2015 Beckenbach Book Prize Winner

The Beckenbach Book Prize, established in 1986, is the successor to the MAA Book Prize established in 1982. It is named for the late Edwin Beckenbach, a long-time leader in the publications program of the Association and a well-known professor of mathematics at the University of California at Los Angeles. The Prize of $2,500 is intended to recognize the author(s) of a distinguished, innovative book published by the MAA and to encourage the writing of such books. The award is not given on a regularly scheduled basis. To be considered for the Beckenbach Prize a book must have been published during the five years preceding the Award.

The 2015 Beckenbach Book Prize winner is:

Lobachevski Illuminated

By Seth Braver

PDF Price: $28.00

Print-on-Demand Price: $47.50

Mathematicians of all stripes know that the non-Euclidean revolution was a game-changer in 19^th  century mathematics. But relatively few mathematicians are acquainted with the little book that heralded this revolution: Nikolai Lobachevski’s Theory of Parallels (in German, 1840).

Seth Braver has come to our rescue. In Lobachevski Illuminated, he gives us a translation of the text, accompanies each of its 37 propositions with an extensive commentary, and places these ideas in their proper historical context. As a result, Braver has done nothing less than give new life to an old masterpiece.

The reader of Lobachevski Illuminated will encounter a host of provocative questions, will delve deeply into the history of geometry, and will gain a thorough appreciation of the genius of Nikolai Lobachevski.

New: How Euler Did Even More

How Euler Did Even More

By C. Edward Sandifer
Spectrum Series

"Read Euler, read Euler, he is master of us all," LaPlace exhorted us. And it is true, Euler writes with unerring grace and ease. He is exceptionally clear thinking and clear speaking. It is a joy and a pleasure to follow him. It is especially so with Ed Sandifer as your guide. Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This volume is the second collection of Sandifer's "How Euler Did It" columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context.

Pick up your copy today at the MAA Store!

Prefer an ebook? Visit the MAA eBooks Store.

New eBook: Game Theory through Examples

Game Theory through Examples

by Erich Prisner

Classroom Resource Materials

Game Theory through Examples is a thorough introduction to elementary game theory, covering finite games with complete information.

The core philosophy underlying this volume is that abstract concepts are best learned when encountered first (and repeatedly) in concrete settings. Thus, the essential ideas of game theory are here presented in the context of actual games, real games much more complex and rich than the typical toy examples. All the fundamental ideas are here: Nash equilibria, backward induction, elementary probability, imperfect information, extensive and normal form, mixed and behavioral strategies. The active-learning, example-driven approach makes the text suitable for a course taught through problem solving. Students will be thoroughly engaged by the extensive classroom exercises, compelling homework problems and nearly sixty projects in the text. Also available are approximately eighty Java applets and three dozen Excel spreadsheets in which students can play games and organize information in order to acquire a gut feeling to help in the analysis of the games. Mathematical exploration is a deep form of play, that maxim is embodied in this book.

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Order your copy today!

Sophie's Diary: A Mathematical Novel

Check out this video on Sophie's Diary by Dora Musielak.

Purchase Musielak's book today in the MAA Store or the MAA eBooks Store.

Now in the MAA Store

Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem by Al Cuoco and Joseph J. Rotman Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers–II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems. This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily “end up on the blackboard.'' Order your copy today in the MAA Store! List Price: $60.00 MAA Member: $48.00

Beyond the Quadratic Formula by Ron Irving The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial’s coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject. Order your copy today in the MAA Store! List Price: $55.00 MAA Member: $44.00

Debbie Gochenaur Reviews Uncommon Mathematical Excursions

Debbie Gochenaur reviews Uncommon Mathematical Excursions: Polynomia and Related Realms by Dan Kalman as part of MAA Reviews. Offering an assortment of topics in the algebra, geometry, and calculus curricula, this book is intended as an enrichment for those familiar with these topics at the upper-secondary or introductory college math level. While the book may be geared especially for teachers who have taught their courses enough times to be thoroughly comfortable with the content, advanced students, as well as scientists and mathematicians in general, may find topics within this book intriguing. It has the potential to appeal to a broad audience. The book is meant to guide the readers in exploring ideas that are related to his/her core mathematical knowledge. The book is divided into three parts — The Province of Polynomia, Maxiministan, and The Calculusian Republic. Kalman ensures that the reader can make connections to known undergraduate mathematics and advanced secondary topics in the algebra, geometry, and calculus domains; he works to help the reader make extensions and perhaps understand more clearly the depth of mathematics in these seemingly elementary topics. Overall, the reader may be surprised by aspects of a particular topic that will lead to a greater understanding and appreciation for the mathematics. Read the full review here. Purchase your copy in the MAA Store.