscovering Mathematics provides a fresh view of mathematics for those who already like the subject, and offers a second chance for those who think they don’t. Classroom Resource Materials, Volume 39 2011; 207 pp.; softcover; ISBN: 978-0-88385-780-9; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: CLRM/39

Beautiful Mathematics Martin Erickson This book is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin’s sequence to the zeta function, and from hypercubes to infinity squared. In each case, the mathematics is compelling, elegant, simple, and beautiful. Who should read this book? There is something new for any mathematically-minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Spectrum, Volume 67 2011; 177 pp.; hardcover; ISBN: 978-0-88385-576-8; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: SPEC/67

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 16 Expeditions in Mathematics Tatiana Shubin, Gerald L. Alexanderson, and David F. Hayes, Editors This book is the second volume based on lectures for pre-college students given by prominent mathematicians in the Bay Area Mathematical Adventures (BAMA). This book reflects the flavor of the BAMA lectures and the excitement they have generated among the high school and middle school students in the Silicon Valley. The topics cover a wide range of mathematical subjects each treated by a leading proponent of the subject at levels designed to challenge and attract students whose mathematical interests are just beginning. In addition, the treatments given here will intrigue and enchant a more mature mathematician. Spectrum, Volume 68 2011; 312 pp.; hardcover; ISBN: 978-0-88385-571-3; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: SPEC/68

Mathematics Galore! The First Five Years of the St. Mark’s Institute of Mathematics James Tanton Mathematics Galore! showcases some of the best activities and student outcomes of the St. Mark's Institute of Mathematics and invites you to engage the mathematics yourself! Revel in the delight of deep intellectual play and marvel at the heights to which young scholars can rise. Based on 26 essays and eight additional pieces, Mathematics Galore! offers a large sample of mathematical tidbits and trea- sures, each immediately enticing, and each a gateway to layers of surprising depth and conundrum. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, or simply enjoy for yourself the bounty of research questions and intriguing puzzlers that lie within. Classroom Resource Materials, Volume 41 2012; 271 pp.; hardcover; ISBN: 978-0-88385-776-2; List US$52; Institutional member US$41.60; Individual AMS & MAA members US$39; Order code: CLRM/41

In the Dark On the Sunny Side A Memoir of an Out-of-Sight Mathematician Larry W. Baggett Misfortune struck one June day in 1944, when a five-year-old boy was forever blinded following an accident he suffered with a paring knife. Few people become internationally recognized research mathematicians and famously successful university professors of that erudite subject, and not surprisingly a minuscule number of those few are visually impaired. In the Dark on the Sunny Side tells the story of one such individual. Larry Baggett was main-streamed in school long before main-streaming was at all common. Besides describing the various successes and failures Baggett experienced living in the dark on the sunny side, he displays in this volume his love of math and music by interspersing short musings on both topics, such as discussing how to figure out how many dominoes are in a set, the intricacies of jazz chord progressions, and the mysterious Comma of Pythagoras. Spectrum, Volume 71 2012; 206 pp.; hardcover; ISBN: 978-0-88385-581-2; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: SPEC/71

A Mathematician Comes of Age Steven G. Krantz This book is about the concept of mathematical maturity, which is central to a mathematics education. The goal of a mathematics education is to transform the student from someone who treats mathematical ideas empirically and intuitively to someone who treats mathematical ideas analyti- cally and can control and manipulate them effectively. Put more directly, a mathematically mature person is one who can read, analyze, and evaluate proofs. And, most significantly, he/she is one who can create proofs. For this is what modern mathematics is all about: coming up with new ideas and validating them with proofs. This text turns the idea of mathematical maturity from a topic for coffee- room conversation to a topic for analysis and serious consideration. Spectrum, Volume 72 2012; 137 pp.; hardcover; ISBN: 978-0-88385-578-2; List US$56; Institutional member US$44.80; Individual AMS & MAA members US$42; Order code: SPEC/72

ORDER ONLINE bookstore.ams.org 17 Sophie’s Diary A Mathematical Novel: Second Edition Dora Musielak Hidden behind a man’s name, Sophie Germain's brilliance as a mathematician was first discovered by three of the greatest scholars of the eighteenth century, Lagrange, Gauss, and Legendre. In Sophie’s Diary, Germain comes to life through a fictionalized journal that intertwines mathematics with historical descriptions of the brutal events that took place in Paris between 1789 and 1793. This format provides a plausible perspective of how a young Sophie could have learned mathematics on her own—both fascinated by numbers and eager to master tough subjects without a teacher’s guidance. Her passion for mathematics is integrated into her personal life as an escape from societal outrage. Sophie’s Diary is suitable for a variety of readers—both young and old, mathematicians and novices—who will be inspired and enlightened on a field of study made easy, as told through the intellectual and personal struggles of an exceptional young woman. Spectrum, Volume 73 2012; 279 pp.; hardcover; ISBN: 978-0-88385-577-5; List US$43; Institutional member US$34.40; Individual AMS & MAA members US$32.25; Order code: SPEC/73

Martin Gardner in the Twenty-First Century Michael Henle and Brian Hopkins, Editors Martin Gardner enormously expanded the field of recreational mathematics with the Mathematical Games columns he wrote for Scientific American for over 25 years and the more than 70 books he published. He also had a long relationship with the Mathematical Association of America, publishing articles in MAA journals right up to his death in 2010. This book collects the articles Gardner wrote for the MAA in the twenty-first century, together with other articles the MAA published from 1999 to 2012 that spring from and comment on his work. Spectrum, Volume 75 2012; 297 pp.; softcover; ISBN: 978-0-88385-913-1; List US$41; Institutional member US$32.80; Individual AMS & MAA members US$30.75; Order code: SPEC/75

Six Sources of Collapse A Mathematician’s Perspective on How Things Can Fall Apart in the Blink of an Eye Charles R. Hadlock Beginning with one of the most remarkable ecological collapses of recent time, that of the passenger pigeon, Hadlock goes on to survey collapse processes across the entire spectrum of the natural and man-made world. He takes us through extreme weather events, technological disasters, evolutionary processes, crashing markets and companies, the chaotic nature of Earth’s orbit, revolutionary political change, the spread and elimination of disease, and many other fascinating cases. His key thesis is that one or more of six fundamental dynamics consistently show up across this wide range and can all be best described and investigated using fundamental mathematical concepts. They include low probability events, group dynamics, evolutionary games, instability, nonlinearity, and network effects, all of which are explained in readily understandable terms. Spectrum, Volume 76 2012; 207 pp.; hardcover; ISBN: 978-0-88385-579-9; List US$52; Institutional member US$41.60; Individual AMS & MAA members US$39; Order code: SPEC/76

| Bridge to Abstract Mathematics Ralph W. Oberste-Vorth, Aristides Mouzakitis, and Bonita A. Lawrence A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented. AMS/MAA Textbooks, Volume 22 2012; 232 pp.; hardcover; ISBN: 978-0-88385-779-3; List US$62; Institutional member US$49.60; Individual AMS & MAA members US$46.50; Order code: TEXT/22

401-455-4000 (Worldwide)401-455-4000 (Worldwide) ORDER BY PHONE ORDER BY PHONE 800-321-4267 (US and Canada)800-321-4267 (US and Canada) 18 | Distilling Ideas An Introduction to Mathematical Thinking (Graphs, Groups, Calculus) Brian P. Katz and Michael Starbird Mathematics is not a spectator sport; successful students of mathematics grapple with ideas for themselves. Distilling Ideas presents a carefully designed sequence of exercises and theorem statements that challenge students to create proofs and concepts. As students meet these challenges, they discover strategies of proofs and strategies of thinking beyond mathematics. In other words, Distilling Ideas helps its users to develop the skills, attitudes, and habits of mind of a mathematician, and to enjoy the process of distilling and exploring ideas. AMS/MAA Textbooks, Volume 24 2013; 171 pp.; softcover; ISBN: 978-1-93951-203-1; List US$56; Institutional member US$44.80; Individual AMS & MAA members US$42; Order code: TEXT/24

101 Careers in Mathematics Third Edition Andrew Sterrett, Editor This third edition of the immensely popular 101 Careers in Mathematics contains updates on the career paths of individuals profiled in the first and second editions, along with many new profiles. The authors of the essays in this volume describe a wide variety of careers for which a background in the mathematical sciences is useful. The degrees earned by the authors profiled here range from bachelor’s to master’s to PhD in approximately equal numbers. Most of the writers use the mathematical sciences on a daily basis in their work, while others rely on the general problem-solving skills acquired in mathematics as they deal with complex issues. Classroom Resource Materials, Volume 47 2014; 335 pp.; softcover; ISBN: 978-0-88385-786-1; List US$36; Institutional member US$28.80; Individual AMS & MAA members US$27; Order code: CLRM/47

Mathematicians on Creativity Peter Borwein, Peter Liljedahl, and Helen Zhai, Editors This book aims to shine a light on some of the issues of mathematical creativity. It is neither a philo- sophical treatise nor the presentation of experimental results, but a compilation of reflections from top-caliber working mathematicians. In their own words, they discuss the art and practice of their work. This approach highlights creative components of the field, illustrates the dramatic variation by individual, and hopes to express the vibrancy of creative minds at work. Mathematicians on Creativity is meant for a general audience and is probably best read by browsing. Spectrum, Volume 79 2014; 199 pp.; softcover; ISBN: 978-0-88385-574-4; List US$36; Institutional member US$28.80; Individual AMS & MAA members US$27; Order code: SPEC/79

How Euler Did Even More C. Edward Sandifer Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s How Euler Did It columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context. Spectrum, Volume 77 2015; 236 pp.; softcover; ISBN: 978-0-88385-584-3; List US$36; Institutional member US$28.80; Individual AMS & MAA members US$27; Order code: SPEC/77

ORDER ONLINE bookstore.ams.org 19 A Century of Advancing Mathematics Stephen F. Kennedy, Donald J. Albers, Gerald L. Alexanderson, Della Dumbaugh, Frank A. Faris, Deanna B. Haunsperger, and Paul Zorn, Editors This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics. More mathematics has been created and published since 1915 than in all of previous recorded history. We’ve solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA’s first century. Mathematics is the most thrilling, the most human area of intellectual inquiry. You will find in this volume compelling proof of that claim. Spectrum, Volume 81 2015; 423 pp.; hardcover; ISBN: 978-0-88385-588-1; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: SPEC/81

Half a Century of Pythagoras Magazine Alex van den Brandhof, Jan Guichelaar, and Arnout Jaspers, Editors Half a Century of Pythagoras Magazine is a selection of the best and most inspiring articles from this Dutch magazine for recreational mathematics. The book contains a mix of easy yet original puzzles, more challenging and at least as original problems, as well as playful introductions to a plethora of subjects in algebra, geometry, topology, number theory, and more. Concepts like the sudoku and the magic square are given a whole new dimension. Some are no more than cute little brainteasers which can be solved in a minute, others touch on profound mathematics and can keep the reader entranced indefinitely. Smart high school students and anyone else with a sharp and inquisitive mind will find in this book a treasure trove which is rich enough to keep his or her mind engaged for many weeks and months. Spectrum, Volume 82 2015; 302 pp.; softcover; ISBN: 978-0-88385-587-4; List US$45; Institutional member US$36; Individual AMS & MAA members US$33.75; Order code: SPEC/82

I, Mathematician Peter Casazza, Steven G. Krantz, and Randi D. Ruden, Editors Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting, and thought-provoking. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here. Spectrum, Volume 83 2015; 273 pp.; softcover; ISBN: 978-0-88385-585-0; List US$52; Institutional member US$41.60; Individual AMS & MAA members US$39; Order code: SPEC/83

Math through the Ages A Gentle History for Teachers and Others Expanded Second Edition William P. Berlinghoff and Fernando Q. Gouvêa Where did math come from? Who thought up all those algebra symbols, and why? What’s the story behind ... negative numbers? 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. AMS/MAA Textbooks, Volume 32 2015; 331 pp.; hardcover; ISBN: 978-1-93951-212-3; List US$60.50; Institutional member US$48.40; Individual AMS & MAA members US$45.38; Order code: TEXT/32

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 20 Coloring Book of Complex Function Representations Julie Barnes, William Kreahling, and Beth Schaubroeck Have you ever seen a mathematical object that was so intriguing that anyone, regardless of mathematical background, could appreciate its aesthetic beauty? If so, did you stop to color it? Now is your chance. Explore the beauty of mathematics in this collection of intricate pictures related to complex- valued functions. Any of these images could pass for designs found in some of the many coloring books for adults seen in stores today and are displayed here for you to color. While looking at the coloring pages, you can read about the author’s quest to find interesting images. Their tale includes expeditions on the complex plane, work with families of complex functions, visits to Julia sets, unexpected results from a typo, random explorations, and a final send-off from a well-known cartoon character. Grab your colored pencils and enjoy coloring these functions. 2017; 40 pp.; softcover; ISBN: 978-0-88385-591-1; List US$16.67; Institutional member US$13.34; Individual AMS & MAA members US$12.50; Order code: MMBK/8

Portal through Mathematics Journey to Advanced Thinking O. A. Ivanov Translated by Robert G. Burns Portal through Mathematics is a collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. The book is organized into 29 themes, each a topic from algebra, geometry or calculus and each launched from an opening puzzle or problem. There are excursions into number theory, solid geometry, physics and combinatorics. Always there is an emphasis on surprise and delight. And every theme begins at a level approachable with minimal background requirements. With well over 250 puzzles and problems, there is something here sure to appeal to everyone. Every fan of mathematics will find enjoyment in it. Anneli Lax New Mathematical Library, Volume 47 2017; 304 pp.; softcover; ISBN: 978-0-88385-651-2; List US$55; Institutional member US$44; Individual AMS & MAA members US$41.25; Order code: NML/47

