ams maa · illustrated special relativity through its paradoxes a fusion of linear algebra,...

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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 32 Analysis 33 Applications 34 Calculus 34 Differential Equations 34 Discrete Mathematics & Combinatorics 35 General Interest 39 Geometry & Topology 40 Logic & Foundations 40 Math Education 41 Mathematical Physics 42 Number Theory 42 Probability & Statistics

43 Index

49 Ordering Information

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ALGEBRA & ALGEBRAIC GEOMETRY

| Field Theory and Its Classical ProblemsCharles Robert HadlockField 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, polyno-mials 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

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Elementary Mathematical ModelsOrder Aplenty and a Glimpse of ChaosDan KalmanThe 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 GroupsA Problem-Oriented Introduction via Matrix GroupsHarriet PollatsekThis textbook is a complete introduction to Lie groups for undergraduate students. The only prereq-uisites 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.


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 ModelsAn Applied Approach to College AlgebraSheldon P. Gordon and Florence S. GordonThis 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.


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

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A Guide to Advanced Linear AlgebraSteven H. WeintraubLinear 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 CurvesKeith KendigThis 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 intu-ition 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 invita-tion 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


A Guide to Groups, Rings, and FieldsFernando Q. GouvêaThis 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.



Beyond the Quadratic FormulaRon IrvingThe 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 solu-tions 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

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Illustrated Special Relativity through Its ParadoxesA Fusion of Linear Algebra, Graphics, and RealityJohn dePillis and Jose WudkaIllustrated 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

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Learning Modern AlgebraFrom Early Attempts to Prove Fermat’s Last TheoremAl Cuoco and Joseph J. RotmanLearning 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 them-selves, 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


When Life is LinearFrom Computer Graphics to BracketologyTim ChartierFrom 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 applica-tion, 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

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ANALYSIS

A Course in Mathematical ModelingDouglas 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 vari-ables, 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 AnalysisPathways to Advanced Problem Solving and Undergraduate ResearchHongwei ChenExcursions 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 under-graduate 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 AnalysisRalph P. BoasSecond Edition revised by Harold P. BoasIdeal 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 AnalysisSteven G. KrantzThis 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 sophisti-cated 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






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Varieties of IntegrationC. Ray RosentraterVarieties 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.



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The Lebesgue Integral for UndergraduatesWilliam JohnstonThis 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

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An Invitation to Real AnalysisLuis F. MorenoAn 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 RegularizationMark S. GockenbachInverse problems occur frequently in science and technology, when-ever 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 prob-lems 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






Exercises in (Mathematical) StyleStories of Binomial CoefficientsJohn McClearyWhat 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


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A Radical Approach to Real AnalysisSecond EditionDavid BressoudIn 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


APPLICATIONS

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Game Theory and StrategyPhilip D. StraffinThis book is an introduction to mathematical game theory, which might better be called the math-ematical 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 MathematicsRobert Edward LewandThis 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






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The Mathematics of Games and GamblingSecond EditionEdward PackelThis 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

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Elementary CryptanalysisA Mathematical Approach, Second EditionAbraham SinkovRevised 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

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Mathematical Interest TheorySecond EditionLeslie Jane Federer Vaaler and James W. DanielMathematical 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


Student Solution Manual for Mathematical Interest TheoryLeslie Jane Federer VaalerThis 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






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Game Theory through ExamplesErich PrisnerGame 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

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The Heart of CalculusExplorations and ApplicationsPhilip M. Anselone and John W. LeeThis book contains enrichment material for courses in first and second year calculus, differential equa-tions, 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

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Introduction to the Mathematics of Computer GraphicsNathan CarterThis 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.


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

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Common Sense MathematicsEthan D. Bolker and Maura B. MastCommon 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






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Discovering Discrete Dynamical SystemsAimee Johnson, Kathleen Madden, and Ayse SahinDiscovering Discrete Dynamical Systems is a math-ematics 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 explora-tion, 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

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Teaching Statistics Using BaseballSecond EditionJim AlbertTeaching 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

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Calculus DeconstructedA Second Course in First-Year CalculusZbigniew H. NiteckiCalculus 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






The Calculus CollectionA Resource for AP* and BeyondCaren L. Diefenderfer and Roger B. Nelsen, EditorsThe 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


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Counterexamples in CalculusSergiy KlymchukCounterexamples 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.



Calculus and Its OriginsDavid PerkinsCalculus and Its Origins is primarily a collection of results that show how calculus came to be, begin-ning 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 CalculusSergiy Klymchuk and Susan StaplesParadoxes 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






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Cameos for CalculusVisualization in the First-Year CourseRoger B. NelsenA 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


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College CalculusA One-Term Course for Students With Previous Calculus ExperienceMichael E. Boardman and Roger B. NelsenCollege 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


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Calculus for the Life SciencesA Modeling ApproachJames L. Cornette and Ralph A. AckermanFreshman 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.


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 PerkinsCertain 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 indi-vidual 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

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DIFFERENTIAL EQUATIONS

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Ordinary Differential EquationsFrom Calculus to Dynamical Systems

Virginia W. NoonburgThis 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


DISCRETE MATHEMATICS & COMBINATORICS

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CombinatoricsA Problem Oriented ApproachDaniel A. MarcusThe 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.



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Proofs that Really CountThe Art of Combinatorial ProofArthur T. Benjamin and Jennifer J. QuinnMathematics 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





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CombinatoricsA Guided TourDavid R. MazurCombinatorics 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


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Graph TheoryA Problem Oriented ApproachDaniel A. MarcusGraph 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.



GENERAL INTERESTEulerThe Master of Us AllWilliam DunhamLeonhard 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 infor-mation 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 VIAmerican High School Mathematics Examinations 1989-1994Leo J. SchneiderThe 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






Calculus GemsBrief Lives and Memorable MomentsGeorge F. SimmonsCalculus 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 intel-lectual 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 ContextJeff SuzukiWhat 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 RiddleMicromégas and the Measure of All ThingsAndrew J. SimosonDid 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 math-ematics. 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 SportsJoseph A. Gallian, EditorThis 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 math-ematics 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







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A Historian Looks BackThe Calculus as Algebra and Selected WritingsJudith V. GrabinerJudith 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 math-ematics. 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

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An Episodic History of MathematicsMathematical Culture Through Problem SolvingSteven G. KrantzAn 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 math-ematical 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.



Rediscovering MathematicsYou Do the MathShai SimonsonRediscovering 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 math-ematics 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.



Beautiful MathematicsMartin EricksonThis 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







Expeditions in MathematicsTatiana Shubin, Gerald L. Alexanderson, and David F. Hayes, EditorsThis 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 math-ematical 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


Mathematics Galore!The First Five Years of the St. Mark’s Institute of MathematicsJames TantonMathematics 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 SideA Memoir of an Out-of-Sight MathematicianLarry W. BaggettMisfortune 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 surpris-ingly 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


A Mathematician Comes of AgeSteven G. KrantzThis book is about the concept of mathematical maturity, which is central to a mathematics educa-tion. 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






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Sophie’s DiaryA Mathematical Novel: Second EditionDora MusielakHidden 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 histor-ical 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


Martin Gardner in the Twenty-First CenturyMichael Henle and Brian Hopkins, EditorsMartin 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 CollapseA Mathematician’s Perspective on How Things Can Fall Apart in the Blink of an EyeCharles R. HadlockBeginning 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 understand-able terms. Spectrum, Volume 76


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Bridge to Abstract MathematicsRalph W. Oberste-Vorth, Aristides Mouzakitis, and Bonita A. LawrenceA Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theo-rems 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


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Distilling IdeasAn Introduction to Mathematical Thinking (Graphs, Groups, Calculus)Brian P. Katz and Michael StarbirdMathematics is not a spectator sport; successful students of mathematics grapple with ideas for them-selves. 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.


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 MathematicsThird EditionAndrew Sterrett, EditorThis 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 math-ematical 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.


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 CreativityPeter Borwein, Peter Liljedahl, and Helen Zhai, EditorsThis 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 MoreC. Edward SandiferSandifer 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






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A Century of Advancing MathematicsStephen F. Kennedy, Donald J. Albers, Gerald L. Alexanderson, Della Dumbaugh, Frank A. Faris, Deanna B. Haunsperger, and Paul Zorn, EditorsThis 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 math-ematics 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 compel-ling proof of that claim.Spectrum, Volume 81


Half a Century of Pythagoras MagazineAlex van den Brandhof, Jan Guichelaar, and Arnout Jaspers, EditorsHalf 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


I, MathematicianPeter Casazza, Steven G. Krantz, and Randi D. Ruden, EditorsMathematicians have pondered the psychology of the members of our tribe probably since math-ematics 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


Math through the AgesA Gentle History for Teachers and Others Expanded Second EditionWilliam P. Berlinghoff and Fernando Q. GouvêaWhere 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






Coloring Book of Complex Function RepresentationsJulie Barnes, William Kreahling, and Beth SchaubroeckHave you ever seen a mathematical object that was so intriguing that anyone, regardless of math-ematical 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, unex-pected 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 MathematicsJourney to Advanced ThinkingO. A. IvanovTranslated by Robert G. BurnsPortal 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 geom-etry, 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


American Mathematics 1890–1913Catching Up to EuropeSteve BattersonAt 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


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A TeXas Style Introduction to ProofRon Taylor and Patrick X. RaultA 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 easy-going 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

bookstore.ams.org/mmbk-8




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Episodes from the Early History of MathematicsAsger AaboeAmong 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

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Geometry RevisitedH. S. M. Coxeter and S. L. GreitzerAmong 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


Complex Numbers and GeometryLiang-shin HahnThe 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 indepen-dently. 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


Topology Now!Robert Messer and Philip StraffinTopology 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



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Methods for Euclidean GeometryOwen Byer, Felix Lazebnik, and Deirdre L. SmeltzerEuclidean 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


Exploring Advanced Euclidean Geometry with GeoGebraGerard A. VenemaThis 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 under-standing of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.