American Mathematics 1890–1913 Catching Up to Europe Steve Batterson At the turn of the twentieth century, mathematical scholarship in the United States underwent a stun- ning transformation. In 1890, no American professor was producing mathematical research worthy of international attention. Graduate students were then advised to pursue their studies abroad. By the start of World War I, the standing of American mathematics had radically changed. George David Birkhoff, Leonard Dickson, and others were turning out cutting edge investigations that attracted notice in the intellectual centers of Europe. Harvard, Chicago, and Princeton maintained graduate programs comparable to those overseas. This book explores the people, timing, and factors behind this rapid advance. Spectrum, Volume 85 2017; 230 pp.; softcover; ISBN: 978-0-88385-590-4; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: SPEC/85

| A TeXas Style Introduction to Proof Ron Taylor and Patrick X. Rault A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the “bridge course”) that also introduces TeX as a tool students can use to communicate their work. As befitting “textless” text, the book is, as one reviewer characterized it, “minimal.” Written in an easygoing style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult. AMS/MAA Textbooks, Volume 35 2017; 161 pp.; softcover; ISBN: 978-1-93951-213-0; List US$50; Institutional member US$40; Individual member US$37.50; Order code: TEXT/35

ORDER ONLINE bookstore.ams.org 21 ONLY Episodes from the Early History of Mathematics Asger Aaboe Among other things, Aaboe shows us how the Babylonians did calculations, how Euclid proved that there are infinitely many primes, how Ptolemy constructed a trigonometric table in his Almagest, and how Archimedes trisected the angle. Some of the topics may be familiar to the reader, while others will seem surprising or be new. Anneli Lax New Mathematical Library, Volume 13 1998; 133 pp.; ISBN: 978-0-88385-928-5; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: NML/13.E

GEOMETRY & TOPOLOGY

| Geometry Revisited H. S. M. Coxeter and S. L. Greitzer Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley’s remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed. Anneli Lax New Mathematical Library, Volume 19 1967; 193 pp.; softcover; ISBN: 978-0-88385-619-2; List US$31; Institutional member US$24.80; Individual AMS & MAA members US$23.25; Order code: NML/19

Complex Numbers and Geometry Liang-shin Hahn The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained—no background in complex numbers is assumed—and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more. AMS/MAA Textbooks, Volume 1 1994; 192 pp.; softcover; ISBN: 978-0-88385-510-2; List US$30; Institutional member US$24; Individual AMS & MAA members US$22.50; Order code: TEXT/1

Topology Now! Robert Messer and Philip Straffin Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. AMS/MAA Textbooks, Volume 7 2006; 240 pp.; hardcover; ISBN: 978-0-88385-744-1; List US$62; Institutional member US$49.60; Individual AMS & MAA members US$46.50; Order code: TEXT/7

401-455-4000 (Worldwide)401-455-4000 (Worldwide) ORDER BY PHONE ORDER BY PHONE 800-321-4267 (US and Canada)800-321-4267 (US and Canada) 22 Methods for Euclidean Geometry Owen Byer, Felix Lazebnik, and Deirdre L. Smeltzer Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students’ appreciation of the subject and of mathematics as a whole. Classroom Resource Materials, Volume 37 2010; 461 pp.; hardcover; ISBN: 978-0-88385-763-2; List US$72; Institutional member US$57.60; Individual AMS & MAA members US$54; Order code: CLRM/37

Exploring Advanced Euclidean Geometry with GeoGebra Gerard A. Venema This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry. Classroom Resource Materials, Volume 44 2013; 129 pp.; hardcover; ISBN: 978-0-88385-784-7; List US$52; Institutional member US$41.60; Individual AMS & MAA members US$39; Order code: CLRM/44

New Horizons in Geometry Tom M. Apostol and Mamikon A. Mnatsakanian New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems that are often surprising and sometimes astounding. The hundreds of full color illustrations by Mamikon are visually enticing and provide great motivation to read further and savor the wonderful results. Dolciani Mathematical Expositions, Volume 47 2013; 513 pp.; hardcover; ISBN: 978-1-4704-4335-1; List US$83; AMS & MAA members US$66.40; Order code: DOL/47

Proofs Without Words III Further Exercises in Visual Thinking Roger B. Nelsen Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs. Classroom Resource Materials, Volume 52 2015; 187 pp.; softcover; ISBN: 978-0-88385-790-8; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: CLRM/52

ORDER ONLINE bookstore.ams.org ORDER ONLINE bookstore.ams.org 23 A Mathematical Space Odyssey Solid Geometry in the 21st Century Claudi Alsina and Roger B. Nelsen Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. This book presents techniques for proving a variety of geometric results in three dimensions. Special attention is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, as well as many new and classical results. The book includes a selection of challenges for each chapter with solutions, references and a complete index. The text is aimed at secondary school and college and university teachers as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students. Dolciani Mathematical Expositions, Volume 50 2015; 271 pp.; hardcover; ISBN: 978-0-88385-358-0; List US$55; Institutional member US$44; Individual AMS & MAA members US$41.25; Order code: DOL/50

| Thinking Geometrically A Survey of Geometries Thomas Q. Sibley 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. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software. AMS/MAA Textbooks, Volume 26 2015; 559 pp.; hardcover; ISBN: 978-1-93951-208-6; List US$77; Institutional member US$61.60; Individual AMS & MAA members US$57.75; Order code: TEXT/26

| Geometry Illuminated An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry Matthew Harvey Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and, as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very ‘visual’ subject. This book hopes to takes full advantage of that with an extensive use of illustrations as guides. AMS/MAA Textbooks, Volume 30 2015; 543 pp.; hardcover; ISBN: 978-1-93951-211-6; List US$70; Institutional member US$56; Individual AMS & MAA members US$52.50; Order code: TEXT/30

Near the Horizon An Invitation to Geometric Optics Henk W. Broer Near the Horizon starts out by considering several optical phenomena that can occur when the sun is near the horizon which are a result of the way that the atmosphere affects the geometry of light rays. Broer starts his book with the Fermat principle (rays of light take least-time paths) and deduces from it laws for refraction and reflection. The book is written in a very personal and engaging style. Broer is passionate about the subject and its history, and his passion helps carry the reader along. The result is readable and charming. Carus Mathematical Monographs, Volume 33 2016; 163 pp.; hardcover; ISBN: 978-0-88385-142-5; List US$63; Institutional member US$50.40; Individual AMS & MAA members US$47.25; Order code: CAR/33

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 24 MATH EDUCATION The William Lowell Putnam Mathematical Competition Problems and Solutions 1938–1964 A. M. Gleason, R. E. Greenwood, and L. M. Kelly, Editors Back by popular demand, we are pleased to reissue this outstanding collection of problems and solutions from the Putnam Competitions covering the years 1938-1964. Problemists the world over, including all past and future Putnam Competitors, will revel in mastering the difficulties posed by this collection of problems from the first 25 William Lowell Putnam Competitions. Solutions to all 347 problems are given. In some cases multiple solutions are included, some which contestants could reasonably be expected to find under examination conditions, and others which are more elegant or utilize more sophisticated techniques. There is great appeal here for all; teachers, students, and all those who love good problems and see them as an entree to beautiful and powerful ideas. Problem Books, Volume 1 1980; 673 pp.; softcover; ISBN: 978-0-88385-462-4; List US$58; Institutional member US$46.40; Individual AMS & MAA members US$43.50; Order code: PRB/1

The William Lowell Putnam Mathematical Competition Problems and Solutions 1965–1984 Gerald L. Alexanderson, Leonard F. Klosinski, and Loren C. Larson, Editors The Putnam Competition has been providing a challenge to gifted college mathematics students since 1928. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions. Problem Books, Volume 2 1985; 147 pp.; softcover; ISBN: 978-0-88385-463-1; List US$36; Institutional member US$28.80; Individual member US$27; Order code: PRB/2

The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary Kiran S. Kedlaya, Bjorn Poonen, and Ravi Vakil This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. Problem Books, Volume 6 2002; 337 pp.; softcover; ISBN: 978-0-88385-827-1; List US$58; Institutional member US$46.40; Individual AMS & MAA members US$43.50; Order code: PRB/6

The Contest Problem Book VII American Mathematics Competitions, 1995–2000 Contests Harold B. Reiter This is the seventh book of problems and solutions from the Mathematics Competitions. Contest Problem Book VII chronicles 275 problems from the American Mathematics Contests (AMC 12 and AMC 10 for the years 1995 through 2000, including the 50th Anniversary AHSME issued in 1999). Twenty-three additional problems with solutions are included. A Problem Index classifies the 275 problems in to the following subject areas: Algebra, Complex Numbers, Discrete Mathematics (including Counting Problems), Logic, and Discrete Probability, Geometry (including Three Dimensional Geometry), Number Theory (including Divisibility, Representation, and Modular Arithmetic), Statistics, and Trigonometry. The American Mathematics Contests are intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school. Problem Books, Volume 15 2006; 183 pp.; softcover; ISBN: 978-0-88385-821-9; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: PRB/15

ORDER ONLINE bookstore.ams.org 25 First Steps for Math Olympians Using the American Mathematics Competitions J. Douglas Faires A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. Problem Books, Volume 16 2006; 307 pp.; hardcover; ISBN: 978-0-88385-824-0; List US$55; Institutional member US$44; Individual AMS & MAA members US$41.25; Order code: PRB/16

| Number Theory Through Inquiry David C. Marshall, Edward Odell, and Michael Starbird Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry. AMS/MAA Textbooks, Volume 9 2007; 140 pp.; hardcover; ISBN: 978-0-88385-751-9; List US$58; Institutional member US$46.40; Individual AMS & MAA members US$43.50; Order code: TEXT/9

Sink or Float? Thought Problems in Math and Physics Keith Kendig Sink or Float: Thought Problems in Math and Physics is a collection of problems drawn from mathematics and the real world. Its multiple-choice format forces the reader to become actively involved in deciding upon the answer. The book’s aim is to show just how much can be learned by using everyday common sense. The problems are all concrete and understandable by nearly anyone, meaning that not only will students become caught up in some of the questions, but professional mathematicians, too, will easily get hooked. The more than 250 questions cover a wide swath of classical math and physics. Each problem's solution, with explanation, appears in the answer section at the end of the book. A notable feature is the generous sprinkling of boxes appearing throughout the text. These contain historical asides or little-known facts. The book will find a natural home in the classroom. Dolciani Mathematical Expositions, Volume 33 2008; 375 pp.; hardcover; ISBN: 978-0-88385-339-9; List US$63; Institutional member US$50.40; Individual member US$47.25; Order code: DOL/33

The Contest Problem Book IX American Mathematics Competitions (AMC 12) 2001–2007 David Wells and J. Douglas Faires This is the ninth book of problems and solutions from the American Mathematics Competitions (AMC) contests. It chronicles 325 problems from the thirteen AMC 12 contests given in the years between 2001 and 2007. The problems have all been edited to ensure that they conform to the current style of the AMC 12 competitions. Graphs and figures have been redrawn to make them more consistent in form and style, and the solutions to the problems have been both edited and supplemented. A problem index at the back of the book classifies the problems into subject areas of Algebra, Arithmetic, Complex Numbers, Counting, Functions, Geometry, Graphs, Logarithms, Logic, Number Theory, Polynomials, Probability, Sequences, Statistics, and Trigonometry. Problem Books, Volume 18 2008; 220 pp.; softcover; ISBN: 978-0-88385-826-4; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: PRB/18

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 26 The Contest Problem Book VIII American Mathematics Competitions (AMC 10) 2000–2007 J. Douglas Faires and David Wells For more than 50 years, the Mathematical Association of America has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools. In the year 2000, the Mathematical Association of America initiated the American Mathematics Competitions 10 (AMC 10) for students up to grade 10. The Contest Problem Book VIII is the first collection of problems from that competition covering the years 2001–2007. There are 350 problems from the first 14 contests included in this collection. A Problem Index at the back of the book classifies the problems into the following major subject areas: Algebra and Arithmetic, Sequences and Series, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, Solid Geometry, Discrete Probability, Statistics, Number Theory, and Logic. Problem Books, Volume 19 2008; 212 pp.; softcover; ISBN: 978-0-88385-825-7; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: PRB/19

Hungarian Problem Book IV Robert Barrington Leigh and Andy Liu The Eötvös Mathematics Competition is the oldest high school mathematics competition in the world, dating back to 1894. This book is a continuation of Hungarian Problem Book III and takes the contest through 1963. Forty-eight problems in all are presented in this volume. Problems are clas- sified under combinatorics, graph theory, number theory, divisibility, sums and differences, algebra, geometry, tangent lines and circles, geometric inequalities, combinatorial geometry, trigonometry and solid geometry. Multiple solutions to the problems are presented along with background material. Problem Books, Volume 23 2011; 115 pp.; softcover; ISBN: 978-0-88385-831-8; List US$43; Institutional member US$34.40; Individual AMS & MAA members US$32.25; Order code: PRB/23

| Mathematics for Secondary School Teachers Elizabeth George Bremigan, Ralph J. Bremigan, and John D. Lorch Mathematics for Secondary School Teachers discusses topics of central importance in the secondary school mathematics curriculum, including functions, polynomials, trigonometry, exponential and logarithmic functions, number and operation, and measurement. The text provides a balance of discovery learning and direct instruction. Activities and exercises address the range of learning objec- tives appropriate for future teachers. Beyond the obvious goals of conceptual understanding and computational fluency, readers are invited to devise mathematical explanations and arguments, create examples and visual representations, remediate typical student errors and misconceptions, and analyze student work. A rich collection of exercises of widely varying degrees of difficulty is integrated with the text. Activities and exercises are easily adapted to the settings of individual assignments, group projects, and classroom discussions. AMS/MAA Textbooks, Volume 21 2011; 417 pp.; hardcover; ISBN: 978-0-88385-773-1; List US$67; Institutional member US$53.60; Individual AMS & MAA members US$50.25; Order code: TEXT/21

A Mathematical Orchard Problems and Solutions Mark I. Krusemeyer, George T. Gilbert, and Loren C. Larson This volume is a republication and expansion of the much-loved Wohascum County Problem Book, published in 1993. The original 130 problems have been retained and supplemented by an additional 78 problems. The puzzles contained within, which are accessible but never routine, have been specially selected for their mathematical appeal, and detailed solutions are provided. The reader will encounter puzzles involving calculus, algebra, discrete mathematics, geometry and number theory, and the volume includes an appendix identifying the prerequisite knowledge for each problem. This collection will provide enjoyment for seasoned problem solvers and for those who wish to hone their skills. Problem Books, Volume 24 2012; 397 pp.; softcover; ISBN: 978-0-88385-833-2; List US$52; Institutional member US$41.60; Individual AMS & MAA members US$39; Order code: PRB/24

ORDER ONLINE bookstore.ams.org 27 More Fallacies, Flaws, and Flimflam Edward J. Barbeau Mistakes in mathematical reasoning can range from outlandish blunders to deep and subtle oversights that evade even the most watchful eye. This book represents the second collection of such errors to be compiled by Edward Barbeau. Like Barbeau’s previous book, Mathematical Fallacies, Flaws and Flimflam, material is drawn from a variety of sources including the work of students, textbooks, the media, and even professional mathematicians. The errors presented here serve both to entertain, and to emphasize the need to subject even the most ‘obvious’ assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. Each item is carefully analyzed and the source of the error is exposed. Spectrum, Volume 74 2013; 171 pp.; softcover; ISBN: 978-0-88385-580-5; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: SPEC/74

ONLY Textbooks, Testing, Training How We Discourage Thinking Stephen S. Willoughby Stephen S. Willoughby has taught mathematics for 59 years and he has seen everything. Some of it has annoyed him; some has inspired him. This little book is something of a valedictory and he shares some parting thoughts as he contemplates the end of his teaching career. Willoughby has strong, cogent, and mostly negative opinions about textbooks, standardized testing, and teacher training. These opinions have been forged in the cauldron of the classroom of a deeply caring teacher. They might not please readers, but they ought to make them think. They should spark needed debate in our community. Spectrum, Volume 80 2014; 55 pp.; ISBN: 978-1-61444-803-7; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: SPEC/80.E

| Arithmetical Wonderland Andy Liu 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. 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 are learning Elementary Number Theory from Alice. The reader is carried along in this academic exploration. Thus many formal proofs are converted to soothing everyday language. Classroom Resource Materials, Volume 48 2015; 223 pp.; hardcover; ISBN: 978-0-88385-789-2; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: CLRM/48

Trigonometry A Clever Study Guide James Tanton This guide covers the story of trigonometry. It is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject you may have taken or are currently taking. (These notes will be tough going for those encountering trigonometry for the very first time!) Problem Books, Volume 25 2015; 211 pp.; softcover; ISBN: 978-0-88385-836-3; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: PRB/25

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 28 A Gentle Introduction to the American Invitational Mathematics Exam Scott A. Annin This book is a celebration of mathematical problem solving at the level of the high school American Invitational Mathematics Examination. There is no other book on the market focused on the AIME. It is intended, in part, as a resource for comprehensive study and practice for the AIME competition for students, teachers, and mentors. This book is also intended for anyone who enjoys solving problems as a recreational pursuit. The AIME contains many problems that have the power to foster enthusiasm for mathematics; the problems are fun, engaging, and addictive. There are more than 250 fully-solved problems in the book. In some cases, multiple solutions are presented to highlight variable approaches. Problem Books, Volume 26 2015; 398 pp.; softcover; ISBN: 978-0-88385-835-6; List US$56; Institutional member US$44.80; Individual AMS & MAA members US$42; Order code: PRB/26

Euclidean Geometry in Mathematical Olympiads Evan Chen This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. Problem Books, Volume 27 2016; 311 pp.; softcover; ISBN: 978-0-88385-839-4; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: PRB/27

ONLY Soviet Union Mathematical Olympiad Grades, 8, 9, and 10 Andy C. F. Liu, Editor The olympiad movement in the former Soviet Union was initially city-based with what was then Leningrad taking the lead in 1934, followed by Moscow in 1935. In 1961, the national Russian Mathematical Olympiad was founded. In 1967, the contest was renamed the Soviet Union Mathematical Olympiad. Later, somewhat confusingly, a new Russian Mathematical Olympiad was organized. To make the distinction, the first six contests under the umbrella of the Soviet Union Mathematical Olympiad are included. The coverage is also extended to 1992 when the Soviet Union had dissolved and the contest should properly have been called the Mathematical Olympiad of the Independent States. The contest ceased operation after this one-time affair. The book is divided into three parts, one for each grade level group of contests. Each part has its own problem classification and problem index chapters. Also included, in appendices, are grade 11 contests and solutions from 1963–1966. Problem Books, Volume 28 2016; 389 pp.; ISBN: 978-1-61444-408-4; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: PRB/28.E

NUMBER THEORY Biscuits of Number Theory Arthur T. Benjamin and Ezra Brown, Editors In Biscuits of Number Theory, the editors have chosen articles that are exceptionally well-written and that can be appreciated by anyone who has taken (or is taking) a first course in number theory. The collection is divided into seven chapters: Arithmetic; Primes; Irrationality and Continued Fractions; 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 Biscuits in order. Dip into them anywhere: pick something from the table of contents that strikes your fancy, and have at it. If the end of an article leaves you wondering what happens next, then by all means dive in and do some research. You just might discover something new! Dolciani Mathematical Expositions, Volume 34 2009; 311 pp.; hardcover; ISBN: 978-0-88385-340-5; List US$64; Institutional member US$51.20; Individual AMS & MAA members US$48; Order code: DOL/34 ORDER ONLINE bookstore.ams.org 29 Which Numbers Are Real? Michael Henle Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Classroom Resource Materials, Volume 42 2012; 219 pp.; hardcover; ISBN: 978-0-88385-777-9; List US$53; Institutional member US$42.40; Individual AMS & MAA members US$39.75; Order code: CLRM/42

The Riemann Hypothesis Roland van der Veen and Jan van de Craats The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 … Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions.The present book is a first exploration of this fascinating, unknown world. Anneli Lax New Mathematical Library, Volume 46 2015; 144 pp.; softcover; ISBN: 978-0-88385-650-5; List US$45; Institutional member US$36; Individual AMS & MAA members US$33.75; Order code: NML/46

| Invitation to Number Theory Second Edition Oystein Ore Revised and updated by John J. Watkins and Robin Wilson Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular poly- gons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. Anneli Lax New Mathematical Library, Volume 49 2017; 134 pp.; softcover; ISBN: 978-0-88385-653-6; List US$48; AMS & MAA members US$38.40; Order code: NML/49

| An Open Door to Number Theory Duff Campbell Using a geometric and intuitive approach, this well-written, inviting textbook is designed for a one-semester, junior-level course in elementary number theory. The text features over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. Readers will be well prepared for a second-semester course focusing on algebraic number theory. AMS/MAA Textbooks, Volume 39 2018; approximately 290 pp.; hardcover; ISBN: 978-1-4704-4348-1; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: TEXT/39

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ALGEBRA & ALGEBRAIC GEOMETRY

ONLY ONLY Vectors and Matrices The Theory of Linear Algebra Cyrus Colton MacDuffee Algebraic Numbers Problem Book Carus Mathematical Monographs, Second Edition Paul R. Halmos Volume 7 Harry Pollard and Dolciani Mathematical 1943; 203 pp.; Harold G. Diamond Expositions, Volume 16 ISBN: 978-1-61444-007-9; 1995; 333 pp.; List US$30 Carus Mathematical Monographs, ISBN: 978-1-61444-212-7; Institutional member US$24; Volume 9 List US$40; Individual AMS & MAA members 1975; 162 pp.; hardcover; Institutional member US$32; US$22.50; Order code: CAR/7.E ISBN: 978-0-88385-018-3; Individual AMS & MAA members List US$40; US$30; Order code: DOL/16.E Institutional member US$32; Individual member US$30; ONLY Order code: CAR/9 Rings and Ideals Neal H. McCoy ONLY The Sensual Carus Mathematical Monographs, (quadratic) Form Volume 8 Noncommutative Rings John Horton Conway 1948; 216 pp.; I. N. Herstein ISBN: 978-1-61444-008-6; Carus Mathematical Monographs, List US$30; Carus Mathematical Monographs, Volume 26 Institutional member US$24; Volume 15 1997; 152 pp.; softcover; Individual AMS & MAA members 1994; 202 pp.; ISBN: 978-0-88385-040-4; US$22.50; Order code: CAR/8.E ISBN: 978-1-61444-015-4; List US$35; List US$46; Institutional member US$28; Institutional member US$36.80; Individual AMS & MAA members Individual member US$34.50; Order US$26.25; Order code: CAR/26 code: CAR/15.E Groups and | Their Graphs Israel Grossman and Visual Group Theory Wilhelm Magnus Nathan Carter Anneli Lax New Mathematical Classroom Resource Materials, Library, Volume 14 Volume 32 1964; 195 pp.; softcover; 2009; 295 pp.; hardcover; ISBN: 978-0-88385-614-7; ISBN: 978-0-88385-757-1; List US$30; List US$75; Institutional member US$24; Institutional member US$60; Individual AMS & MAA members Individual AMS & MAA members US$22.50; Order code: NML/14 US$56.25; Order code: CLRM/32

ORDER ONLINE bookstore.ams.org 31 ANALYSIS

ONLY Analytic Functions of Mathematical Modeling Resources For The Study a Complex Variable in the Environment of Real Analysis David Raymond Curtiss Charles R. Hadlock Robert L. Brabenec Carus Mathematical Monographs, AMS/MAA Textbooks, Volume 3 AMS/MAA Textbooks, Volume 4 Volume 2 1998; 302 pp.; softcover; 2004; 231 pp.; hardcover; 1926; 173 pp.; ISBN: 978-1-61444-002-4; List ISBN: 978-0-88385-709-0; List US$66; ISBN: 978-0-88385-737-3; List US$50; US$50; Institutional member US$40; Institutional member US$52.80; Institutional member US$40; Individual AMS & MAA members US$37.50; Individual AMS & MAA members US$49.50; Individual AMS & MAA members US$37.50; Order code: CAR/2.E Order code: TEXT/3 Order code: TEXT/4

ONLY | Fourier Series and A Panorama of Fourier Series Orthogonal Polynomials Harmonic Analysis Rejendra Bhatia Dunham Jackson Steven G. Krantz AMS/MAA Textbooks, Volume 5 Carus Mathematical Monographs, Carus Mathematical Monographs, 2005; 120 pp.; softcover; Volume 6 Volume 27 ISBN: 978-0-88385-740-3; List US$50; Institutional member US$40; 1941; 234 pp.; ISBN: 978-1-61444-006-2; List 1999; 357 pp.; hardcover; Individual AMS & MAA members US$37.50; US$30; Institutional member US$24; ISBN: 978-0-88385-031-2; List US$53; Order code: TEXT/5 Individual AMS & MAA members US$22.50; Institutional member US$42.40; Order code: CAR/6.E Individual AMS & MAA members US$39.75; Order code: CAR/27

Real Infinite Series The Schwarz Function Daniel D. Bonar and and Its Applications Inequalities from Michael J. Khoury Jr. AMS/MAA Textbooks, Volume 8 Philip J. Davis Complex Analysis John P. D’Angelo 2006; 264 pp.; hardcover; Carus Mathematical Monographs, ISBN: 978-0-88385-745-8; List US$60; Volume 17 Carus Mathematical Monographs, Institutional member US$48; 1974; 228 pp.; softcover; Volume 28 Individual AMS & MAA members US$45; ISBN: 978-0-88385-046-6; List US$38; 2002; 264 pp.; hardcover; Order code: TEXT/8 Institutional member US$30.40; ISBN: 978-0-88385-033-6; List US$35; Individual AMS & MAA members US$28.50; Institutional member US$28; Order code: CAR/17 Individual AMS & MAA members US$26.25; Order code: CAR/28 ONLY ONLY Exploratory Examples A Garden of Integrals for Real Analysis Frank E. Burk The Generalized Dolciani Mathematical Expositions, Joanne E. Snow and Kirk E. Weller Volume 31 Riemann Integral Classroom Resource Materials, 2007; 281 pp.; ISBN: 978-1-61444-209-7; List Robert M. McLeod Volume 20 US$35; Institutional member US$28; Carus Mathematical Monographs, 2003; 160 pp.; softcover; Individual AMS & MAA members US$26.25; Volume 20 ISBN: 978-0-88385-734-2; List US$40; Order code: DOL/31.E Institutional member US$32; 1980; 275 pp.; ISBN: 978-1-61444-020-8; Individual AMS & MAA members US$30; List US$54; Institutional member US$43.20; Order code: CLRM/20 Individual AMS & MAA members US$40.50; Order code: CAR/20.E A Guide To Complex Variables Steven G. Krantz ONLY Complex Analysis: Dolciani Mathematical Expositions, Volume 32 A Primer of Real Functions The Geometric Viewpoint 2008; 183 pp.; hardcover; Fourth Edition Second Edition ISBN: 978-0-88385-338-2; List US$51; Ralph P. Boas and Harold P. Boas Steven G. Krantz Institutional member US$40.80; Individual AMS & MAA members US$38.25; Carus Mathematical Monographs, Carus Mathematical Monographs, Order code: DOL/32 Volume 13 Volume 23 1996; 305 pp.; ISBN: 978-1-61444-013-0; 2004; 219 pp.; hardcover; List US$37; Institutional member US$29.60; ISBN: 978-0-88385-035-0; List US$56; Individual AMS & MAA members US$27.75; Institutional member US$44.80; Order code: CAR/13.E Individual AMS & MAA members US$42; Order code: CAR/23