New Horizons in GeometryTom M. Apostol and Mamikon A. MnatsakanianNew 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.


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 IIIFurther Exercises in Visual ThinkingRoger B. NelsenProofs without words (PWWs) are figures or diagrams that help the reader see why a particular math-ematical 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







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A Mathematical Space OdysseySolid Geometry in the 21st CenturyClaudi Alsina and Roger B. NelsenSolid 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

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Thinking GeometricallyA Survey of GeometriesThomas Q. SibleyThis 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 inde-pendent 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.



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Geometry IlluminatedAn Illustrated Introduction to Euclidean and Hyperbolic Plane GeometryMatthew HarveyGeometry 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.



Near the HorizonAn Invitation to Geometric OpticsHenk W. BroerNear 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







MATH EDUCATIONThe William Lowell Putnam Mathematical CompetitionProblems and Solutions 1938–1964A. M. Gleason, R. E. Greenwood, and L. M. Kelly, EditorsBack by popular demand, we are pleased to reissue this outstanding collec-tion 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 CompetitionProblems and Solutions 1965–1984Gerald L. Alexanderson, Leonard F. Klosinski, and Loren C. Larson, EditorsThe 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 solu-tions 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 1985–2000Problems, Solutions, and CommentaryKiran S. Kedlaya, Bjorn Poonen, and Ravi VakilThis 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, sepa-rate from the full solution and background information about the competition.

Problem Books, Volume 6


The Contest Problem Book VIIAmerican Mathematics Competitions, 1995–2000 ContestsHarold B. ReiterThis 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


bookstore.ams.org/prb-1




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First Steps for Math OlympiansUsing the American Mathematics CompetitionsJ. Douglas FairesA 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

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Number Theory Through InquiryDavid C. Marshall, Edward Odell, and Michael StarbirdNumber 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.



Sink or Float?Thought Problems in Math and PhysicsKeith KendigSink or Float: Thought Problems in Math and Physics is a collection of problems drawn from math-ematics 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 IXAmerican Mathematics Competitions (AMC 12) 2001–2007David Wells and J. Douglas FairesThis 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 supple-mented. 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







The Contest Problem Book VIIIAmerican Mathematics Competitions (AMC 10) 2000–2007J. Douglas Faires and David WellsFor more than 50 years, the Mathematical Association of America has been engaged in the construc-tion 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 collec-tion 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


Hungarian Problem Book IVRobert Barrington Leigh and Andy LiuThe 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


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Mathematics for Secondary School TeachersElizabeth George Bremigan, Ralph J. Bremigan, and John D. LorchMathematics 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


A Mathematical OrchardProblems and SolutionsMark I. Krusemeyer, George T. Gilbert, and Loren C. LarsonThis 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 enjoy-ment 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





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More Fallacies, Flaws, and FlimflamEdward J. BarbeauMistakes 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, text-books, the media, and even professional mathematicians. The errors presented here serve both to entertain, and to empha-

size 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


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Textbooks, Testing, TrainingHow We Discourage ThinkingStephen S. WilloughbyStephen 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

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Arithmetical WonderlandAndy LiuArithmetical Wonderland is intended as an unorthodox mathematics textbook for students in elemen-tary 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.



TrigonometryA Clever Study GuideJames TantonThis 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






A Gentle Introduction to the American Invitational Mathematics ExamScott A. AnninThis 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 OlympiadsEvan ChenThis 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

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Soviet Union Mathematical OlympiadGrades, 8, 9, and 10Andy C. F. Liu, EditorThe 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 THEORYBiscuits of Number TheoryArthur T. Benjamin and Ezra Brown, EditorsIn 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





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Which Numbers Are Real?Michael HenleEveryone knows the real numbers, those fundamental quantities that make possible all of math-ematics 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.



The Riemann HypothesisRoland van der Veen and Jan van de CraatsThe 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


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Invitation to Number TheorySecond EditionOystein OreRevised and updated by John J. Watkins and Robin WilsonNumber 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

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An Open Door to Number TheoryDuff CampbellUsing 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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BACKLIST

ONLY Vectors and MatricesCyrus Colton MacDuffeeCarus Mathematical Monographs, Volume 7

1943; 203 pp.; ISBN: 978-1-61444-007-9; List US$30 Institutional member US$24; Individual AMS & MAA members US$22.50; Order code: CAR/7.E

ONLY Rings and IdealsNeal H. McCoyCarus Mathematical Monographs, Volume 8

1948; 216 pp.; ISBN: 978-1-61444-008-6; List US$30; Institutional member US$24; Individual AMS & MAA members US$22.50; Order code: CAR/8.E

Groups and Their GraphsIsrael Grossman and Wilhelm MagnusAnneli Lax New Mathematical Library, Volume 14


The Theory of Algebraic NumbersSecond EditionHarry Pollard and Harold G. DiamondCarus Mathematical Monographs, Volume 9

1975; 162 pp.; hardcover; ISBN: 978-0-88385-018-3; List US$40; Institutional member US$32; Individual member US$30; Order code: CAR/9

ONLY Noncommutative RingsI. N. HersteinCarus Mathematical Monographs, Volume 15

1994; 202 pp.; ISBN: 978-1-61444-015-4; List US$46; Institutional member US$36.80; Individual member US$34.50; Order code: CAR/15.E

ONLY Linear Algebra Problem BookPaul R. HalmosDolciani Mathematical Expositions, Volume 16

1995; 333 pp.; ISBN: 978-1-61444-212-7; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: DOL/16.E

The Sensual (quadratic) FormJohn Horton ConwayCarus Mathematical Monographs, Volume 26

1997; 152 pp.; softcover; ISBN: 978-0-88385-040-4; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: CAR/26

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Visual Group TheoryNathan CarterClassroom Resource Materials, Volume 32


ALGEBRA & ALGEBRAIC GEOMETRY









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ANALYSISONLY Analytic Functions of a Complex VariableDavid Raymond CurtissCarus Mathematical Monographs, Volume 2


ONLY Fourier Series and Orthogonal PolynomialsDunham JacksonCarus Mathematical Monographs, Volume 6


The Schwarz Function and Its ApplicationsPhilip J. DavisCarus Mathematical Monographs, Volume 17

1974; 228 pp.; softcover; ISBN: 978-0-88385-046-6; List US$38; Institutional member US$30.40; Individual AMS & MAA members US$28.50; Order code: CAR/17

ONLY The Generalized Riemann IntegralRobert M. McLeodCarus Mathematical Monographs, Volume 20

1980; 275 pp.; ISBN: 978-1-61444-020-8; List US$54; Institutional member US$43.20; Individual AMS & MAA members US$40.50; Order code: CAR/20.E

ONLY A Primer of Real FunctionsFourth EditionRalph P. Boas and Harold P. BoasCarus Mathematical Monographs, Volume 13


Mathematical Modeling in the EnvironmentCharles R. HadlockAMS/MAA Textbooks, Volume 3


A Panorama of Harmonic AnalysisSteven G. KrantzCarus Mathematical Monographs, Volume 27


Inequalities from Complex AnalysisJohn P. D’AngeloCarus Mathematical Monographs, Volume 28

2002; 264 pp.; hardcover; ISBN: 978-0-88385-033-6; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: CAR/28

Exploratory Examples for Real AnalysisJoanne E. Snow and Kirk E. WellerClassroom Resource Materials, Volume 20

2003; 160 pp.; softcover; ISBN: 978-0-88385-734-2; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: CLRM/20

Complex Analysis: The Geometric ViewpointSecond EditionSteven G. KrantzCarus Mathematical Monographs, Volume 23

2004; 219 pp.; hardcover; ISBN: 978-0-88385-035-0; List US$56; Institutional member US$44.80; Individual AMS & MAA members US$42; Order code: CAR/23

Resources For The Study of Real AnalysisRobert L. BrabenecAMS/MAA Textbooks, Volume 4


| Fourier SeriesRejendra BhatiaAMS/MAA Textbooks, Volume 5


Real Infinite SeriesDaniel D. Bonar and Michael J. Khoury Jr.AMS/MAA Textbooks, Volume 8


ONLY A Garden of IntegralsFrank E. BurkDolciani Mathematical Expositions, Volume 31

2007; 281 pp.; ISBN: 978-1-61444-209-7; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: DOL/31.E

A Guide To Complex VariablesSteven G. KrantzDolciani Mathematical Expositions, Volume 32


















A Guide to Advanced Real AnalysisGerald B. FollandDolciani Mathematical Expositions, Volume 37


A Guide to Real VariablesSteven G. KrantzDolciani Mathematical Expositions, Volume 38


Randomness and Recurrence in Dynamical SystemsA Real Analysis ApproachRodney NillsenCarus Mathematical Monographs, Volume 31


Explorations in Complex AnalysisMichael A. Brilleslyper, Michael J. Dorff, Jane M. McDougall, James S. Rolf, Lisbeth E. Schaubroeck, Richard L. Stankewitz, and Kenneth StephensonClassroom Resource Materials, Volume 40


APPLICATIONS

ONLY Mathematical StatisticsHenry L. RietzCarus Mathematical Monographs, Volume 3