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 32 A Guide to Advanced Randomness and Recurrence Explorations in Real Analysis in Dynamical Systems Complex Analysis Gerald B. Folland A Real Analysis Approach Michael A. Brilleslyper, Dolciani Mathematical Expositions, Rodney Nillsen Michael J. Dorff, Volume 37 Carus Mathematical Monographs, Jane M. McDougall, James S. Rolf, 2009; 107 pp.; hardcover; Volume 31 Lisbeth E. Schaubroeck, ISBN: 978-0-88385-343-6; List US$51; 2010; 357 pp.; hardcover; Richard L. Stankewitz, and Institutional member US$40.80; ISBN: 978-0-88385-043-5; List US$65; Kenneth Stephenson Individual AMS & MAA members US$38.25; Institutional member US$52; Classroom Resource Materials, Volume 40 Order code: DOL/37 Individual AMS & MAA members US$48.75; 2012; 373 pp.; hardcover; Order code: CAR/31 ISBN: 978-0-88385-778-6; List US$62; Institutional member US$49.60; Individual AMS & MAA members US$46.50; Order code: CLRM/40 A Guide to Real Variables Steven G. Krantz Dolciani Mathematical Expositions, Volume 38 2009; 147 pp.; hardcover; ISBN: 978-0-88385-344-3; List US$51; Institutional member US$40.80; Individual AMS & MAA members US$38.25; Order code: DOL/38

APPLICATIONS

ONLY ONLY ONLY Mathematical Statistics Mathematical Methods Over and Over Again Henry L. Rietz in Science Gengzhe Chang and Carus Mathematical Monographs, George Pólya Thomas W. Sederberg Volume 3 Anneli Lax New Mathematical Library, Anneli Lax New Mathematical Library, Volume 39 1927; 181 pp.; ISBN: 978-1-61444-003-1; Volume 26 List US$46; Institutional member US$36.80; 1997; 309 pp.; ISBN: 978-0-88385-953-7; 1977; 234 pp.; ISBN: 978-0-88385-941-4; Individual AMS & MAA members US$34.50; List US$28; Institutional member US$22.40; List US$25; Institutional member US$20; Order code: CAR/3.E Individual AMS & MAA members US$21; Individual AMS & MAA members US$18.75; Order code: NML/39.E Order code: NML/26.E Supplementary Material ONLY Statistical Independence and Solutions Manual in Probability, Analysis, Random Walks and for Mathematical Modeling and Number Theory Electric Networks in the Environment Mark Kac Peter G. Doyle and J. Laurie Snell Charles R. Hadlock AMS/MAA Textbooks, Volume 37 Carus Mathematical Monographs, Carus Mathematical Monographs, Volume 12 Volume 22 1998; 199 pp.; softcover; ISBN: 978-0-88385-713-7; List US$17; 1959; 94 pp.; softcover; 1984; 159 pp.; ISBN: 978-1-61444-022-2; Institutional member US$13.60; ISBN: 978-0-88385-025-1; List US$25; List US$66; Institutional member US$52.80; Individual AMS & MAA members US$12.75; Institutional member US$20; Individual AMS & MAA members US$49.50; Order code: TEXT/37 Individual AMS & MAA members US$18.75; Order code: CAR/22.E Order code: CAR/12 Identification Numbers and Check Digit Schemes ONLY Joseph Kirtland She Does Math! Classroom Resource Materials, Volume 18 Celestial Mechanics Real-Life Problems from 2000; 174 pp.; softcover; Harry Pollard Women on the Job ISBN: 978-0-88385-720-5; List US$42; Carus Mathematical Monographs, Marla Parker, Editor Institutional member US$33.60; Volume 18 Individual AMS & MAA members US$31.50; Classroom Resource Materials, Volume 4 Order code: CLRM/18 1976; 134 pp.; ISBN: 978-1-61444-018-5; 1995; 253 pp.; softcover; List US$46; Institutional member US$36.80; ISBN: 978-0-88385-702-1; List US$35; Individual AMS & MAA members US$34.50; Institutional member US$28; Order code: CAR/18.E Individual AMS & MAA members US$26.25; Order code: CLRM/4

ORDER ONLINE bookstore.ams.org 33 CALCULUS

ONLY Student Research Projects ONLY in Calculus Calculus of Variations Marcus Cohen, Edward D. Gaughan, Calculus Mysteries Gilbert Ames Bliss Arthur Knoebel, Douglas S. Kurtz, and Thrillers Carus Mathematical Monographs, and David Pengelley R. Grant Woods Volume 1 Spectrum, Volume 6 Classroom Resource Materials, Volume 9 1925; 189 pp.; ISBN: 978-1-61444-001-7; 1991; 216 pp.; softcover; 1998; 131 pp.; ISBN: 978-1-61444-114-4; List US$30; List US$46; Institutional member US$36.80; ISBN: 978-0-88385-503-4; List US$35; Institutional member US$24; Individual AMS & MAA members US$34.50; Institutional member US$28; Individual AMS & MAA members US$22.50; Order code: CAR/1.E Individual AMS & MAA members US$26.25; Order code: CLRM/9.E Order code: SPEC/6

ONLY The Hitchhiker’s Guide |ONLY to Calculus What Is Calculus About? Calculus Michael Spivak W. W. Sawyer An Active Approach with Projects Classroom Resource Materials, Volume 2 Anneli Lax New Mathematical Library, Stephen Hilbert, Diane D. Schwartz, Volume 2 1995; 122 pp.; softcover; ISBN: 978-0-88385-812-7; List US$25; Stan Seltzer, and John Maceli 1962; 118 pp.; ISBN: 978-0-88385-920-9; Institutional member US$20; Classroom Resource Materials, Volume 36 List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Individual AMS & MAA members US$18.75; 2010; 307 pp.; ISBN: 978-0-88385-972-8; Order code: CLRM/2 Order code: NML/2.E List US$34; Institutional member US$27.20; Individual AMS & MAA members US$25.50; Order code: CLRM/36.E

DIFFERENTIAL EQUATIONS Ordinary Differential Equations A Brief Eclectic Tour David A. Sánchez Classroom Resource Materials, Volume 19 2002; 132 pp.; softcover; ISBN: 978-0-88385-723-6; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: CLRM/19

DISCRETE MATHEMATICS & COMBINATORICS

ONLY ONLY Combinatorial Mathematics From Error-Correcting Codes Graphs and Their Uses Herbert John Ryser Through Sphere Packings Oystein Ore Carus Mathematical Monographs, Anneli Lax New Mathematical Library, Volume 14 to Simple Groups Volume 34 1963; 154 pp.; ISBN: 978-1-61444-014-7; Thomas M. Thompson 1990; 153 pp.; ISBN: 978-0-88385-949-0; List US$50; Institutional member US$40; Carus Mathematical Monographs, List US$25; Institutional member US$20; Individual AMS & MAA members US$37.50; Volume 21 Individual AMS & MAA members US$18.75; Order code: CAR/14.E 1983; 228 pp.; softcover; Order code: NML/34.E ISBN: 978-0-88385-037-4; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: CAR/21

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ONLY Maxima and Minima Writing Mathematics Well Without Calculus A Manual for Authors A History of Mathematics Ivan Niven Leonard Gillman in America Before 1900 Dolciani Mathematical Expositions, 1987; 49 pp.; softcover; Volume 6 ISBN: 978-0-88385-443-3; List US$25; D. E. Smith and Jekuthiel Ginsburg Institutional member US$20; 1981; 303 pp.; hardcover; Carus Mathematical Monographs, Individual AMS & MAA members US$18.75; ISBN: 978-0-88385-306-1; List US$50; Volume 5 Order code: MMBK/7 Institutional member US$40; 1934; 209 pp.; ISBN: 978-1-61444-005-5; Individual AMS & MAA members US$37.50; List US$30; Institutional member US$24; Order code: DOL/6 Individual AMS & MAA members US$22.50; Order code: CAR/5.E ONLY Riddles of the Sphinx And Other Mathematical Puzzle Tales Great Moments in Mathematics Martin Gardner The Contest Problem Book I Before 1650 Anneli Lax New Mathematical Library, Volume 32 Annual High School Mathematics Howard Eves 1987; 164 pp.; softcover; Examination 1950–1960 Dolciani Mathematical Expositions, ISBN: 978-0-88385-632-1; List US$36; Volume 5 Charles T. Salkind Institutional member US$28.80; Anneli Lax New Mathematical Library, 1983; 270 pp.; ISBN: 978-1-61444-214-1; Individual AMS & MAA members US$27; Volume 5 List US$30; Institutional member US$24; Order code: NML/32 Individual AMS & MAA members US$22.50; 1961; 154 pp.; softcover; Order code: DOL/5.E ISBN: 978-0-88385-605-5; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: NML/5 USA Mathematical Olympiads Great Moments in Mathematics 1972-1986 ONLY After 1650 Murray S. Klamkin Howard Eves Anneli Lax New Mathematical Library, Volume 33 Mathematics of Choice Dolciani Mathematical Expositions, How to Count without Counting Volume 7 1988; 127 pp.; softcover; ISBN: 978-0-88385-634-5; List US$25; 1983; 263 pp.; softcover; Ivan Niven Institutional member US$20; ISBN: 978-0-88385-311-5; List US$35; Anneli Lax New Mathematical Library, Individual AMS & MAA members US$18.75; Institutional member US$28; Volume 15 Order code: NML/33 Individual AMS & MAA members US$26.25; 1965; 202 pp.; ISBN: 978-0-88385-930-8; Order code: DOL/7 List US$28; Institutional member US$22.40; More Mathematical Morsels Individual AMS & MAA members US$21; Ross Honsberger Order code: NML/15.E Dolciani Mathematical Expositions, Volume 10 The Role of Mathematics 1991; 322 pp.; softcover; ONLY ISBN: 978-0-88385-314-6; List US$28; Institutional in Science member US$22.40; Ingenuity in Mathematics M. M. Schiffer and L. Bowden Individual member US$21; Order code: DOL/10 Ross Honsberger Anneli Lax New Mathematical Library, Anneli Lax New Mathematical Library, Volume 30 Volume 23 1984; 207 pp.; softcover; Mathematical Cranks 1970; 206 pp.; ISBN: 978-0-88385-938-4; ISBN: 978-0-88385-630-7; List US$51; Underwood Dudley List US$25; Institutional member US$20; Institutional member US$40.80; Spectrum, Volume 4 Individual AMS & MAA members US$18.75; Individual AMS & MAA members US$38.25; Order code: NML/23.E Order code: NML/30 1992; 372 pp.; softcover; ISBN: 978-0-88385-507-2; List US$30; Institutional member US$24; Individual AMS & MAA members US$22.50; Order code: SPEC/4 International Mathematical The Contest Problem Book III The Search for E.T. Bell Charles T. Salkind and Olympiads 1978–1985 James M. Earl and forty supplemental problems Also Known as John Taine Anneli Lax New Mathematical Library, Murray S. Klamkin Constance Reid Volume 25 Spectrum, Volume 7 Anneli Lax New Mathematical Library, 1973; 186 pp.; softcover; Volume 31 1993; 372 pp.; hardcover; ISBN: 978-0-88385-625-3; List US$25; ISBN: 978-0-88385-508-9; List US$25; 1986; 142 pp.; softcover; Institutional member US$20; Institutional member US$20; ISBN: 978-0-88385-631-4; List US$32; Individual AMS & MAA members US$18.75; Individual AMS & MAA members US$18.75; Institutional member US$25.60; Order code: NML/25 Order code: SPEC/7 Individual AMS & MAA members US$24; Order code: NML/31

ORDER ONLINE bookstore.ams.org 35 ONLY Lion Hunting & Other Interdisciplinary Lively Mathematical Pursuits Application Projects Algebra and Tiling A Collection of Mathematics, David C. Arney, Editor Homorphisms in the Service of Geometry Verse and Stories Classroom Resource Materials, Volume 6 Sherman K. Stein and Sándor Szabó Ralph P. Boas Jr. 1997; 222 pp.; softcover; Carus Mathematical Monographs, Gerald L. Alexanderson and ISBN: 978-0-88385-706-9; List US$26; Volume 25 Dale H. Mugler, Editors Institutional member US$20.80; 1994; 209 pp.; ISBN: 978-1-61444-024-6; Individual AMS & MAA members US$19.50; Dolciani Mathematical Expositions, List US$46; Institutional member US$36.80; Order code: CLRM/6 Volume 15 Individual AMS & MAA members US$34.50; Order code: CAR/25.E 1995; 308 pp.; softcover; ISBN: 978-0-88385-323-8; List US$45; Institutional member US$36; The Trisectors Individual AMS & MAA members US$33.75; Diophantus and Underwood Dudley Order code: DOL/15 Spectrum, Volume 16 Diophantine Equations 1994; 184 pp.; softcover; Isabella Grigoryevna Bashmakova ISBN: 978-0-88385-514-0; List US$25; ONLY Dolciani Mathematical Expositions, Institutional member US$20; Volume 20 Individual AMS & MAA members US$18.75; Episodes in Nineteenth 1997; 90 pp.; softcover; Order code: SPEC/16 and Twentieth Century ISBN: 978-0-88385-526-3; List US$27; Institutional member US$21.60; Euclidean Geometry Individual AMS & MAA members US$20.25; ONLY Ross Honsberger Order code: DOL/20 Anneli Lax New Mathematical Library, The Words of Mathematics Volume 37 Numerology or An Etymological Dictionary of 1995; 174 pp.; ISBN: 978-0-88385-951-3; What Pythagoras Wrought Mathematical Terms in English List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Underwood Dudley Steven Schwartzman Order code: NML/37.E Spectrum, Volume 19 Spectrum, Volume 17 1997; 316 pp.; softcover; 1994; 261 pp.; ISBN: 978-1-61444-501-2; ISBN: 978-0-88385-524-9; List US$30; List US$28; Institutional member US$22.40; |ONLY Institutional member US$24; Individual AMS & MAA members US$21; Individual AMS & MAA members US$22.50; Order code: SPEC/17.E Essentials of Mathematics Order code: SPEC/19 Introduction to Theory, Proof, All the Math That’s Fit to Print and the Professional Culture Magic Tricks, Articles from The Manchester Guardian Margie Hale Card Shuffling and Keith Devlin Classroom Resource Materials, Volume 21 Dynamic Computer Memories Spectrum, Volume 9 1996; 180 pp.; ISBN: 978-0-88385-982-7; 1994; 330 pp.; softcover; List US$56; Institutional member US$44.80; S. Brent Morris ISBN: 978-0-88385-515-7; List US$25; Individual member US$42; Spectrum, Volume 22 Institutional member US$20; Order code: CLRM/21.E 1998; 148 pp.; softcover; Individual AMS & MAA members US$18.75; ISBN: 978-0-88385-527-0; List US$36; Order code: SPEC/9 Institutional member US$28.80; From Erdo˝s to Kiev Individual AMS & MAA members US$27; Learn from the Masters Problems of Olympiad Caliber Order code: SPEC/22 Ross Honsberger Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, Dolciani Mathematical Expositions, Twenty Years Before Volume 17 and Victor Katz, Editors 1996; 257 pp.; softcover; the Blackboard Classroom Resource Materials, Volume 3 ISBN: 978-0-88385-324-5; List US$30; The Lessons and Humor of 1995; 303 pp.; softcover; Institutional member US$24; a Mathematics Teacher ISBN: 978-0-88385-703-8; List US$40; Individual AMS & MAA members US$22.50; Michael Stueben Institutional member US$32; Order code: DOL/17 Individual AMS & MAA members US$30; with Diane Sandford Order code: CLRM/3 Spectrum, Volume 24 ONLY 1998; 155 pp.; softcover; ISBN: 978-0-88385-525-6; List US$25; Which Way Did the Bicycle Go? Institutional member US$20; Individual AMS & MAA members US$18.75; And Other Intriguing Order code: SPEC/24 Mathematical Mysteries D. E. Konhauser, Dan Velleman, and Stan Wagon Dolciani Mathematical Expositions, Volume 18 1996; 235 pp.; ISBN: 978-1-61444-220-2; List US$36; Institutional member US$28.80; Individual AMS & MAA members US$27; Order code: DOL/18.E

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 36 Archimedes Remarkable Mathematics Mathematical Circles What Did He Do Besides Cry Eureka? From Euler to von Neumann Revisited Mathematical and Circles Sherman Stein Ioan James Squared, Volume II Classroom Resource Materials, Volume 11 Spectrum, Volume 34 Howard W. Eves 1999; 155 pp.; softcover; 2002; 433 pp.; softcover; Spectrum, Volume 39 ISBN: 978-0-88385-718-2; List US$25; ISBN: 978-0-52152-094-2; List US$55; 2003; 196 pp.; hardcover; Institutional member US$20; Institutional member US$44; ISBN: 978-0-88385-543-0; List US$25; Individual AMS & MAA members US$18.75; Individual AMS & MAA members US$41.25; Institutional member US$20; Order code: CLRM/11 Order code: SPEC/34 Individual AMS & MAA members US$18.75; Order code: SPEC/39 Mathematical Treks ONLY From Surreal Numbers to Magic Circles Writing Projects for Solve This Ivars Peterson Mathematics Courses Spectrum, Volume 35 Math Activities for Students and Clubs Crushed Clowns, Cars, and Coffee to Go 2002; 170 pp.; softcover; James Tanton Annalisa Crannell, Gavin LaRose, ISBN: 978-0-88385-537-9; List US$35; Thomas Ratliff, and Elyn Rykken Classroom Resource Materials, Volume 17 Institutional member US$28; Classroom Resource Materials, Volume 25 2000; 219 pp.; ISBN: 978-1-61444-106-9; Individual AMS & MAA members US$26.25; List US$30; Institutional member US$24; Order code: SPEC/35 2004; 118 pp.; ISBN: 978-1-61444-113-7; Individual AMS & MAA members US$22.50; List US$30; Order code: CLRM/25.E Order code: CLRM/17.E Oval Track and Other Permutation Puzzles Mathematical Delights Mathematical Puzzle Tales And Just Enough Group Theory Ross Honsberger Martin Gardner to Solve Them Dolciani Mathematical Expositions, Volume 28 Spectrum, Volume 28 John O. Kiltinen 2000; 151 pp.; softcover; 2004; 252 pp.; softcover; Classroom Resource Materials, Volume 23 ISBN: 978-0-88385-533-1; List US$27; ISBN: 978-0-88385-334-4; List US$28; Institutional member US$21.60; 2003; 305 pp.; softcover; Institutional member US$22.40; Individual AMS & MAA members US$20.25; ISBN: 978-0-88385-725-0; List US$43; Individual AMS & MAA members US$21; Order code: SPEC/28 Institutional member US$34.40; Order code: DOL/28 Individual AMS & MAA members US$32.25; Order code: CLRM/23 The Random Walks of USA and International George Pólya Mathematical Diamonds Mathematical Olympiads 2003 Titu Andreescu and Zuming Feng, Gerald L. Alexanderson Ross Honsberger Editors Spectrum, Volume 29 Dolciani Mathematical Expositions, Problem Books, Volume 13 2000; 303 pp.; softcover; Volume 26 2004; 85 pp.; softcover; ISBN: 978-0-88385-528-7; List US$30; 2003; 241 pp.; softcover; ISBN: 978-0-88385-817-2; List US$30; Institutional member US$24; ISBN: 978-0-88385-332-0; List US$35; Institutional member US$24; Individual AMS & MAA members US$22.50; Institutional member US$28; Individual AMS & MAA members US$22.50; Order code: SPEC/29 Individual AMS & MAA members US$26.25; Order code: PRB/13 Order code: DOL/26

Mathematical Reminiscences Howard Eves A Friendly Mathematics Sherlock Holmes in Spectrum, Volume 30 Competition Babylon and Other Tales of 2001; 184 pp.; softcover; Thirty-Five Years of Teamwork in Indiana Mathematical History ISBN: 978-0-88385-535-5; List US$25; Marlow Anderson, Victor Katz, Institutional member US$20; Rick Gillman, Editor Individual AMS & MAA members US$18.75; Problem Books, Volume 8 and Robin Wilson, Editors Order code: SPEC/30 2003; 185 pp.; softcover; Spectrum, Volume 43 ISBN: 978-0-88385-808-0; List US$25; 2004; 387 pp.; hardcover; Institutional member US$20; ISBN: 978-0-88385-546-1; List US$50; 777 Mathematical Individual AMS & MAA members US$18.75; Institutional member US$40; Conversation Starters Order code: PRB/8 Individual AMS & MAA members US$37.50; Order code: SPEC/43 John dePillis Spectrum, Volume 32 Mathematical Circles 2002; 344 pp.; softcover; Mathematical Circles Adieu and Return USA and International ISBN: 978-0-88385-540-9; List US$55; to Mathematical Circles, Volume III Mathematics Olympiads 2004 Institutional member US$44; Howard W. Eves Individual AMS & MAA members US$41.25; Titu Andreescu, Zuming Feng, Order code: SPEC/32 Spectrum, Volume 36 and Po-Shen Lolt, Editors 2003; 186 pp.; hardcover; Problem Books, Volume 14 ISBN: 978-0-88385-544-7; List US$25; 2005; 100 pp.; softcover; Institutional member US$20; ISBN: 978-0-88385-819-6; List US$34; Individual AMS & MAA members US$18.75; Institutional member US$27.20; Order code: SPEC/36 Individual AMS & MAA members US$25.50; Order code: PRB/14

ORDER ONLINE bookstore.ams.org 37 Mathematical Apocrypha Redux The Early Mathematics More Stories and Anecdotes of of Leonhard Euler Mathematicians and the Mathematical C. Edward Sandifer Proof and Other Dilemmas Steven G. Krantz, Editor Spectrum, Volume 50 Mathematics and Philosophy Spectrum, Volume 44 2007; 416 pp.; hardcover; Bonnie Gold and Roger A. Simons 2005; 294 pp.; softcover; ISBN: 978-0-88385-559-1; List US$30; Spectrum, Volume 59 ISBN: 978-0-88385-554-6; List US$46; Institutional member US$24; 2008; 346 pp.; hardcover; ISBN: 978-0-88385- Institutional member US$36.80; Individual AMS & MAA members US$22.50; 567-6; List US$55; Institutional member US$44; Individual AMS & MAA members US$34.50; Order code: SPEC/50 Individual AMS & MAA members US$41.25; Order code: SPEC/44 Order code: SPEC/59 Euler and Modern Science R. L. Moore N. N. Bogolyubov, G. K. Mikhaı˘lov, Mathematician and Teacher and A. P. Yushevich, Editors John Parker Translated from Russian Who Gave You the Epsilon? by Robert Burns Spectrum, Volume 45 and Other Tales of Mathematical History Spectrum, Volume 53 2005; 387 pp.; hardcover; Marlow Anderson, Victor Katz, and ISBN: 978-0-88385-550-8; List US$54; 2007; 425 pp.; hardcover; Robin Wilson, Editors Institutional member US$43.20; ISBN: 978-0-88385-564-5; List US$26; Individual AMS & MAA members US$40.50; Institutional member US$20.80; Spectrum, Volume 63 Order code: SPEC/45 Individual AMS & MAA members US$19.50; Order 2009; 431 pp.; hardcover; code: SPEC/53 ISBN: 978-0-88385-569-0; List US$67; Institutional member US$53.60; Reality Conditions Individual AMS & MAA members US$50.25; Short Mathematical Fiction Euler At 300 Order code: SPEC/63 Alex Kasman An Appreciation Spectrum, Volume 46 Robert F. Bradley, 2005; 247 pp.; softcover; Lawrence A. D’Antonio, and ONLY ISBN: 978-0-88385-552-2; List US$38; C. Edward Sandifer, Editors Charming Proofs Institutional member US$30.40; Spectrum, Volume 54 Individual AMS & MAA members US$28.50; A Journey into Elegant Mathematics Order code: SPEC/46 2007; 298 pp.; hardcover; ISBN: 978-0-88385-565-2; List US$30; Claudi Alsina and Roger B. Nelsen Institutional member US$24; Dolciani Mathematical Expositions, Individual AMS & MAA members US$22.50; Volume 42 Order code: SPEC/54 ONLY 2010; 295 pp.; ISBN: 978-1-61444-201-1; List US$38; Institutional member US$30.40; Math Made Visual Individual AMS & MAA members US$28.50; Creating Images for Order code: DOL/42.E Understanding Mathematics Claudi Alsina and Roger B. Nelsen The Harmony of the World Classroom Resource Materials, Volume 28 75 Years of Mathematics Magazine ONLY 2006; 173 pp.; ISBN: 978-1-61444-100-7; Gerald L. Alexanderson List US$30; Institutional member US$24; and Peter Ross, Editors Lobachevski Illuminated Individual AMS & MAA members US$22.50; Spectrum, Volume 56 Seth Braver Order code: CLRM/28.E 2007; 287 pp.; hardcover; Spectrum, Volume 69 ISBN: 978-0-88385-560-7; List US$25; 2011; 227 pp.; ISBN: 978-0-88385-979-7; The Edge of the Universe Institutional member US$20; List US$38; Institutional member US$30.40; Celebrating Ten Years of Math Horizons Individual AMS & MAA members US$18.75; Individual AMS & MAA members US$28.50; Order code: SPEC/56 Order code: SPEC/69.E Deanna Haunsperger and Stephen Kennedy, Editors The Magic Numbers Spectrum, Volume 48 2006; 303 pp.; hardcover; of the Professor ISBN: 978-0-88385-555-3; List US$58; Owen O’Shea and Institutional member US$46.40; Underwood Dudley Individual AMS & MAA members US$43.50; Spectrum, Volume 57 Order code: SPEC/48 2007; 168 pp.; hardcover; ISBN: 978-0-88385-557-7; 99 Points of Intersection List US$25; Institutional member US$20; Examples, Pictures, Proofs Individual AMS & MAA members US$18.75; Order code: SPEC/57 Hans Walser Spectrum, Volume 49 2006; 153 pp.; hardcover; Is Mathematics Inevitable? ISBN: 978-0-88385-553-9; List US$49; A Miscellany Institutional member US$39.20; Underwood Dudley, Editor Individual AMS & MAA members US$36.75; Spectrum, Volume 58 Order code: SPEC/49 2008; 325 pp.; hardcover; ISBN: 978-0-88385-566-9; List US$58; Institutional member US$46.40; Individual AMS & MAA members US$43.50; Order code: SPEC/58

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ONLY ONLY ONLY Projective Geometry Geometric Transformations III Differential Geometry John Wesley Young I. G. Yaglom and Its Applications Carus Mathematical Monographs, Anneli Lax New Mathematical Library, John Oprea Volume 4 Volume 24 Classroom Resource Materials, Volume 30 1930; 185 pp.; ISBN: 978-1-61444-004-8; 1973; 237 pp.; ISBN: 978-0-88385-939-1; 2007; 469 pp.; ISBN: 978-1-61444-608-8; List US$30; Institutional member US$24; List US$25; Institutional member US$20; List US$42; Institutional member US$33.60; Individual AMS & MAA members US$22.50; Individual AMS & MAA members US$18.75; Individual AMS & MAA members US$31.50; Order code: CAR/4.E Order code: NML/24.E Order code: CLRM/30.E