Statistical Independence in Probability, Analysis, and Number TheoryMark KacCarus Mathematical Monographs, Volume 12

1959; 94 pp.; softcover; ISBN: 978-0-88385-025-1; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: CAR/12

ONLY Celestial MechanicsHarry PollardCarus Mathematical Monographs, Volume 18


ONLY Mathematical Methods in ScienceGeorge PólyaAnneli Lax New Mathematical Library, Volume 26


ONLY Random Walks and Electric NetworksPeter G. Doyle and J. Laurie SnellCarus Mathematical Monographs, Volume 22


She Does Math!Real-Life Problems from Women on the JobMarla Parker, EditorClassroom Resource Materials, Volume 4


ONLY Over and Over AgainGengzhe Chang and Thomas W. SederbergAnneli Lax New Mathematical Library, Volume 39

1997; 309 pp.; ISBN: 978-0-88385-953-7; List US$28; Institutional member US$22.40; Individual AMS & MAA members US$21; Order code: NML/39.E

Supplementary Material and Solutions Manual for Mathematical Modeling in the EnvironmentCharles R. HadlockAMS/MAA Textbooks, Volume 37


Identification Numbers and Check Digit SchemesJoseph KirtlandClassroom Resource Materials, Volume 18















34


CALCULUS

ONLY Calculus of VariationsGilbert Ames BlissCarus Mathematical Monographs, Volume 1


ONLY What Is Calculus About?W. W. SawyerAnneli Lax New Mathematical Library, Volume 2


Student Research Projects in CalculusMarcus Cohen, Edward D. Gaughan, Arthur Knoebel, Douglas S. Kurtz, and David PengelleySpectrum, Volume 6


The Hitchhiker’s Guide to CalculusMichael SpivakClassroom Resource Materials, Volume 2


ONLY Calculus Mysteries and ThrillersR. Grant WoodsClassroom Resource Materials, Volume 9


|ONLY CalculusAn Active Approach with ProjectsStephen Hilbert, Diane D. Schwartz, Stan Seltzer, and John MaceliClassroom Resource Materials, Volume 36


DIFFERENTIAL EQUATIONSOrdinary Differential EquationsA Brief Eclectic TourDavid A. SánchezClassroom Resource Materials, Volume 19


DISCRETE MATHEMATICS & COMBINATORICS

ONLY Combinatorial MathematicsHerbert John RyserCarus Mathematical Monographs, Volume 14


From Error-Correcting Codes Through Sphere Packings to Simple GroupsThomas M. ThompsonCarus Mathematical Monographs, Volume 21

1983; 228 pp.; softcover; ISBN: 978-0-88385-037-4; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: CAR/21

ONLY Graphs and Their UsesOystein OreAnneli Lax New Mathematical Library, Volume 34













GENERAL INTEREST

ONLY A History of Mathematics in America Before 1900D. E. Smith and Jekuthiel GinsburgCarus Mathematical Monographs, Volume 5


The Contest Problem Book IAnnual High School Mathematics Examination 1950–1960Charles T. SalkindAnneli Lax New Mathematical Library, Volume 5


ONLY Mathematics of ChoiceHow to Count without CountingIvan NivenAnneli Lax New Mathematical Library, Volume 15


ONLY Ingenuity in MathematicsRoss HonsbergerAnneli Lax New Mathematical Library, Volume 23


The Contest Problem Book IIICharles T. Salkind and James M. EarlAnneli Lax New Mathematical Library, Volume 25


Maxima and Minima Without CalculusIvan NivenDolciani Mathematical Expositions, Volume 6

1981; 303 pp.; hardcover; ISBN: 978-0-88385-306-1; List US$50; Institutional member US$40; Individual AMS & MAA members US$37.50; Order code: DOL/6

ONLY Great Moments in Mathematics Before 1650Howard EvesDolciani Mathematical Expositions, Volume 5

1983; 270 pp.; ISBN: 978-1-61444-214-1; List US$30; Institutional member US$24; Individual AMS & MAA members US$22.50; Order code: DOL/5.E

Great Moments in MathematicsAfter 1650Howard EvesDolciani Mathematical Expositions, Volume 7

1983; 263 pp.; softcover; ISBN: 978-0-88385-311-5; List US$35; Institutional member US$28; Individual AMS & MAA members US$26.25; Order code: DOL/7

The Role of Mathematics in ScienceM. M. Schiffer and L. BowdenAnneli Lax New Mathematical Library, Volume 30


International Mathematical Olympiads 1978–1985and forty supplemental problemsMurray S. KlamkinAnneli Lax New Mathematical Library, Volume 31


Writing Mathematics WellA Manual for AuthorsLeonard Gillman1987; 49 pp.; softcover; ISBN: 978-0-88385-443-3; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: MMBK/7

Riddles of the SphinxAnd Other Mathematical Puzzle TalesMartin GardnerAnneli Lax New Mathematical Library, Volume 32


USA Mathematical Olympiads 1972-1986Murray S. KlamkinAnneli Lax New Mathematical Library, Volume 33


More Mathematical MorselsRoss HonsbergerDolciani Mathematical Expositions, Volume 10

1991; 322 pp.; softcover; ISBN: 978-0-88385-314-6; List US$28; Institutional member US$22.40; Individual member US$21; Order code: DOL/10

Mathematical CranksUnderwood DudleySpectrum, Volume 4


The Search for E.T. BellAlso Known as John TaineConstance ReidSpectrum, Volume 7












bookstore.ams.org/mmbk-7






36


ONLY Algebra and TilingHomorphisms in the Service of GeometrySherman K. Stein and Sándor SzabóCarus Mathematical Monographs, Volume 25


The TrisectorsUnderwood DudleySpectrum, Volume 16


ONLY The Words of MathematicsAn Etymological Dictionary of Mathematical Terms in EnglishSteven SchwartzmanSpectrum, Volume 17

1994; 261 pp.; ISBN: 978-1-61444-501-2; List US$28; Institutional member US$22.40; Individual AMS & MAA members US$21; Order code: SPEC/17.E

All the Math That’s Fit to PrintArticles from The Manchester GuardianKeith DevlinSpectrum, Volume 9


Learn from the MastersFrank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, EditorsClassroom Resource Materials, Volume 3

1995; 303 pp.; softcover; ISBN: 978-0-88385-703-8; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: CLRM/3

Lion Hunting & Other Mathematical PursuitsA Collection of Mathematics, Verse and StoriesRalph P. Boas Jr.Gerald L. Alexanderson and Dale H. Mugler, EditorsDolciani Mathematical Expositions, Volume 15


ONLY Episodes in Nineteenth and Twentieth Century Euclidean GeometryRoss HonsbergerAnneli Lax New Mathematical Library, Volume 37


|ONLY Essentials of MathematicsIntroduction to Theory, Proof, and the Professional CultureMargie HaleClassroom Resource Materials, Volume 21

1996; 180 pp.; ISBN: 978-0-88385-982-7; List US$56; Institutional member US$44.80; Individual member US$42; Order code: CLRM/21.E

From Erdos to KievProblems of Olympiad CaliberRoss HonsbergerDolciani Mathematical Expositions, Volume 17


ONLY Which Way Did the Bicycle Go?And Other Intriguing Mathematical MysteriesD. E. Konhauser, Dan Velleman, and Stan WagonDolciani 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

Interdisciplinary Lively Application ProjectsDavid C. Arney, EditorClassroom Resource Materials, Volume 6


Diophantus and Diophantine EquationsIsabella Grigoryevna BashmakovaDolciani Mathematical Expositions, Volume 20


Numerology or What Pythagoras WroughtUnderwood DudleySpectrum, Volume 19


Magic Tricks, Card Shuffling and Dynamic Computer MemoriesS. Brent MorrisSpectrum, Volume 22


Twenty Years Before the BlackboardThe Lessons and Humor of a Mathematics TeacherMichael Stuebenwith Diane SandfordSpectrum, Volume 24


















ArchimedesWhat Did He Do Besides Cry Eureka?Sherman SteinClassroom Resource Materials, Volume 11


ONLY Solve ThisMath Activities for Students and ClubsJames TantonClassroom Resource Materials, Volume 17


Mathematical Puzzle TalesMartin GardnerSpectrum, Volume 28


The Random Walks of George PólyaGerald L. AlexandersonSpectrum, Volume 29


Mathematical ReminiscencesHoward EvesSpectrum, Volume 30


777 Mathematical Conversation StartersJohn dePillisSpectrum, Volume 32


Remarkable MathematicsFrom Euler to von NeumannIoan JamesSpectrum, Volume 34


Mathematical TreksFrom Surreal Numbers to Magic CirclesIvars PetersonSpectrum, Volume 35


Oval Track and Other Permutation PuzzlesAnd Just Enough Group Theory to Solve ThemJohn O. KiltinenClassroom Resource Materials, Volume 23


Mathematical DiamondsRoss HonsbergerDolciani Mathematical Expositions, Volume 26


A Friendly Mathematics CompetitionThirty-Five Years of Teamwork in IndianaRick Gillman, EditorProblem Books, Volume 8


Mathematical CirclesMathematical Circles Adieu and Return to Mathematical Circles, Volume IIIHoward W. EvesSpectrum, Volume 36


Mathematical CirclesRevisited Mathematical and Circles Squared, Volume IIHoward W. EvesSpectrum, Volume 39


Writing Projects for Mathematics CoursesCrushed Clowns, Cars, and Coffee to GoAnnalisa Crannell, Gavin LaRose, Thomas Ratliff, and Elyn RykkenClassroom Resource Materials, Volume 25

2004; 118 pp.; ISBN: 978-1-61444-113-7; List US$30; Order code: CLRM/25.E

Mathematical DelightsRoss HonsbergerDolciani Mathematical Expositions, Volume 28

2004; 252 pp.; softcover; ISBN: 978-0-88385-334-4; List US$28; Institutional member US$22.40; Individual AMS & MAA members US$21; Order code: DOL/28

USA and International Mathematical Olympiads 2003Titu Andreescu and Zuming Feng, EditorsProblem Books, Volume 13


Sherlock Holmes in Babylon and Other Tales of Mathematical HistoryMarlow Anderson, Victor Katz, and Robin Wilson, EditorsSpectrum, Volume 43


USA and International Mathematics Olympiads 2004Titu Andreescu, Zuming Feng, and Po-Shen Lolt, EditorsProblem Books, Volume 14




















38


Mathematical Apocrypha ReduxMore Stories and Anecdotes of Mathematicians and the MathematicalSteven G. Krantz, EditorSpectrum, Volume 44


R. L. MooreMathematician and TeacherJohn ParkerSpectrum, Volume 45


Reality ConditionsShort Mathematical FictionAlex KasmanSpectrum, Volume 46


ONLY Math Made VisualCreating Images for Understanding MathematicsClaudi Alsina and Roger B. NelsenClassroom Resource Materials, Volume 28


The Edge of the UniverseCelebrating Ten Years of Math HorizonsDeanna Haunsperger and Stephen Kennedy, EditorsSpectrum, Volume 48


99 Points of IntersectionExamples, Pictures, ProofsHans WalserSpectrum, Volume 49


The Early Mathematics of Leonhard EulerC. Edward SandiferSpectrum, Volume 50


Euler and Modern ScienceN. N. Bogolyubov, G. K. Mikhaılov, and A. P. Yushevich, EditorsTranslated from Russian by Robert BurnsSpectrum, Volume 53


Euler At 300An AppreciationRobert F. Bradley, Lawrence A. D’Antonio, and C. Edward Sandifer, EditorsSpectrum, Volume 54


The Harmony of the World75 Years of Mathematics MagazineGerald L. Alexanderson and Peter Ross, EditorsSpectrum, Volume 56


The Magic Numbers of the ProfessorOwen O’Shea and Underwood DudleySpectrum, Volume 57


Is Mathematics Inevitable?A MiscellanyUnderwood Dudley, EditorSpectrum, Volume 58


Proof and Other DilemmasMathematics and PhilosophyBonnie Gold and Roger A. SimonsSpectrum, Volume 59


Who Gave You the Epsilon?and Other Tales of Mathematical HistoryMarlow Anderson, Victor Katz, and Robin Wilson, EditorsSpectrum, Volume 63


ONLY Charming ProofsA Journey into Elegant MathematicsClaudi Alsina and Roger B. NelsenDolciani Mathematical Expositions, Volume 42

2010; 295 pp.; ISBN: 978-1-61444-201-1; List US$38; Institutional member US$30.40; Individual AMS & MAA members US$28.50; Order code: DOL/42.E

ONLY Lobachevski IlluminatedSeth BraverSpectrum, Volume 69

2011; 227 pp.; ISBN: 978-0-88385-979-7; List US$38; Institutional member US$30.40; Individual AMS & MAA members US$28.50; Order code: SPEC/69.E


















GEOMETRY & TOPOLOGY

ONLY Projective GeometryJohn Wesley YoungCarus Mathematical Monographs, Volume 4


ONLY Geometric InequalitiesNicholas D. KazarinoffAnneli Lax New Mathematical Library, Volume 4


Geometric Transformations II. M. YaglomAnneli Lax New Mathematical Library, Volume 8


|ONLY First Concepts of TopologyThe Geometry of Mappings of Segments, Curves, Circles, and DisksW. G. Chin and N. E. SteenrodAnneli Lax New Mathematical Library, Volume 18


ONLY Geometric Transformations III. M. YaglomAnneli Lax New Mathematical Library, Volume 21


ONLY Geometric Transformations IIII. G. YaglomAnneli Lax New Mathematical Library, Volume 24


Old and New Unsolved Problems in Plane Geometry and Number TheoryVictor Klee and Stan WagonDolciani Mathematical Expositions, Volume 11

1991; 333 pp.; softcover; ISBN: 978-0-88385-315-3; List US$32; Institutional member US$25.60; Individual AMS & MAA members US$24; Order code: DOL/11

ONLY Knot TheoryCharles LivingstonCarus Mathematical Monographs, Volume 24


ONLY Non-Euclidean GeometrySixth EditionH. S. M. CoxeterSpectrum, Volume 23


Geometry from AfricaMathematical and Educational ExplorationsPaulus GerdesClassroom Resource Materials, Volume 10


ONLY Differential Geometry and Its ApplicationsJohn OpreaClassroom Resource Materials, Volume 30


A Guide to TopologySteven G. KrantzDolciani Mathematical Expositions, Volume 40


Geometric Transformations IVCircular TransformationsI. M. YaglomTranslated by A. Shenitzer.Anneli Lax New Mathematical Library, Volume 44


Icons of MathematicsAn Exploration of Twenty Key ImagesClaudi Alsina and Roger B. NelsenDolciani Mathematical Expositions, Volume 45

2011; 327 pp.; hardcover; ISBN: 978-0-88385-352-8; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: DOL/45















40


MATH EDUCATION

ONLY

The Contest Problem Book IIAnnual High School Contests 1961–1965Charles T. SalkindAnneli Lax New Mathematical Library, Volume 17


ONLY

International Math Olympiads1959–1977Samuel GreitzerAnneli Lax New Mathematical Library, Volume 27


ONLY The Contest Problem Book IVAnnual High School Mathematics Examinations, 1973–1982Ralph A. Artino, Anthony M. Gaglione, and Niel ShellAnneli Lax New Mathematical Library, Volume 29


ONLY Five Hundred Mathematical ChallengesEdward J. Barbeau, Murray S. Klamkin, and William O. J. MoserSpectrum, Volume 14

1995; 227 pp.; ISBN: 978-1-61444-507-4; List US$28; Institutional member US$22.40; Individual AMS & MAA members US$21; Order code: SPEC/14.E

ONLY Contest Problem Book VAmerican High School Mathematics Examinations and American Invitational Mathematics Examinations, 1983–1988George Berzsenyi and Stephen B. MaurerAnneli Lax New Mathematical Library, Volume 38


Inverse ProblemsActivities for UndergraduatesCharles W. GroetschClassroom Resource Materials, Volume 12


ONLY Mathematical Fallacies, Flaws, and FlimflamEdward J. BarbeauSpectrum, Volume 25


Hungarian Problem Book IIIBased on the Eötvös Competitions: 1929–1943Andy LiuAnneli Lax New Mathematical Library, Volume 42




Mathematical MiniaturesSvetoslav Savchev and Titu AndreescuAnneli Lax New Mathematical Library, Volume 43


International Math Olympiads, 1986–1999Marcin E. KuczmaProblem Books, Volume 10

2003; 192 pp.; softcover; ISBN: 978-0-88385-811-0; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: PRB/10

LOGIC & FOUNDATIONSLogic as AlgebraPaul Halmos and Steven GivantDolciani Mathematical Expositions, Volume 21


ONLY A Tour Through Mathematical LogicRobert S. WolfCarus Mathematical Monographs, Volume 30
















Mathematical Olympiads 2000–2001Problems and Solutions from Around the WorldTitu Andreescu, Zuming Feng, and George Lee Jr., EditorsProblem Books, Volume 11




ONLY Mathematical ConnectionsA Companion for Teachers and OthersAl CuocoClassroom Resource Materials, Volume 27


| Understanding Our Quantitative WorldJanet Andersen and Todd SwansonAMS/MAA Textbooks, Volume 6


Creative MathematicsH. S. WallClassroom Resource Materials, Volume 31


USA and International Mathematical Olympiads 2005Zuming Feng, Melanie Matchett Wood, and Cecil RousseauProblem Books, Volume 17


Uncommon Mathematical ExcursionsPolynomia and Related RealmsDan KalmanDolciani Mathematical Expositions, Volume 35


When Less is MoreVisualizing Basic InequalitiesClaudi Alsina and Roger B. NelsenDolciani Mathematical Expositions, Volume 36

2009; 181 pp.; hardcover; ISBN: 978-0-88385-342-9; List US$60; Institutional member US$48; Individual AMS & MAA members US$45; Order code: DOL/36

AHA! SolutionsMartin EricksonProblem Books, Volume 20

2009; 207 pp.; hardcover; ISBN: 978-0-88385-829-5; List US$56; Institutional member US$44.80; Individual AMS & MAA members US$42; Order code: PRB/20

ONLY Keeping It R.E.A.L.Research Experiences for All LearnersCarla D. Martin and Anthony TongenClassroom Resource Materials, Volume 38


MATHEMATICAL PHYSICS

| ONLY From Pythagoras to EinsteinKurt O. FriedrichsAnneli Lax New Mathematical Library, Volume 16













42


NUMBER THEORY

ONLY The Arithmetic Theory of Quadratic FormsBurton W. JonesCarus Mathematical Monographs, Volume 10


ONLY An Introduction to InequalitiesEdwin Beckenback and Richard BellmanAnneli Lax New Mathematical Library, Volume 3


ONLY The Lore of Large NumbersPhilip J. DavisAnneli Lax New Mathematical Library, Volume 6