ONLY Geometric Inequalities Old and New Unsolved A Guide to Topology Nicholas D. Kazarinoff Problems in Plane Geometry Steven G. Krantz Anneli Lax New Mathematical Library, and Number Theory Dolciani Mathematical Expositions, Volume 4 Victor Klee and Stan Wagon Volume 40 1961; 132 pp.; ISBN: 978-0-88385-922-3; 2009; 107 pp.; hardcover; List US$25; Institutional member US$20; Dolciani Mathematical Expositions, ISBN: 978-0-88385-346-7; List US$51; Individual AMS & MAA members US$18.75; Volume 11 Institutional member US$40.80; Order code: NML/4.E 1991; 333 pp.; softcover; Individual AMS & MAA members US$38.25; ISBN: 978-0-88385-315-3; List US$32; Order code: DOL/40 Institutional member US$25.60; Individual AMS & MAA members US$24; Order code: DOL/11 Geometric Transformations I I. M. Yaglom ONLY Geometric Transformations IV Anneli Lax New Mathematical Library, Circular Transformations Volume 8 Knot Theory I. M. Yaglom 1962; 133 pp.; softcover; Charles Livingston ISBN: 978-0-88385-608-6; List US$35; Translated by A. Shenitzer. Institutional member US$28; Carus Mathematical Monographs, Anneli Lax New Mathematical Library, Individual AMS & MAA members US$26.25; Volume 24 Volume 44 Order code: NML/8 1993; 240 pp.; ISBN: 978-1-61444-023-9; 2009; 285 pp.; softcover; List US$46; Institutional member US$36.80; ISBN: 978-0-88385-648-2; List US$48; Individual AMS & MAA members US$34.50; Institutional member US$38.40; | Order code: CAR/24.E Individual AMS & MAA members US$36; ONLY Order code: NML/44 First Concepts of Topology The Geometry of Mappings of Segments, ONLY Curves, Circles, and Disks Non-Euclidean Geometry W. G. Chin and N. E. Steenrod Sixth Edition Icons of Mathematics Anneli Lax New Mathematical Library, H. S. M. Coxeter An Exploration of Twenty Key Images Volume 18 Spectrum, Volume 23 Claudi Alsina and Roger B. Nelsen 1966; 160 pp.; ISBN: 978-0-88385-933-9; List US$25; Institutional member US$20; 1998; 336 pp.; ISBN: 978-1-61444-516-6; Dolciani Mathematical Expositions, Individual AMS & MAA members US$18.75; List US$30; Institutional member US$24; Volume 45 Order code: NML/18.E Individual AMS & MAA members US$22.50; 2011; 327 pp.; hardcover; Order code: SPEC/23.E ISBN: 978-0-88385-352-8; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; ONLY Geometry from Africa Order code: DOL/45 Mathematical and Educational Geometric Transformations II Explorations I. M. Yaglom Paulus Gerdes Anneli Lax New Mathematical Library, Classroom Resource Materials, Volume 10 Volume 21 1999; 210 pp.; softcover; 1968; 189 pp.; ISBN: 978-0-88385-936-0; ISBN: 978-0-88385-715-1; List US$49; List US$25; Institutional member US$20; Institutional member US$39.20; Individual AMS & MAA members US$18.75; Individual AMS & MAA members US$36.75; Order code: NML/21.E Order code: CLRM/10

ORDER ONLINE bookstore.ams.org 39 LOGIC & FOUNDATIONS Logic as Algebra ONLY Paul Halmos and Steven Givant Dolciani Mathematical Expositions, Volume 21 A Tour Through Mathematical Logic 1998; 141 pp.; softcover; ISBN: 978-0-88385-327-6; List US$33; Robert S. Wolf Institutional member US$26.40; Individual AMS & MAA members US$24.75; Carus Mathematical Monographs, Volume 30 Order code: DOL/21 2005; 397 pp.; ISBN: 978-1-61444-028-4; List US$42; Institutional member US$33.60; Individual AMS & MAA members US$31.50; Order code: CAR/30.E

MATH EDUCATION

ONLY ONLY Hungarian Problem Book III Based on the Eötvös Competitions: The Contest Problem Five Hundred 1929–1943 Book II Mathematical Challenges Andy Liu Edward J. Barbeau, Anneli Lax New Mathematical Library, Annual High School Contests Murray S. Klamkin, and Volume 42 William O. J. Moser 2001; 163 pp.; softcover; 1961–1965 ISBN: 978-0-88385-644-4; List US$30; Spectrum, Volume 14 Charles T. Salkind Institutional member US$24; Anneli Lax New Mathematical Library, 1995; 227 pp.; ISBN: 978-1-61444-507-4; Individual AMS & MAA members US$22.50; Volume 17 List US$28; Institutional member US$22.40; Order code: NML/42 Individual AMS & MAA members US$21; 1966; 112 pp.; ISBN: 978-0-88385-932-2; Order code: SPEC/14.E List US$25; Institutional member US$20; USA and International Individual AMS & MAA members US$18.75; Order code: NML/17.E ONLY Mathematical Olympiads 2001 Titu Andreescu and Zuming Feng, Contest Problem Book V Editors ONLY American High School Mathematics Problem Books, Volume 7 Examinations and American Invitational 2002; 122 pp.; softcover; International Mathematics Examinations, 1983–1988 ISBN: 978-0-88385-809-7; List US$25; Institutional member US$20; Math Olympiads George Berzsenyi Individual AMS & MAA members US$18.75; 1959–1977 and Stephen B. Maurer Order code: PRB/7 Anneli Lax New Mathematical Library, Samuel Greitzer Volume 38 Anneli Lax New Mathematical Library, 1997; 286 pp.; ISBN: 978-0-88385-952-0; Volume 27 List US$30; Institutional member US$24; 1978; 204 pp.; ISBN: 978-0-88385-942-1; Individual AMS & MAA members US$22.50; Mathematical Miniatures List US$25; Institutional member US$20; Order code: NML/38.E Individual AMS & MAA members US$18.75; Svetoslav Savchev Order code: NML/27.E and Titu Andreescu Inverse Problems Anneli Lax New Mathematical Library, Activities for Undergraduates Volume 43 ONLY Charles W. Groetsch 2003; 223 pp.; softcover; Classroom Resource Materials, Volume 12 ISBN: 978-0-88385-645-1; List US$35; Institutional member US$28; The Contest Problem Book IV 1999; 222 pp.; softcover; Individual AMS & MAA members US$26.25; ISBN: 978-0-88385-716-8; List US$35; Order code: NML/43 Annual High School Institutional member US$28; Mathematics Examinations, Individual AMS & MAA members US$26.25; 1973–1982 Order code: CLRM/12 Ralph A. Artino, Anthony M. Gaglione, ONLY International Math Olympiads, and Niel Shell 1986–1999 Anneli Lax New Mathematical Library, Mathematical Fallacies, Flaws, Volume 29 Marcin E. Kuczma 1982; 184 pp.; ISBN: 978-0-88385-944-5; and Flimflam Problem Books, Volume 10 List US$25; Institutional member US$20; Edward J. Barbeau 2003; 192 pp.; softcover; Individual AMS & MAA members US$18.75; Spectrum, Volume 25 ISBN: 978-0-88385-811-0; List US$40; Order code: NML/29.E Institutional member US$32; 2000; 167 pp.; ISBN: 978-1-61444-518-0; Individual AMS & MAA members US$30; List US$25; Institutional member US$20; Order code: PRB/10 Individual AMS & MAA members US$18.75; Order code: SPEC/25.E

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 40 Mathematical Olympiads | 2000–2001 Problems and Solutions from Understanding Our When Less is More Around the World Quantitative World Visualizing Basic Inequalities Titu Andreescu, Zuming Feng, Janet Andersen and Todd Swanson Claudi Alsina and Roger B. Nelsen Dolciani Mathematical Expositions, and George Lee Jr., Editors AMS/MAA Textbooks, Volume 6 Volume 36 Problem Books, Volume 11 2005; 303 pp.; hardcover; 2009; 181 pp.; hardcover; 2003; 282 pp.; softcover; ISBN: 978-0-88385-738-0; List US$58; ISBN: 978-0-88385-342-9; List US$60; ISBN: 978-0-88385-810-3; List US$31; Institutional member US$46.40; Institutional member US$48; Institutional member US$24.80; Individual AMS & MAA members US$43.50; Individual AMS & MAA members US$45; Individual AMS & MAA members US$23.25; Order code: TEXT/6 Order code: DOL/36 Order code: PRB/11

USA and International Mathematical Olympiads 2002 Creative Mathematics Titu Andreescu and Zuming Feng, AHA! Solutions H. S. Wall Editors Martin Erickson Classroom Resource Materials, Volume 31 Problem Books, Volume 12 Problem Books, Volume 20 2006; 195 pp.; hardcover; 2003; 79 pp.; softcover; 2009; 207 pp.; hardcover; ISBN: 978-0-88385-750-2; List US$54; ISBN: 978-0-88385-815-8; List US$35; ISBN: 978-0-88385-829-5; List US$56; Institutional member US$43.20; Institutional member US$28; Institutional member US$44.80; Individual AMS & MAA members US$40.50; Individual AMS & MAA members US$26.25; Individual AMS & MAA members US$42; Order code: CLRM/31 Order code: PRB/12 Order code: PRB/20 USA and International ONLY Mathematical Olympiads 2005 ONLY Zuming Feng, Melanie Matchett Mathematical Connections Wood, and Cecil Rousseau Keeping It R.E.A.L. A Companion for Teachers and Others Research Experiences for All Learners Problem Books, Volume 17 Al Cuoco 2006; 80 pp.; softcover; Carla D. Martin and Classroom Resource Materials, Volume 27 ISBN: 978-0-88385-823-3; List US$34; Anthony Tongen 2005; 239 pp.; ISBN: 978-1-61444-123-6; Institutional member US$27.20; Classroom Resource Materials, Volume 38 List US$30; Institutional member US$24; Individual AMS & MAA members US$25.50; 2011; 129 pp.; ISBN: 978-0-88385-961-2; Individual AMS & MAA members US$22.50; Order code: PRB/17 List US$34; Institutional member US$27.20; Order code: CLRM/27.E Individual AMS & MAA members US$25.50; Uncommon Mathematical Order code: CLRM/38.E Excursions Polynomia and Related Realms Dan Kalman Dolciani Mathematical Expositions, Volume 35 2009; 265 pp.; hardcover; ISBN: 978-0-88385-341-2; List US$62; Institutional member US$49.60; Individual AMS & MAA members US$46.50; Order code: DOL/35

MATHEMATICAL PHYSICS

| ONLY From Pythagoras to Einstein Kurt O. Friedrichs Anneli Lax New Mathematical Library, Volume 16 1965; 88 pp.; ISBN: 978-0-88385-931-5; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: NML/16.E

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ONLY ONLY Conjecture and Proof Continued Fractions Miklós Laczkovich The Arithmetic Theory of Classroom Resource Materials, Volume 15 C. D. Olds Quadratic Forms 2001; 118 pp.; softcover; Burton W. Jones Anneli Lax New Mathematical Library, ISBN: 978-0-88385-722-9; List US$37; Volume 9 Institutional member US$29.60; Carus Mathematical Monographs, 1963; 162 pp.; ISBN: 978-0-88385-926-1; Individual AMS & MAA members US$27.75; Volume 10 List US$25; Institutional member US$20; Order code: CLRM/15 1950; 212 pp.; ISBN: 978-1-61444-010-9; Individual AMS & MAA members US$18.75; List US$46; Institutional member US$36.80; Order code: NML/9.E Individual AMS & MAA members US$34.50; Order code: CAR/10.E ONLY Ergodic Theory of Numbers ONLY Dedekind Sums Karma Dajani and Cor Kraaikamp Carus Mathematical Monographs, An Introduction to Inequalities Hans Rademacher Volume 29 and Emil Grosswald Edwin Beckenback 2002; 190 pp.; hardcover; and Richard Bellman Carus Mathematical Monographs, ISBN: 978-0-88385-034-3; List US$25; Volume 16 Institutional member US$20; Anneli Lax New Mathematical Library, 1972; 102 pp.; ISBN: 978-1-61444-016-1; Individual AMS & MAA members US$18.75; Volume 3 List US$44; Institutional member US$35.20; Order code: CAR/29 1961; 133 pp.; ISBN: 978-0-88385-921-6; Individual AMS & MAA members US$33; List US$25; Institutional member US$20; Order code: CAR/16.E Individual AMS & MAA members US$18.75; Order code: NML/3.E ONLY ONLY Numbers: Rational ONLY and Irrational Irrational Numbers Ivan Niven The Lore of Large Numbers Ivan Niven Anneli Lax New Mathematical Library, Philip J. Davis Carus Mathematical Monographs, Volume 1 Anneli Lax New Mathematical Library, Volume 11 2002; 140 pp.; ISBN: 978-0-88385-919-3; Volume 6 1985; 164 pp.; ISBN: 978-1-61444-011-6; List US$50; List US$28; Institutional member US$22.40; Individual AMS & MAA members US$21; 1961; 165 pp.; ISBN: 978-0-88385-987-2; Institutional member US$40; Order code: NML/1.E List US$25; Institutional member US$20; Individual AMS & MAA members US$37.50; Individual AMS & MAA members US$18.75; Order code: CAR/11.E Order code: NML/6.E Power Play Edward J. Barbeau A Guide to Elementary Spectrum, Volume 92 Number Theory Uses of Infinity 1997; 185 pp.; softcover; ISBN: 978-0-88385-523-2; List US$30; Underwood Dudley Leo Zippin Institutional member US$24; Dolciani Mathematical Expositions, Anneli Lax New Mathematical Library, Individual AMS & MAA members US$22.50; Volume 41 Volume 7 Order code: SPEC/92 2009; 141 pp.; hardcover; 1962; 151 pp.; softcover; ISBN: 978-0-88385-347-4; List US$51; ISBN: 978-0-88385-607-9; List US$40; Institutional member US$40.80; Institutional member US$32; ONLY Individual AMS & MAA members US$38.25; Individual AMS & MAA members US$30; Order code: DOL/41 Order code: NML/7 The Geometry of Numbers C. D. Olds, Anneli Lax, and Giuliana Davidoff Anneli Lax New Mathematical Library, Volume 41 2000; 176 pp.; ISBN: 978-0-88385-955-1; List US$30; Institutional member US$24; Individual AMS & MAA members US$22.50; Order code: NML/41.E