Uses of InfinityLeo ZippinAnneli Lax New Mathematical Library, Volume 7

1962; 151 pp.; softcover; ISBN: 978-0-88385-607-9; List US$40; Institutional member US$32; Individual AMS & MAA members US$30; Order code: NML/7

ONLY Continued FractionsC. D. OldsAnneli Lax New Mathematical Library, Volume 91963; 162 pp.; ISBN: 978-0-88385-926-1; List US$25; Institutional member US$20; Individual AMS & MAA members US$18.75; Order code: NML/9.E

ONLY Dedekind SumsHans Rademacher and Emil GrosswaldCarus Mathematical Monographs, Volume 16

1972; 102 pp.; ISBN: 978-1-61444-016-1; List US$44; Institutional member US$35.20; Individual AMS & MAA members US$33;

Order code: CAR/16.E

ONLY Irrational NumbersIvan NivenCarus Mathematical Monographs,

Volume 11


Power PlayEdward J. BarbeauSpectrum, Volume 92


ONLY The Geometry of NumbersC. D. Olds, Anneli Lax, and Giuliana DavidoffAnneli Lax New Mathematical Library, Volume 41


Conjecture and ProofMiklós LaczkovichClassroom Resource Materials, Volume 15


Ergodic Theory of NumbersKarma Dajani and Cor KraaikampCarus Mathematical Monographs, Volume 29


ONLY Numbers: Rational and IrrationalIvan NivenAnneli Lax New Mathematical Library, Volume 1


A Guide to Elementary Number TheoryUnderwood DudleyDolciani Mathematical Expositions, Volume 41


PROBABILITY & STATISTICSStudies in Probability TheoryVolume 18 of Studies on MathematicsMurray Rosenblatt, EditorAMS/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














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101 Careers in Mathematics 19

777 Mathematical Conversation Starters . . . 37

99 Points of Intersection . . . 38

Aaboe, Asger . . . . . . . . . . . 22

Ackerman, Ralph A. . . . . . 12

AHA! Solutions . . . . . . . . . 41

Albers, Donald J. . . . . . . . 20

Albert, Jim. . . . . . . . . . . . . 10

Alexanderson, Gerald L. . . . . 17, 20, 25, 36, 37, 38

Algebra and Tiling . . . . . . . 36

All the Math That’s Fit to Print . . . . . . . . . . . . . . 36

Alsina, Claudi . . . . . . . . . . .24, 38, 39, 41

American Mathematics 1890–1913 . . . . . . . . . . . 21

Analytic Functions of a Complex Variable . . . . . 32

Andersen, Janet . . . . . . . . 41

Anderson, Marlow . . . 37, 38

Andreescu, Titu . . . 37, 40, 41

Annin, Scott A. . . . . . . . . . 29

Anselone, Philip M. . . . . . . 9

Apostol, Tom M. . . . . . . . 23

Archimedes . . . . . . . . . . . . . 37

The Arithmetic Theory of Quadratic Forms . . . . . 42

Arithmetical Wonderland . . 28

Arney, David C. . . . . . . . . 36

Artino, Ralph A. . . . . . . . . 40

Baggett, Larry W.. . . . . . . . 17

Barbeau, Edward J. . . . . . . . . . . . . . .28, 40, 42

Barnes, Julie . . . . . . . . . . . 21

Bashmakova, Isabella Grigoryevna . . . . . . . . . . 36

Batterson, Steve . . . . . . . . 21

Beautiful Mathematics . . . . 16

Beckenback, Edwin . . . . . 42

Bekken, Otto . . . . . . . . . . 36

Bellman, Richard . . . . . . . 42

Benjamin, Arthur T. . . 13, 29

Berlinghoff, William P. . . 20

Berzsenyi, George . . . . . . . 40

Beyond the Quadratic Formula . . . . . . 3

Bhatia, Rejendra . . . . . . . . 32

Biscuits of Number Theory . 29

Bliss, Gilbert Ames . . . . . . 34

Boardman, Michael E. . . . 12

Boas, Harold P. . . . . . . . . . 32

Boas, Ralph P. . . . . . 5, 32, 36

Bogolyubov, N. N. . . . . . . 38

Bolker, Ethan D. . . . . . . . . . 9

Bonar, Daniel D. . . . . . . . 32

Borwein, Peter . . . . . . . . . 19

Bowden, L. . . . . . . . . . . . . 35

Brabenec, Robert L. . . . . . 32

Bradley, Robert F. . . . . . . . 38

Braver, Seth . . . . . . . . . . . . 38

Bremigan, Elizabeth George . . . . . . . . . . . . . . . . . . . . 27

Bremigan, Ralph J. . . . . . . 27

Bressoud, David . . . . . . . . . 7

Bridge to Abstract Mathematics . . . . . . . . . . 18

Brilleslyper, Michael A. . . 33

Broer, Henk W. . . . . . . . . . 24

Brown, Ezra . . . . . . . . . . . 29

Burk, Frank E. . . . . . . . . . . 32

Byer, Owen . . . . . . . . . . . . 23

Calculus . . . . . . . . . . . . . . . 34

Calculus and Its Origins . . . 11

The Calculus Collection . . . 11

Calculus Deconstructed . . . 10

Calculus for the Life Sciences . . . . . . . . . . 12

Calculus Gems . . . . . . . . . . 15

Calculus Mysteries and Thrillers . . . . . . . . . . 34

Calculus of Variations . . . . . 34

Cameos for Calculus . . . . . . 12

Campbell, Duff . . . . . . . . 30

Carter, Nathan . . . . . . . 9, 31

Casazza, Peter . . . . . . . . . . 20

Celestial Mechanics . . . . . . 33

A Century of Advancing Mathematics . . . . . . . . . . 20

Chang, Gengzhe . . . . . . . . 33

Charming Proofs . . . . . . . . 38

Chartier, Tim . . . . . . . . . . . 4

Chen, Evan . . . . . . . . . . . . 29

Chen, Hongwei . . . . . . . . . 5

Chin, W. G. . . . . . . . . . . . . 39

Cohen, Marcus . . . . . . . . . 34

College Calculus . . . . . . . . . 12

Coloring Book of Complex Function Representations . 21

Combinatorial Mathematics 34

Combinatorics by Daniel A. Marcus . . . 13

Combinatorics by David R. Mazur . . . . 14

INDEX

BY TITLE &

AUTHOR

44


Common Sense Mathematics . . . . . . . . 9

Complex Analysis: The Geometric Viewpoint . . . . . . . . . . . . . . . . . . . .32

Complex Numbers and Geometry . . . .22

Conjecture and Proof . . . . . . . . . . . . .42

The Contest Problem Book I . . . . . . . .35

The Contest Problem Book II . . . . . . .40

The Contest Problem Book III . . . . . . .35

The Contest Problem Book IV . . . . . . .40

Contest Problem Book V . . . . . . . . . . .40

The Contest Problem Book VI . . . . . . .14

The Contest Problem Book VII . . . . . .25

The Contest Problem Book VIII . . . . .27

The Contest Problem Book IX . . . . . . .26

Continued Fractions . . . . . . . . . . . . . .42

Conway, John Horton . . . . . . . . . . . 31

Cornette, James L. . . . . . . . . . . . . . .12

Counterexamples in Calculus . . . . . . . 11

A Course in Mathematical Modeling . . 5

Coxeter, H. S. M. . . . . . . . . . . . .22, 39

Crannell, Annalisa . . . . . . . . . . . . . .37

Creative Mathematics . . . . . . . . . . . . . 41

Cryptological Mathematics . . . . . . . . . . 7

Cuoco, Al . . . . . . . . . . . . . . . . . . . 4, 41

Curtiss, David Raymond . . . . . . . . .32

D’Angelo, John P. . . . . . . . . . . . . . . .32

D’Antonio, Lawrence A. . . . . . . . . . .38

Dajani, Karma . . . . . . . . . . . . . . . . .42

Daniel, James W. . . . . . . . . . . . . . . . . 8

Davidoff, Giuliana . . . . . . . . . . . . . .42

Davis, Philip J. . . . . . . . . . . . . . .32, 42

Dedekind Sums . . . . . . . . . . . . . . . . .42

dePillis, John . . . . . . . . . . . . . . . .4, 37

Devlin, Keith . . . . . . . . . . . . . . . . . .36

Diamond, Harold G. . . . . . . . . . . . . 31

Diefenderfer, Caren L. . . . . . . . . . . . 11

Differential Geometry and Its Applications . . . . . . . . . . . .39

Diophantus and Diophantine Equations . . . . . . . . . .36

Discovering Discrete Dynamical Systems . . . . . . . . . . . . . 10

Distilling Ideas . . . . . . . . . . . . . . . . . .19

Dorff, Michael J. . . . . . . . . . . . . . . . .33

Doyle, Peter G. . . . . . . . . . . . . . . . . .33

Dudley, Underwood . . 35, 36, 38, 42

Dumbaugh, Della . . . . . . . . . . . . . . 20

Dunham, William . . . . . . . . . . . . . .14

The Early Mathematics of Leonhard Euler . . . . . . . . . . . . . .38

Earl, James M. . . . . . . . . . . . . . . . . . .35

The Edge of the Universe . . . . . . . . . .38

Elementary Cryptanalysis . . . . . . . . . . . 8

Elementary Mathematical Models. . . . . 2

Episodes from the Early History of Mathematics . . . . .22

Episodes in Nineteenth and Twentieth Century Euclidean Geometry . . . . . .36

An Episodic History of Mathematics . .16

Ergodic Theory of Numbers . . . . . . . .42

Erickson, Martin . . . . . . . . . . . . .16, 41

Essentials of Mathematics . . . . . . . . . .36

Euclidean Geometry in Mathematical Olympiads . . . . . . . .29

Euler and Modern Science . . . . . . . . .38

Euler At 300 . . . . . . . . . . . . . . . . . . .38

Euler . . . . . . . . . . . . . . . . . . . . . . . . .14

Eves, Howard . . . . . . . . . . . . . . .35, 37

Excursions in Classical Analysis . . . . . . 5

Exercises in (Mathematical) Style . . . . 7

Expeditions in Mathematics . . . . . . . .17

Explorations in Complex Analysis . . . .33

Exploratory Examples for Real Analysis . . . . . . . . . . . . . . .32

Exploring Advanced Euclidean Geometry with GeoGebra . . . . . . . .23

Faires, J. Douglas . . . . . . . . . . . .26, 27

Faris, Frank A. . . . . . . . . . . . . . . . . . . 20

Fauvel, John . . . . . . . . . . . . . . . . . . .36

Federer Vaaler, Leslie Jane . . . . . . . . . 8

Feng, Zuming . . . . . . . . . . . .37, 40, 41

Field Theory and Its Classical Problems . . . . . . . . . . . . 2

First Concepts of Topology . . . . . . . . . .39

First Steps for Math Olympians . . . . .26

Five Hundred Mathematical Challenges . . . . . . . .40

Folland, Gerald B. . . . . . . . . . . . . . .33

Fourier Series and Orthogonal Polynomials . . . . . . . . .32

Fourier Series . . . . . . . . . . . . . . . . . . .32

Friedrichs, Kurt O. . . . . . . . . . . . . . . 41

A Friendly Mathematics Competition .37

From Erdos to Kiev . . . . . . . . . . . . . . .36

From Error-Correcting Codes Through Sphere Packings to Simple Groups . .34

From Pythagoras to Einstein . . . . . . . . 41

Functions, Data, and Models . . . . . . . . 2

Gaglione, Anthony M. . . . . . . . . . . .40

Gallian, Joseph A. . . . . . . . . . . . . . .15

Game Theory and Strategy . . . . . . . . . . 7

Game Theory through Examples . . . . . . 9

A Garden of Integrals . . . . . . . . . . . . .32

Gardner, Martin . . . . . . . . . . . . .35, 37

Gaughan, Edward D. . . . . . . . . . . . .34

The Generalized Riemann Integral . . .32

A Gentle Introduction to the American Invitational Mathematics Exam . . .29

Geometric Inequalities . . . . . . . . . . . .39

Geometric Transformations I . . . . . . . .39

Geometric Transformations II . . . . . . .39

Geometric Transformations III . . . . . .39

Geometric Transformations IV . . . . . .39

Geometry from Africa . . . . . . . . . . . . .39

Geometry Illuminated . . . . . . . . . . . . .24

The Geometry of Numbers . . . . . . . . .42

Geometry Revisited . . . . . . . . . . . . . . .22

Gerdes, Paulus . . . . . . . . . . . . . . . . .39

Gilbert, George T. . . . . . . . . . . . . . . .27

Gillman, Leonard . . . . . . . . . . . . . . .35

Gillman, Rick . . . . . . . . . . . . . . . . . .37

Ginsburg, Jekuthiel . . . . . . . . . . . . .35

Givant, Steven . . . . . . . . . . . . . . . . .40

Gleason, A. M. . . . . . . . . . . . . . . . . .25

Gockenbach, Mark S. . . . . . . . . . . . . . 6

Gold, Bonnie . . . . . . . . . . . . . . . . . .38

Gordon, Florence S. . . . . . . . . . . . . . . 2

Gordon, Sheldon P. . . . . . . . . . . . . . . 2

Gouvêa, Fernando Q. . . . . . . . . . .3, 20

Grabiner, Judith V. . . . . . . . . . . . . . .16

Graph Theory . . . . . . . . . . . . . . . . . . .14

Graphs and Their Uses . . . . . . . . . . . .34

Great Moments in Mathematics Before 1650 . . . . . . . . . . . . . . . . . .35

Great Moments in Mathematics After 1650 . . . . . . . . . . . . . . . . . . .35

Greenwood, R. E. . . . . . . . . . . . . . . .25

Greitzer, S. L. . . . . . . . . . . . . . . . . . .22

Greitzer, Samuel . . . . . . . . . . . . . . . .40

Groetsch, Charles W. . . . . . . . . . . . .40

Grossman, Israel . . . . . . . . . . . . . . . 31

Grosswald, Emil . . . . . . . . . . . . . . . .42

Groups and Their Graphs . . . . . . . . . . 31

Guichelaar, Jan . . . . . . . . . . . . . . . . . 20

A Guide to Advanced Linear Algebra . . 3

A Guide to Advanced Real Analysis . .33

A Guide To Complex Variables . . . . . .32

A Guide to Elementary Number Theory . . . . . . . . . . . . . . . .42

A Guide to Functional Analysis . . . . . . 5

A Guide to Groups, Rings, and Fields . . 3

A Guide to Plane Algebraic Curves . . . . 3

A Guide to Real Variables . . . . . . . . . .33

A Guide to Topology . . . . . . . . . . . . . .39

Hadlock, Charles R. . . . . 2, 18, 32, 33

Hahn, Liang-shin . . . . . . . . . . . . . . .22

Hale, Margie . . . . . . . . . . . . . . . . . . .36

Half a Century of Pythagoras Magazine . . . . . . . . . . . 20

Halmos, Paul . . . . . . . . . . . . . . .31, 40

The Harmony of the World . . . . . . . . .38

Harvey, Matthew . . . . . . . . . . . . . . .24

Haunsperger, Deanna . . . . . . . .20, 38

Hayes, David F. . . . . . . . . . . . . . . . . .17


The Heart of Calculus . . . . . . . . . . . . . 9

Henle, Michael . . . . . . . . . . . . . .18, 30

Herstein, I. N. . . . . . . . . . . . . . . . . . . 31

Hilbert, Stephen . . . . . . . . . . . . . . . .34

A Historian Looks Back . . . . . . . . . . .16

A History of Mathematics in America Before 1900 . . . . . . . . .35

The Hitchhiker’s Guide to Calculus . .34

Honsberger, Ross . . . . . . . . 35, 36, 37

Hopkins, Brian . . . . . . . . . . . . . . . . .18

How Euler Did Even More . . . . . . . . .19

Hungarian Problem Book III . . . . . . .40

Hungarian Problem Book IV . . . . . . .27

I, Mathematician . . . . . . . . . . . . . . . . 20

Icons of Mathematics . . . . . . . . . . . . .39

Identification Numbers and Check Digit Schemes . . . . . . . . . . .33

Illustrated Special Relativity through Its Paradoxes . . . . . . . . . . . . 4

In the Dark On the Sunny Side . . . . .17

Inequalities from Complex Analysis . .32

Ingenuity in Mathematics . . . . . . . . . .35

Interdisciplinary Lively Application Projects . . . . . . . . . . . . .36

International Math Olympiads, 1959–1977 . . . . . . . . . . . . . . . . . .40

International Math Olympiads, 1986–1999 . . . . . . . . . . . . . . . . . .40

International Mathematical Olympiads 1978–1985 . . . . . . . . . . . . . . . . . .35