PROBABILITY & STATISTICS Studies in Probability Theory Volume 18 of Studies on Mathematics Murray Rosenblatt, Editor AMS/MAA Studies in Mathematics, Volume 18 1978; 268 pp.; hardcover; ISBN: 978-0-88385-118-0; List US$30; Institutional member US$24; Individual AMS & MAA members US$22.50; Order code: MSTM/18 401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 42 INDEX

BY TITLE & AUTHOR

101 Careers in Mathematics 19 Barnes, Julie ...... 21 Brown, Ezra ...... 29 777 Mathematical Bashmakova, Isabella Burk, Frank E...... 32 Conversation Starters . . . 37 Grigoryevna ...... 36 Byer, Owen ...... 23 99 Points of Intersection . . . 38 Batterson, Steve ...... 21 Calculus ...... 34 Aaboe, Asger ...... 22 Beautiful Mathematics . . . . 16 Calculus and Its Origins . . . 11 Ackerman, Ralph A...... 12 Beckenback, Edwin . . . . . 42 The Calculus Collection . . . 11 AHA! Solutions ...... 41 Bekken, Otto ...... 36 Calculus Deconstructed . . . 10 Albers, Donald J...... 20 Bellman, Richard ...... 42 Calculus for the Albert, Jim...... 10 Benjamin, Arthur T. . . 13, 29 Life Sciences ...... 12 Alexanderson, Gerald L. Berlinghoff, William P. . . 20 Calculus Gems ...... 15 . . . . 17, 20, 25, 36, 37, 38 Berzsenyi, George ...... 40 Calculus Mysteries Algebra and Tiling ...... 36 Beyond the and Thrillers ...... 34 All the Math That’s Fit Quadratic Formula ...... 3 Calculus of Variations . . . . . 34 to Print ...... 36 Bhatia, Rejendra ...... 32 Cameos for Calculus ...... 12 Alsina, Claudi Biscuits of Number Theory . 29 Campbell, Duff ...... 30 ...... 24, 38, 39, 41 Bliss, Gilbert Ames ...... 34 Carter, Nathan ...... 9, 31 American Mathematics 1890–1913 ...... 21 Boardman, Michael E. . . . 12 Casazza, Peter ...... 20 Analytic Functions of Boas, Harold P...... 32 Celestial Mechanics ...... 33 a Complex Variable . . . . . 32 Boas, Ralph P...... 5, 32, 36 A Century of Advancing Andersen, Janet ...... 41 Bogolyubov, N. N...... 38 Mathematics ...... 20 Anderson, Marlow . . . 37, 38 Bolker, Ethan D...... 9 Chang, Gengzhe ...... 33 Andreescu, Titu . . . 37, 40, 41 Bonar, Daniel D...... 32 Charming Proofs ...... 38 Annin, Scott A...... 29 Borwein, Peter ...... 19 Chartier, Tim ...... 4 Anselone, Philip M...... 9 Bowden, L...... 35 Chen, Evan ...... 29 Apostol, Tom M...... 23 Brabenec, Robert L...... 32 Chen, Hongwei ...... 5 Archimedes ...... 37 Bradley, Robert F...... 38 Chin, W. G...... 39 The Arithmetic Theory Braver, Seth ...... 38 Cohen, Marcus ...... 34 of Quadratic Forms . . . . . 42 Bremigan, Elizabeth George College Calculus ...... 12 Arithmetical Wonderland . . 28 ...... 27 Coloring Book of Complex Arney, David C...... 36 Bremigan, Ralph J...... 27 Function Representations . 21 Artino, Ralph A...... 40 Bressoud, David ...... 7 Combinatorial Mathematics 34 Baggett, Larry W...... 17 Bridge to Abstract Combinatorics Mathematics ...... 18 by Daniel A. Marcus . . . 13 Barbeau, Edward J. Brilleslyper, Michael A. . . 33 Combinatorics by David R. Mazur . . . . 14 ...... 28, 40, 42 Broer, Henk W...... 24

ORDER ONLINE bookstore.ams.org 43 Common Sense Mathematics ...... 9 Episodes from the Geometric Transformations II ...... 39 Complex Analysis: The Geometric Early History of Mathematics . . . . .22 Geometric Transformations III ...... 39 Viewpoint ...... 32 Episodes in Nineteenth and Twentieth Geometric Transformations IV ...... 39 Century Euclidean Geometry ...... 36 Complex Numbers and Geometry . . . .22 Geometry from Africa ...... 39 An Episodic History of Mathematics . .16 Conjecture and Proof ...... 42 Geometry Illuminated ...... 24 Ergodic Theory of Numbers ...... 42 The Contest Problem Book I ...... 35 The Geometry of Numbers ...... 42 Erickson, Martin ...... 16, 41 The Contest Problem Book II ...... 40 Geometry Revisited ...... 22 Essentials of Mathematics ...... 36 The Contest Problem Book III ...... 35 Gerdes, Paulus ...... 39 The Contest Problem Book IV ...... 40 Euclidean Geometry in Mathematical Olympiads ...... 29 Gilbert, George T...... 27 Contest Problem Book V ...... 40 Euler and Modern Science ...... 38 Gillman, Leonard ...... 35 The Contest Problem Book VI ...... 14 Euler At 300 ...... 38 Gillman, Rick ...... 37 The Contest Problem Book VII ...... 25 Euler ...... 14 Ginsburg, Jekuthiel ...... 35 The Contest Problem Book VIII . . . . .27 Eves, Howard ...... 35, 37 Givant, Steven ...... 40 The Contest Problem Book IX ...... 26 Excursions in Classical Analysis ...... 5 Gleason, A. M...... 25 Continued Fractions ...... 42 Exercises in (Mathematical) Style . . . . 7 Gockenbach, Mark S...... 6 Conway, John Horton ...... 31 Expeditions in Mathematics ...... 17 Gold, Bonnie ...... 38 Cornette, James L...... 12 Explorations in Complex Analysis . . . .33 Gordon, Florence S...... 2 Counterexamples in Calculus ...... 11 Exploratory Examples Gordon, Sheldon P...... 2 A Course in Mathematical Modeling . . 5 for Real Analysis ...... 32 Gouvêa, Fernando Q...... 3, 20 Coxeter, H. S. M...... 22, 39 Exploring Advanced Euclidean Grabiner, Judith V...... 16 Crannell, Annalisa ...... 37 Geometry with GeoGebra ...... 23 Graph Theory ...... 14 Creative Mathematics ...... 41 Faires, J. Douglas ...... 26, 27 Graphs and Their Uses ...... 34 Cryptological Mathematics ...... 7 Faris, Frank A...... 20 Great Moments in Mathematics Cuoco, Al ...... 4, 41 Fauvel, John ...... 36 Before 1650 ...... 35 Curtiss, David Raymond ...... 32 Federer Vaaler, Leslie Jane ...... 8 Great Moments in Mathematics D’Angelo, John P...... 32 Feng, Zuming ...... 37, 40, 41 After 1650 ...... 35 D’Antonio, Lawrence A...... 38 Field Theory and Greenwood, R. E...... 25 Dajani, Karma ...... 42 Its Classical Problems ...... 2 Greitzer, S. L...... 22 Daniel, James W...... 8 First Concepts of Topology ...... 39 Greitzer, Samuel ...... 40 Davidoff, Giuliana ...... 42 First Steps for Math Olympians . . . . .26 Groetsch, Charles W...... 40 Davis, Philip J...... 32, 42 Five Hundred Grossman, Israel ...... 31 Mathematical Challenges ...... 40 Dedekind Sums ...... 42 Grosswald, Emil ...... 42 Folland, Gerald B...... 33 dePillis, John ...... 4, 37 Groups and Their Graphs ...... 31 Fourier Series and Guichelaar, Jan ...... 20 Devlin, Keith ...... 36 Orthogonal Polynomials ...... 32 A Guide to Advanced Linear Algebra . . 3 Diamond, Harold G...... 31 Fourier Series ...... 32 A Guide to Advanced Real Analysis . .33 Diefenderfer, Caren L...... 11 Friedrichs, Kurt O...... 41 A Guide To Complex Variables ...... 32 Differential Geometry A Friendly Mathematics Competition .37 and Its Applications ...... 39 A Guide to Elementary From Erdo˝s to Kiev ...... 36 Diophantus and Number Theory ...... 42 Diophantine Equations ...... 36 From Error-Correcting Codes Through A Guide to Functional Analysis ...... 5 Sphere Packings to Simple Groups . .34 Discovering Discrete A Guide to Groups, Rings, and Fields . . 3 From Pythagoras to Einstein ...... 41 Dynamical Systems ...... 10 A Guide to Plane Algebraic Curves . . . .3 Functions, Data, and Models ...... 2 Distilling Ideas ...... 19 A Guide to Real Variables ...... 33 Gaglione, Anthony M...... 40 Dorff, Michael J...... 33 A Guide to Topology ...... 39 Gallian, Joseph A...... 15 Doyle, Peter G...... 33 Hadlock, Charles R. . . . . 2, 18, 32, 33 Game Theory and Strategy ...... 7 Dudley, Underwood . . 35, 36, 38, 42 Hahn, Liang-shin ...... 22 Game Theory through Examples ...... 9 Dumbaugh, Della ...... 20 Hale, Margie ...... 36 A Garden of Integrals ...... 32 Dunham, William ...... 14 Half a Century of The Early Mathematics Gardner, Martin ...... 35, 37 Pythagoras Magazine ...... 20 of Leonhard Euler ...... 38 Gaughan, Edward D...... 34 Halmos, Paul ...... 31, 40 Earl, James M...... 35 The Generalized Riemann Integral . . .32 The Harmony of the World ...... 38 The Edge of the Universe ...... 38 A Gentle Introduction to the American Harvey, Matthew ...... 24 Invitational Mathematics Exam . . .29 Elementary Cryptanalysis ...... 8 Haunsperger, Deanna ...... 20, 38 Geometric Inequalities ...... 39 Elementary Mathematical Models. . . . . 2 Hayes, David F...... 17 Geometric Transformations I ...... 39 401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 44 The Heart of Calculus ...... 9 Keeping It R.E.A.L...... 41 Magic Tricks, Card Shuffling and Henle, Michael ...... 18, 30 Kelly, L. M...... 25 Dynamic Computer Memories. . . . .36 Herstein, I. N...... 31 Kendig, Keith ...... 3, 26 Magnus, Wilhelm ...... 31 Hilbert, Stephen ...... 34 Kennedy, Stephen ...... 20, 38 Marcus, Daniel A...... 13, 14 A Historian Looks Back ...... 16 Khoury, Michael J...... 32 Marshall, David C...... 26 A History of Mathematics Kiltinen, John O...... 37 Martin Gardner in the Twenty-First Century ...... 18 in America Before 1900 ...... 35 Kirtland, Joseph ...... 33 Martin, Carla D...... 41 The Hitchhiker’s Guide to Calculus . .34 Klamkin, Murray S...... 35, 40 Mast, Maura B...... 9 Honsberger, Ross ...... 35, 36, 37 Klee, Victor ...... 39 Math Made Visual ...... 38 Hopkins, Brian ...... 18 Klosinski, Leonard F...... 25 Math through the Ages ...... 20 How Euler Did Even More ...... 19 Klymchuk, Sergiy ...... 11 Mathematical Apocrypha Redux . . . . .38 Hungarian Problem Book III ...... 40 Knoebel, Arthur ...... 34 Mathematical Circles ...... 37 Hungarian Problem Book IV ...... 27 Knot Theory ...... 39 Mathematical Connections ...... 41 I, Mathematician ...... 20 Konhauser, D. E...... 36 Mathematical Cranks ...... 35 Icons of Mathematics ...... 39 Kraaikamp, Cor ...... 42 Mathematical Delights ...... 37 Identification Numbers and Krantz, Steven G. Check Digit Schemes ...... 33 ...... 5, 16, 17, 20, 32, 33, 38, 39 Mathematical Diamonds ...... 37 Illustrated Special Relativity Kreahling, William ...... 21 Mathematical Fallacies, through Its Paradoxes ...... 4 Flaws, and Flimflam ...... 40 Krusemeyer, Mark I...... 27 In the Dark On the Sunny Side . . . . .17 Mathematical Interest Theory ...... 8 Kuczma, Marcin E...... 40 Inequalities from Complex Analysis . .32 Mathematical Methods in Science . . .33 Kurtz, Douglas S...... 34 Ingenuity in Mathematics ...... 35 Mathematical Miniatures ...... 40 Laczkovich, Miklós ...... 42 Interdisciplinary Lively Mathematical Modeling Application Projects ...... 36 LaRose, Gavin ...... 37 in the Environment ...... 32 International Math Olympiads, Larson, Loren C...... 25, 27 Mathematical Olympiads 2000–2001 41 1959–1977 ...... 40 Lawrence, Bonita A...... 18 A Mathematical Orchard ...... 27 International Math Olympiads, Lax, Anneli ...... 42 Mathematical Puzzle Tales ...... 37 1986–1999 ...... 40 Lazebnik, Felix ...... 23 Mathematical Reminiscences ...... 37 International Mathematical Olympiads Learn from the Masters ...... 36 1978–1985 ...... 35 A Mathematical Space Odyssey . . . . .24 Learning Modern Algebra ...... 4 An Introduction to Inequalities...... 42 Mathematical Statistics ...... 33 The Lebesgue Integral Mathematical Treks ...... 37 Introduction to the Mathematics for Undergraduates ...... 6 of Computer Graphics ...... 9 A Mathematician Comes of Age . . . . .17 Lee, George ...... 41 Inverse Problems ...... 40 Mathematicians on Creativity ...... 19 Lee, John W...... 9 Invitation to Complex Analysis ...... 5 Mathematics and Sports ...... 15 Leigh, Robert Barrington ...... 27 Invitation to Number Theory ...... 30 Mathematics for Secondary Lewand, Robert Edward ...... 7 An Invitation to Real Analysis ...... 6 School Teachers ...... 27 Lie Groups ...... 2 Irrational Numbers ...... 42 Mathematics Galore! ...... 17 Liljedahl, Peter ...... 19 Irving, Ron ...... 3 Mathematics in Historical Context . . .15 Linear Algebra Problem Book ...... 31 Is Mathematics Inevitable? ...... 38 Mathematics of Choice ...... 35 Linear Inverse Problems Ivanov, O. A...... 21 The Mathematics of and Tikhonov Regularization ...... 6 Games and Gambling ...... 8 Jackson, Dunham ...... 32 Lion Hunting & Other Maurer, Stephen B...... 40 James, Ioan ...... 37 Mathematical Pursuits ...... 36 Maxima and Minima Jaspers, Arnout ...... 20 Liu, Andy ...... 27, 28, 29, 40 Without Calculus ...... 35 Johansson, Bengt ...... 36 Livingston, Charles ...... 39 Mazur, David R...... 14 Johnson, Aimee ...... 10 Lobachevski Illuminated ...... 38 McCleary, John ...... 7 Johnston, William ...... 6 Logic as Algebra ...... 40 McCoy, Neal H...... 31 Jones, Burton W...... 42 Lolt, Po-Shen ...... 37 McDougall, Jane M...... 33 Kac, Mark ...... 33 Lorch, John D...... 27 McLeod, Robert M...... 32 Kalman, Dan ...... 2, 41 The Lore of Large Numbers ...... 42 Messer, Robert ...... 22 Kasman, Alex ...... 38 MacDuffee, Cyrus Colton ...... 31 Methods for Euclidean Geometry . . . .23 Katz, Brian P...... 19 Maceli, John ...... 34 Mikhaı˘lov, G. K...... 38 Katz, Victor ...... 36, 37, 38 Madden, Kathleen ...... 10 Mnatsakanian, Mamikon A...... 23 Kazarinoff, Nicholas D...... 39 The Magic Numbers of the Professor .38 Mooney, Douglas D...... 5 Kedlaya, Kiran S...... 25 More Fallacies, Flaws, and Flimflam .28