An Introduction to Inequalities . . . . . .42

Introduction to the Mathematics of Computer Graphics . . . . . . . . . . . . 9

Inverse Problems . . . . . . . . . . . . . . . . .40

Invitation to Complex Analysis . . . . . . . 5

Invitation to Number Theory . . . . . . . 30

An Invitation to Real Analysis . . . . . . . 6

Irrational Numbers . . . . . . . . . . . . . . .42

Irving, Ron . . . . . . . . . . . . . . . . . . . . . 3

Is Mathematics Inevitable? . . . . . . . . .38

Ivanov, O. A. . . . . . . . . . . . . . . . . . . . 21

Jackson, Dunham . . . . . . . . . . . . . . .32

James, Ioan . . . . . . . . . . . . . . . . . . . .37

Jaspers, Arnout . . . . . . . . . . . . . . . . . 20

Johansson, Bengt . . . . . . . . . . . . . . .36

Johnson, Aimee . . . . . . . . . . . . . . . . 10

Johnston, William . . . . . . . . . . . . . . . 6

Jones, Burton W.. . . . . . . . . . . . . . . .42

Kac, Mark . . . . . . . . . . . . . . . . . . . . .33

Kalman, Dan . . . . . . . . . . . . . . . . 2, 41

Kasman, Alex . . . . . . . . . . . . . . . . . .38

Katz, Brian P. . . . . . . . . . . . . . . . . . .19

Katz, Victor . . . . . . . . . . . . . 36, 37, 38

Kazarinoff, Nicholas D. . . . . . . . . . .39

Kedlaya, Kiran S. . . . . . . . . . . . . . . .25

Keeping It R.E.A.L. . . . . . . . . . . . . . . 41

Kelly, L. M. . . . . . . . . . . . . . . . . . . . .25

Kendig, Keith . . . . . . . . . . . . . . . .3, 26

Kennedy, Stephen . . . . . . . . . . . .20, 38

Khoury, Michael J. . . . . . . . . . . . . . .32

Kiltinen, John O. . . . . . . . . . . . . . . .37

Kirtland, Joseph . . . . . . . . . . . . . . . .33

Klamkin, Murray S. . . . . . . . . . .35, 40

Klee, Victor . . . . . . . . . . . . . . . . . . . .39

Klosinski, Leonard F. . . . . . . . . . . . .25

Klymchuk, Sergiy . . . . . . . . . . . . . . . 11

Knoebel, Arthur . . . . . . . . . . . . . . . .34

Knot Theory . . . . . . . . . . . . . . . . . . . .39

Konhauser, D. E.. . . . . . . . . . . . . . . .36

Kraaikamp, Cor . . . . . . . . . . . . . . . .42

Krantz, Steven G. . . . . . . 5, 16, 17, 20, 32, 33, 38, 39

Kreahling, William . . . . . . . . . . . . . . 21

Krusemeyer, Mark I. . . . . . . . . . . . . .27

Kuczma, Marcin E. . . . . . . . . . . . . . .40

Kurtz, Douglas S. . . . . . . . . . . . . . . .34

Laczkovich, Miklós . . . . . . . . . . . . . .42

LaRose, Gavin . . . . . . . . . . . . . . . . . .37

Larson, Loren C. . . . . . . . . . . . . .25, 27

Lawrence, Bonita A. . . . . . . . . . . . . .18

Lax, Anneli . . . . . . . . . . . . . . . . . . . .42

Lazebnik, Felix . . . . . . . . . . . . . . . . .23

Learn from the Masters . . . . . . . . . . .36

Learning Modern Algebra . . . . . . . . . . . 4

The Lebesgue Integral for Undergraduates . . . . . . . . . . . . . . 6

Lee, George . . . . . . . . . . . . . . . . . . . . 41

Lee, John W. . . . . . . . . . . . . . . . . . . . . 9

Leigh, Robert Barrington . . . . . . . . .27

Lewand, Robert Edward . . . . . . . . . . . 7

Lie Groups . . . . . . . . . . . . . . . . . . . . . . 2

Liljedahl, Peter . . . . . . . . . . . . . . . . .19

Linear Algebra Problem Book . . . . . . . 31

Linear Inverse Problems and Tikhonov Regularization . . . . . . 6

Lion Hunting & Other Mathematical Pursuits . . . . . . . . . .36

Liu, Andy . . . . . . . . . . . 27, 28, 29, 40

Livingston, Charles . . . . . . . . . . . . .39

Lobachevski Illuminated . . . . . . . . . . .38

Logic as Algebra . . . . . . . . . . . . . . . . .40

Lolt, Po-Shen . . . . . . . . . . . . . . . . . .37

Lorch, John D. . . . . . . . . . . . . . . . . .27

The Lore of Large Numbers . . . . . . . .42

MacDuffee, Cyrus Colton . . . . . . . . 31

Maceli, John . . . . . . . . . . . . . . . . . . .34

Madden, Kathleen . . . . . . . . . . . . . . 10

The Magic Numbers of the Professor .38

Magic Tricks, Card Shuffling and Dynamic Computer Memories. . . . .36

Magnus, Wilhelm . . . . . . . . . . . . . . . 31

Marcus, Daniel A. . . . . . . . . . . . .13, 14

Marshall, David C. . . . . . . . . . . . . . .26

Martin Gardner in the Twenty-First Century . . . . . . . . . . . .18

Martin, Carla D. . . . . . . . . . . . . . . . . 41

Mast, Maura B. . . . . . . . . . . . . . . . . . . 9

Math Made Visual . . . . . . . . . . . . . . .38

Math through the Ages . . . . . . . . . . . . 20

Mathematical Apocrypha Redux . . . . .38

Mathematical Circles . . . . . . . . . . . . .37

Mathematical Connections . . . . . . . . . 41

Mathematical Cranks . . . . . . . . . . . . .35

Mathematical Delights . . . . . . . . . . . .37

Mathematical Diamonds . . . . . . . . . .37

Mathematical Fallacies, Flaws, and Flimflam . . . . . . . . . . . .40

Mathematical Interest Theory . . . . . . . . 8

Mathematical Methods in Science . . .33

Mathematical Miniatures . . . . . . . . . .40

Mathematical Modeling in the Environment . . . . . . . . . . . . .32

Mathematical Olympiads 2000–2001 41

A Mathematical Orchard . . . . . . . . . .27

Mathematical Puzzle Tales . . . . . . . . .37

Mathematical Reminiscences . . . . . . .37

A Mathematical Space Odyssey . . . . .24

Mathematical Statistics . . . . . . . . . . .33

Mathematical Treks . . . . . . . . . . . . . .37

A Mathematician Comes of Age . . . . .17

Mathematicians on Creativity . . . . . . .19

Mathematics and Sports . . . . . . . . . . .15

Mathematics for Secondary School Teachers . . . . . . . . . . . . . . . .27

Mathematics Galore! . . . . . . . . . . . . .17

Mathematics in Historical Context . . .15

Mathematics of Choice . . . . . . . . . . . .35

The Mathematics of Games and Gambling . . . . . . . . . . . . 8

Maurer, Stephen B. . . . . . . . . . . . . . .40

Maxima and Minima Without Calculus . . . . . . . . . . . . . .35

Mazur, David R. . . . . . . . . . . . . . . . .14

McCleary, John . . . . . . . . . . . . . . . . . . 7

McCoy, Neal H. . . . . . . . . . . . . . . . . 31

McDougall, Jane M. . . . . . . . . . . . . .33

McLeod, Robert M. . . . . . . . . . . . . . .32

Messer, Robert . . . . . . . . . . . . . . . . .22

Methods for Euclidean Geometry . . . .23

Mikhaılov, G. K. . . . . . . . . . . . . . . . .38

Mnatsakanian, Mamikon A. . . . . . .23

Mooney, Douglas D. . . . . . . . . . . . . . 5

More Fallacies, Flaws, and Flimflam .28

46


More Mathematical Morsels . . . . . . . .35

Moreno, Luis F. . . . . . . . . . . . . . . . . . . 6

Morris, S. Brent. . . . . . . . . . . . . . . . .36

Moser, William O. J.. . . . . . . . . . . . .40

Mouzakitis, Aristides . . . . . . . . . . . .18

Mugler, Dale H. . . . . . . . . . . . . . . . .36

Musielak, Dora . . . . . . . . . . . . . . . . .18

Near the Horizon . . . . . . . . . . . . . . . .24

Nelsen, Roger B. . . . . . . . . . 11, 12, 23, 24, 38, 39, 41

New Horizons in Geometry . . . . . . . .23

Nillsen, Rodney . . . . . . . . . . . . . . . .33

Nitecki, Zbigniew H. . . . . . . . . . . . . 10

Niven, Ivan . . . . . . . . . . . . . . . . .35, 42

Non-Euclidean Geometry . . . . . . . . . .39

Noncommutative Rings . . . . . . . . . . . 31

Noonburg, Virginia W.. . . . . . . . . . .13

Number Theory Through Inquiry . . . .26

Numbers: Rational and Irrational. . . .42

Numerology or What Pythagoras Wrought . . . . . . .36

O’Shea, Owen . . . . . . . . . . . . . . . . . .38

Oberste-Vorth, Ralph W. . . . . . . . . .18

Odell, Edward . . . . . . . . . . . . . . . . .26

Old and New Unsolved Problems in Plane Geometry and Number Theory . . . . . . . . . . . .39

Olds, C. D. . . . . . . . . . . . . . . . . . . . .42

An Open Door to Number Theory . . . 30

Oprea, John . . . . . . . . . . . . . . . . . . .39

Ordinary Differential Equations by Virginia W. Noonburg . . . . . . .13

Ordinary Differential Equations by David A. Sánchez . . . . . . . . . . .34

Ore, Oystein . . . . . . . . . . . . . . . .30, 34

Oval Track and Other Permutation Puzzles . . . . . . .37

Over and Over Again . . . . . . . . . . . . .33

Packel, Edward . . . . . . . . . . . . . . . . . . 8

A Panorama of Harmonic Analysis . . .32

Paradoxes and Sophisms in Calculus . 11

Parker, John . . . . . . . . . . . . . . . . . . .38

Parker, Marla . . . . . . . . . . . . . . . . . .33

Pengelley, David . . . . . . . . . . . . . . . .34

Perkins, David . . . . . . . . . . . . . . 11, 12

Peterson, Ivars . . . . . . . . . . . . . . . . .37

Φ , Π , e , and i . . . . . . . . . . . . . . . . . . .12

Pollard, Harry . . . . . . . . . . . . . . .31, 33

Pollatsek, Harriet . . . . . . . . . . . . . . . . 2

Pólya, George . . . . . . . . . . . . . . . . . .33

Poonen, Bjorn . . . . . . . . . . . . . . . . .25

Portal through Mathematics . . . . . . . . 21

Power Play . . . . . . . . . . . . . . . . . . . . .42

A Primer of Real Functions . . . . . . . .32

Prisner, Erich . . . . . . . . . . . . . . . . . . . 9

Projective Geometry . . . . . . . . . . . . . .39

Proof and Other Dilemmas . . . . . . . .38

Proofs that Really Count . . . . . . . . . . .13

Proofs Without Words III . . . . . . . . . .23

Quinn, Jennifer J. . . . . . . . . . . . . . . .13

R. L. Moore . . . . . . . . . . . . . . . . . . . .38

Rademacher, Hans . . . . . . . . . . . . . .42

A Radical Approach to Real Analysis . . 7

Random Walks and Electric Networks . . . . . . . . . . . . . .33

The Random Walks of George Pólya . .37

Randomness and Recurrence in Dynamical Systems . . . . . . . . . . .33

Ratliff, Thomas . . . . . . . . . . . . . . . . .37

Rault, Patrick X. . . . . . . . . . . . . . . . . 21

Real Infinite Series . . . . . . . . . . . . . . .32

Reality Conditions . . . . . . . . . . . . . . .38

Rediscovering Mathematics . . . . . . . . .16

Reid, Constance . . . . . . . . . . . . . . . .35

Reiter, Harold B. . . . . . . . . . . . . . . . .25

Remarkable Mathematics . . . . . . . . . .37

Resources For The Study of Real Analysis . . . . . . . . . . . . . . . .32

Riddles of the Sphinx . . . . . . . . . . . . .35

The Riemann Hypothesis . . . . . . . . . . 30

Rietz, Henry L. . . . . . . . . . . . . . . . . .33

Rings and Ideals . . . . . . . . . . . . . . . . . 31

The Role of Mathematics in Science . .35

Rolf, James S. . . . . . . . . . . . . . . . . . .33

Rosenblatt, Murray . . . . . . . . . . . . . .42

Rosentrater, C. Ray . . . . . . . . . . . . . . . 6

Ross, Peter . . . . . . . . . . . . . . . . . . . . .38

Rotman, Joseph J. . . . . . . . . . . . . . . . . 4

Rousseau, Cecil . . . . . . . . . . . . . . . . . 41

Ruden, Randi D. . . . . . . . . . . . . . . . . 20

Rykken, Elyn . . . . . . . . . . . . . . . . . . .37

Ryser, Herbert John . . . . . . . . . . . . .34

Sahin, Ayse . . . . . . . . . . . . . . . . . . . . 10

Salkind, Charles T. . . . . . . . . . . .35, 40

Sánchez, David A. . . . . . . . . . . . . . .34

Sandifer, C. Edward . . . . . . . . . .19, 38

Savchev, Svetoslav . . . . . . . . . . . . . .40

Sawyer, W. W. . . . . . . . . . . . . . . . . . .34

Schaubroeck, Beth . . . . . . . . . . . . . . 21

Schaubroeck, Lisbeth E. . . . . . . . . . .33

Schiffer, M. M. . . . . . . . . . . . . . . . . .35

Schneider, Leo J. . . . . . . . . . . . . . . . .14

Schwartzman, Steven . . . . . . . . . . . .36

Schwartz, Diane D. . . . . . . . . . . . . .34

The Schwarz Function and Its Applications . . . . . . . . . . . .32

The Search for E.T. Bell . . . . . . . . . . .35

Sederberg, Thomas W. . . . . . . . . . . .33

Seltzer, Stan . . . . . . . . . . . . . . . . . . .34

The Sensual (quadratic) Form . . . . . . 31

She Does Math! . . . . . . . . . . . . . . . . .33

Shell, Niel . . . . . . . . . . . . . . . . . . . . .40

Sherlock Holmes in Babylon and Other Tales of Mathematical History . . . . .37

Shubin, Tatiana . . . . . . . . . . . . . . . .17

Sibley, Thomas Q. . . . . . . . . . . . . . .24

Simmons, George F. . . . . . . . . . . . . .15

Simonson, Shai . . . . . . . . . . . . . . . .16

Simons, Roger A. . . . . . . . . . . . . . . .38

Simoson, Andrew J. . . . . . . . . . . . . .15

Sink or Float? . . . . . . . . . . . . . . . . . . .26

Sinkov, Abraham . . . . . . . . . . . . . . . . 8

Six Sources of Collapse . . . . . . . . . . . .18

Smeltzer, Deirdre L. . . . . . . . . . . . . .23

Smith, D. E. . . . . . . . . . . . . . . . . . . .35

Snell, J. Laurie . . . . . . . . . . . . . . . . .33

Snow, Joanne E. . . . . . . . . . . . . . . . .32

Solve This . . . . . . . . . . . . . . . . . . . . . .37

Sophie’s Diary . . . . . . . . . . . . . . . . . .18

Soviet Union Mathematical Olympiad . . . . . . . . .29

Spivak, Michael . . . . . . . . . . . . . . . .34

Stankewitz, Richard L. . . . . . . . . . . .33

Staples, Susan . . . . . . . . . . . . . . . . . . 11

Starbird, Michael . . . . . . . . . . . .19, 26

Statistical Independence in Probability, Analysis, and Number Theory . . . . .33

Steenrod, N. E. . . . . . . . . . . . . . . . . .39

Stein, Sherman K. . . . . . . . . . . . . . . .36

Stein, Sherman . . . . . . . . . . . . . . . . .37

Stephenson, Kenneth . . . . . . . . . . . .33

Sterrett, Andrew . . . . . . . . . . . . . . . .19

Straffin, Philip . . . . . . . . . . . . . . .7, 22

Student Research Projects in Calculus . . . . . . . . . . . . . . . . . . .34

Student Solution Manual for Mathematical Interest Theory . . . . . . 8

Studies in Probability Theory . . . . . . .42

Stueben, Michael . . . . . . . . . . . . . . .36

Supplementary Material and Solutions Manual for Mathematical Modeling in the Environment . . . . . . . . . . . . .33

Suzuki, Jeff . . . . . . . . . . . . . . . . . . . .15

Swanson, Todd . . . . . . . . . . . . . . . . . 41

Swetz, Frank . . . . . . . . . . . . . . . . . . .36

Swift, Randall J. . . . . . . . . . . . . . . . . . 5

Szabó, Sándor . . . . . . . . . . . . . . . . . .36

Tanton, James . . . . . . . . . . . 17, 28, 37

Taylor, Ron . . . . . . . . . . . . . . . . . . . . 21

Teaching Statistics Using Baseball . . . 10

A TeXas Style Introduction to Proof . . 21

Textbooks, Testing, Training . . . . . . . .28

The Theory of Algebraic Numbers . . . . 31


Thinking Geometrically . . . . . . . . . . .24

Thompson, Thomas M. . . . . . . . . . .34

Tongen, Anthony . . . . . . . . . . . . . . . 41

Topology Now! . . . . . . . . . . . . . . . . . .22

A Tour Through Mathematical Logic . . . . . . . . . . . .40

Trigonometry . . . . . . . . . . . . . . . . . . .28

The Trisectors . . . . . . . . . . . . . . . . . . .36

Twenty Years Before the Blackboard . .36

Uncommon Mathematical Excursions . 41

Understanding Our Quantitative World . . . . . . . . . . . . . 41

USA and International Mathematical Olympiads 2001 . . . . . . . . . . . . . . .40

USA and International Mathematical Olympiads 2002 . . . . . . . . . . . . . . . 41

USA and International Mathematical Olympiads 2003 . . . . . . . . . . . . . . .37

USA and International Mathematics Olympiads 2004 . . . . . . . . . . . . . . .37

USA and International Mathematical Olympiads 2005 . . . . . . . . . . . . . . . 41

USA Mathematical Olympiads 1972-1986 . . . . . . . . . .35

Uses of Infinity . . . . . . . . . . . . . . . . . .42

Vakil, Ravi . . . . . . . . . . . . . . . . . . . . .25

van de Craats, Jan . . . . . . . . . . . . . . . 30

van den Brandhof, Alex . . . . . . . . . . 20

van der Veen, Roland . . . . . . . . . . . . 30

Varieties of Integration . . . . . . . . . . . . . 6

Vectors and Matrices. . . . . . . . . . . . . . 31

Velleman, Dan . . . . . . . . . . . . . . . . .36

Venema, Gerard A. . . . . . . . . . . . . . .23

Visual Group Theory . . . . . . . . . . . . . . 31

Voltaire’s Riddle . . . . . . . . . . . . . . . . .15

Wagon, Stan . . . . . . . . . . . . . . . .36, 39

Wall, H. S. . . . . . . . . . . . . . . . . . . . . . 41

Walser, Hans . . . . . . . . . . . . . . . . . . .38

Weintraub, Steven H. . . . . . . . . . . . . . 3

Weller, Kirk E. . . . . . . . . . . . . . . . . . .32

Wells, David . . . . . . . . . . . . . . . .26, 27

What Is Calculus About? . . . . . . . . . .34

When Less is More . . . . . . . . . . . . . . . 41

When Life is Linear . . . . . . . . . . . . . . . 4

Which Numbers Are Real? . . . . . . . . . 30

Which Way Did the Bicycle Go? . . . .36

Who Gave You the Epsilon? . . . . . . . .38

The William Lowell Putnam Mathematical Competition 1985–2000 . . . . . . . . . . . . . . . . . .25

The William Lowell Putnam Mathematical Competition . . . . . . .25

Willoughby, Stephen S. . . . . . . . . . .28

Wilson, Robin . . . . . . . . . . . . . .37, 38

Wolf, Robert S. . . . . . . . . . . . . . . . . .40

Woods, R. Grant . . . . . . . . . . . . . . . .34

Wood, Melanie Matchett . . . . . . . . . 41

The Words of Mathematics . . . . . . . . .36

Writing Mathematics Well . . . . . . . . .35

Writing Projects for Mathematics Courses . . . . . . . . . . .37

Wudka, Jose . . . . . . . . . . . . . . . . . . . . 4

Yaglom, I. G. . . . . . . . . . . . . . . . . . . .39

Young, John Wesley . . . . . . . . . . . . .39

Yushevich, A. P. . . . . . . . . . . . . . . . .38

Zhai, Helen . . . . . . . . . . . . . . . . . . . .19

Zippin, Leo . . . . . . . . . . . . . . . . . . . .42

Zorn, Paul . . . . . . . . . . . . . . . . . . . . . 20

48


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