ORDER ONLINE bookstore.ams.org 45 More Mathematical Morsels ...... 35 Projective Geometry ...... 39 The Sensual (quadratic) Form ...... 31 Moreno, Luis F...... 6 Proof and Other Dilemmas ...... 38 She Does Math! ...... 33 Morris, S. Brent...... 36 Proofs that Really Count ...... 13 Shell, Niel ...... 40 Moser, William O. J...... 40 Proofs Without Words III ...... 23 Sherlock Holmes in Babylon and Other Mouzakitis, Aristides ...... 18 Quinn, Jennifer J...... 13 Tales of Mathematical History . . . . .37 Mugler, Dale H...... 36 R. L. Moore ...... 38 Shubin, Tatiana ...... 17 Musielak, Dora ...... 18 Rademacher, Hans ...... 42 Sibley, Thomas Q...... 24 Near the Horizon ...... 24 A Radical Approach to Real Analysis . . 7 Simmons, George F...... 15 Nelsen, Roger B. Random Walks and Simonson, Shai ...... 16 ...... 11, 12, 23, 24, 38, 39, 41 Electric Networks ...... 33 Simons, Roger A...... 38 New Horizons in Geometry ...... 23 The Random Walks of George Pólya . .37 Simoson, Andrew J...... 15 Nillsen, Rodney ...... 33 Randomness and Recurrence Sink or Float? ...... 26 Nitecki, Zbigniew H...... 10 in Dynamical Systems ...... 33 Sinkov, Abraham ...... 8 Niven, Ivan ...... 35, 42 Ratliff, Thomas ...... 37 Six Sources of Collapse ...... 18 Non-Euclidean Geometry ...... 39 Rault, Patrick X...... 21 Smeltzer, Deirdre L...... 23 Noncommutative Rings ...... 31 Real Infinite Series ...... 32 Smith, D. E...... 35 Noonburg, Virginia W...... 13 Reality Conditions ...... 38 Snell, J. Laurie ...... 33 Number Theory Through Inquiry . . . .26 Rediscovering Mathematics ...... 16 Snow, Joanne E...... 32 Numbers: Rational and Irrational. . . .42 Reid, Constance ...... 35 Solve This ...... 37 Numerology or Reiter, Harold B...... 25 Sophie’s Diary ...... 18 What Pythagoras Wrought ...... 36 Remarkable Mathematics ...... 37 Soviet Union O’Shea, Owen ...... 38 Resources For The Study Mathematical Olympiad ...... 29 Oberste-Vorth, Ralph W...... 18 of Real Analysis ...... 32 Spivak, Michael ...... 34 Odell, Edward ...... 26 Riddles of the Sphinx ...... 35 Stankewitz, Richard L...... 33 Old and New Unsolved The Riemann Hypothesis ...... 30 Staples, Susan ...... 11 Problems in Plane Geometry Rietz, Henry L...... 33 Starbird, Michael ...... 19, 26 and Number Theory ...... 39 Rings and Ideals...... 31 Statistical Independence in Probability, Olds, C. D...... 42 The Role of Mathematics in Science . .35 Analysis, and Number Theory . . . . .33 An Open Door to Number Theory . . .30 Rolf, James S...... 33 Steenrod, N. E...... 39 Oprea, John ...... 39 Rosenblatt, Murray ...... 42 Stein, Sherman K...... 36 Ordinary Differential Equations Rosentrater, C. Ray ...... 6 Stein, Sherman ...... 37 by Virginia W. Noonburg ...... 13 Ross, Peter ...... 38 Stephenson, Kenneth ...... 33 Ordinary Differential Equations by David A. Sánchez ...... 34 Rotman, Joseph J...... 4 Sterrett, Andrew ...... 19 Ore, Oystein ...... 30, 34 Rousseau, Cecil ...... 41 Straffin, Philip ...... 7, 22 Oval Track and Ruden, Randi D...... 20 Student Research Projects Other Permutation Puzzles ...... 37 Rykken, Elyn ...... 37 in Calculus ...... 34 Over and Over Again ...... 33 Ryser, Herbert John ...... 34 Student Solution Manual for Mathematical Interest Theory ...... 8 Packel, Edward ...... 8 S¸ahin, Ays¸e ...... 10 Studies in Probability Theory ...... 42 A Panorama of Harmonic Analysis . . .32 Salkind, Charles T...... 35, 40 Stueben, Michael ...... 36 Paradoxes and Sophisms in Calculus . 11 Sánchez, David A...... 34 Supplementary Material Parker, John ...... 38 Sandifer, C. Edward ...... 19, 38 and Solutions Manual for Parker, Marla ...... 33 Savchev, Svetoslav ...... 40 Mathematical Modeling Pengelley, David ...... 34 Sawyer, W. W...... 34 in the Environment ...... 33 Perkins, David ...... 11, 12 Schaubroeck, Beth ...... 21 Suzuki, Jeff ...... 15 Peterson, Ivars ...... 37 Schaubroeck, Lisbeth E...... 33 Swanson, Todd ...... 41 Swetz, Frank ...... 36 Φ , Π , e , and i ...... 12 Schiffer, M. M...... 35 Pollard, Harry ...... 31, 33 Schneider, Leo J...... 14 Swift, Randall J...... 5 Pollatsek, Harriet ...... 2 Schwartzman, Steven ...... 36 Szabó, Sándor ...... 36 Pólya, George ...... 33 Schwartz, Diane D...... 34 Tanton, James ...... 17, 28, 37 Poonen, Bjorn ...... 25 The Schwarz Function Taylor, Ron ...... 21 Portal through Mathematics ...... 21 and Its Applications ...... 32 Teaching Statistics Using Baseball . . . 10 Power Play ...... 42 The Search for E.T. Bell ...... 35 A TeXas Style Introduction to Proof . . 21 A Primer of Real Functions ...... 32 Sederberg, Thomas W...... 33 Textbooks, Testing, Training ...... 28 Prisner, Erich ...... 9 Seltzer, Stan ...... 34 The Theory of Algebraic Numbers . . . . 31

401-455-4000 (Worldwide) ORDER BY PHONE 800-321-4267 (US and Canada) 46 Thinking Geometrically ...... 24 Uses of Infinity ...... 42 Who Gave You the Epsilon? ...... 38 Thompson, Thomas M...... 34 Vakil, Ravi ...... 25 The William Lowell Putnam Tongen, Anthony ...... 41 van de Craats, Jan ...... 30 Mathematical Competition 1985–2000 ...... 25 Topology Now! ...... 22 van den Brandhof, Alex ...... 20 The William Lowell Putnam A Tour Through van der Veen, Roland ...... 30 Mathematical Competition ...... 25 Mathematical Logic ...... 40 Varieties of Integration ...... 6 Willoughby, Stephen S...... 28 Trigonometry ...... 28 Vectors and Matrices...... 31 Wilson, Robin ...... 37, 38 The Trisectors ...... 36 Velleman, Dan ...... 36 Wolf, Robert S...... 40 Twenty Years Before the Blackboard . .36 Venema, Gerard A...... 23 Woods, R. Grant ...... 34 Uncommon Mathematical Excursions . 41 Visual Group Theory ...... 31 Wood, Melanie Matchett ...... 41 Understanding Our Voltaire’s Riddle ...... 15 Quantitative World ...... 41 The Words of Mathematics ...... 36 Wagon, Stan ...... 36, 39 USA and International Mathematical Writing Mathematics Well ...... 35 Olympiads 2001 ...... 40 Wall, H. S...... 41 Writing Projects for USA and International Mathematical Walser, Hans ...... 38 Mathematics Courses ...... 37 Olympiads 2002 ...... 41 Weintraub, Steven H...... 3 Wudka, Jose ...... 4 USA and International Mathematical Weller, Kirk E...... 32 Yaglom, I. G...... 39 Olympiads 2003 ...... 37 Wells, David ...... 26, 27 Young, John Wesley ...... 39 USA and International Mathematics What Is Calculus About? ...... 34 Yushevich, A. P...... 38 Olympiads 2004 ...... 37 When Less is More ...... 41 Zhai, Helen ...... 19 USA and International Mathematical Olympiads 2005 ...... 41 When Life is Linear ...... 4 Zippin, Leo ...... 42 USA Mathematical Which Numbers Are Real? ...... 30 Zorn, Paul ...... 20 Olympiads 1972-1986 ...... 35 Which Way Did the Bicycle Go? . . . .36

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49 SHIPPING INFORMATION* UPS Standard Ground (7–10 business days)—US$4.75 for the rst item and US$1.25 for each additional item UPS 2nd Day Air (2–3 business days)—US$11.30 for the rst item and US$3.30 for each additional item UPS Next Day Air (1–2 business days)—US$16.50 for the rst item and US$4.35 for each additional item International Standard Service (4–6 weeks**)—US$9.75 for the rst item and US$8.25 for each additional item ______NOTE: The delivery times are quoted for actual shipping only. Order processing can take up to 48 hours depending on the day of the week and the time an order is placed. * AMS individual members receive free standard shipping on all purchases. ** Delivery time depends on your country’s available methods and customs requirements. For expedited shipping costs outside of the United States, please contact the Sales & Member Services Department by email: [email protected], or by phone: 401-455-4000. Rates subject to change without notice. PRICING AND PAYMENT • All pricing in US dollars—please remit in US currency. • Prices and publication dates are correct as of October 2017. • Prices, special offers, and publication dates are subject to change without notice. • We accept orders by check, credit card, or bank transfer. BANK TRANSFERS Citizens Bank 1 Citizens Drive Riverside, RI 02915-3000 USA Bank ABA, Swift code, and account numbers or other inquiries and noti cations about wire transfers should be directed to the Sales & Member Services Department at [email protected]. Automated Clearing House (ACH) inquiries, authorization requests, and noti cations should be sent to [email protected]. Transfers should contain name of payer (no titles please) and reason for payment (pro forma number, membership dues, etc.). Fax copy of transfer and order to 1-401-455-4046, Attn: Sales & Member Services Department; or send details of payment by email to [email protected]; or mail to Sales & Member Services Department, AMS, 201 Charles Street, Providence, RI 02904-2213 USA. STANDING ORDERS Standing orders are accepted for most book series offered by the Society. Pro forma invoices are sent to standing order customers prior to the publication of each new volume. Shipment is made upon receipt of payment. A new standing order at list or institutional member price entitles the purchaser to acquire back volumes at a discount. This discount will apply to a one-time purchase of ten or more back volumes in the book series if the order is placed within six months from the date of the new standing order. Contact the Sales & Member Services Department to begin a new standing order. ORDERS FROM OUTSIDE THE UNITED STATES Individual orders worldwide are accepted online at bookstore.ams.org or through the following exclusive agents: • Africa, Europe, Middle East, South Africa, Australia, New Zealand, Oceania: Eurospan Group • Japan: Maruzen Co. Ltd. (Tokyo), Neutrino Inc. (Tokyo) • India: Hindustan Book Agency For book orders in China, South America, or other regions, please contact the Sales & Member Services Department at 1-401-455-4000 or send an email to [email protected].

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