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.

JMM 2015: Teaching Calculus with a Tablet

Attending the Joint Mathematics Meetings in San Antonio, TX, this year? Join us for this MAA Special Session!

Teaching Calculus with a Tablet

Gwyneth Whieldon, Hood College

Integrating technology into the classroom has been a hot topic over the past decade but best practices in the use of tablets, phones, and laptops for mathematics education are still being developed. In this workshop, participants will have a chance to demo the MAA electronic textbook Calculus: Modeling and Application and see how a textbook designed specifically to be read and interacted with on a tablet can be integrated into their own classrooms. We will introduce several apps to supplement an electronic textbook (and, more generally, for use in a technology-based calculus course) and suggest techniques for introducing students to a calculus sequence very different from any math classes they have taken before.

Monday, January 12

3:00-4:15pm

Room 213B

Convention Center

Stop by the MAA Pavilion in the exhibit hall for more information.

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: Doing the Scholarship of Teaching and Learning in Mathematics

Doing the Scholarship of Teaching and Learning in Mathematics

Jacqueline M. Dewar and Curtis D. Bennett, Editors

The Scholarship of Teaching and Learning (SoTL) movement encourages faculty to view teaching “problems” as invitations to conduct scholarly investigations. In this growing field of inquiry faculty bring their disciplinary knowledge and teaching experience to bear on questions of teaching and learning. They systematically gather evidence to develop and support their conclusions. The results are to be peer reviewed and made public for others to build on.

This Notes volume is written expressly for collegiate mathematics faculty who want to know more about conducting scholarly investigations into their teaching and their students’ learning. Conceived and edited by two mathematics faculty, the volume serves as a how-to guide for doing SoTL in mathematics.

The four chapters in Part I provide background on this form of scholarship and specific instructions for undertaking a SoTL investigation in mathematics. Part II contains fifteen examples of SoTL projects in mathematics from fourteen different institutions, both public and private, spanning the spectrum of higher educational institutions from community colleges to research universities. These chapters “reveal the process of doing SoTL” by illustrating many of the concepts, issues, methods and procedures discussed in Part I. An Editors’ Commentary opens each contributed chapter to highlight one or more aspects of the process of doing SoTL revealed within. Toward the end of each chapter the contributing authors describe the benefits that accrued to them and their careers from participating in SoTL.

The final chapter in the volume, the Epilogue, represents a synthesis by the editors of the contributing authors’ perceptions of the value of SoTL. This volume has two goals: to assist mathematics faculty interested in undertaking a scholarly study of their teaching practice and to promote a greater understanding of this work and its value to the mathematics community.

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Purchase your copy today at the MAA eBooks Store.

MAA Books Beat: Playing to Learn Game Theory

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Playing to Learn Game Theory appears in the June/July 2014 issue.

Playing to Learn Game Theory

by Steve Kennedy

Suppose the graph depicted in figure 1 represents a network of communities. Two doctors are planning to set up practice in one of the nine communities. A practice will attract all the patients in every town closest to it (closest means in terms of number of graph edges joining the vertices). In the case of a distance tie, each doctor will attract half the patients in the town. Where should the doctors locate to ensure their best result? (They are not conspiring; each doctor is acting independently and in ignorance of the other’s choice.)

Of course, neither doctor, presumably desiring to maximize her practice, would choose one of the degree-two vertices. The other six vertices look equally valuable. Suppose Doctor A chooses vertex 2. Were Doctor B to choose any of vertices 3, 5, or 8, each doctor would get 4.5 towns’ worth of business. If Doctor B chooses vertex 6, she “wins” by gaining five towns to A’s four. (If she chooses vertex 7, the payoffs are reversed and A wins five to four.)

If we conceive of the competition as a game between the two doctors, then this game has no Nash equilibrium. Each doctor can guarantee herself only four-ninths of the available customers.

The example comes from the new MAA ebook, Game Theory through Examples by Erich Prisner. The Doctor Locator Game is one of scores of clever, rich, interesting games described and analyzed in this lively text. There are also scores of apps, linked to the etext, so that the reader can play the games, the best way to understand them. In the doctor game, the reader can, with two mouse clicks, choose vertices to represent the doctors’ choices and immediately see a color-coded graph giving the division and the count.

The example games introduce and exposit all the important concepts of game theory. The Doctor Locator Game, on a different graph, introduces the idea of a Nash equilibrium and explains how to find one. The obvious next question of their existence is answered by the above example.

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.

New eBook: Textbooks, Testing, Training: How We Discourage Thinking

Textbooks, Testing, Training: How We Discourage Thinking

by Stephen S. Willoughby

Willoughby's essay is a gem. It should be in the hands of every young teacher. I wish that I had read it many years ago. I have no doubt that many of his observations and the information he imparts will remain with me for a while. I certainly hope so. A collection of reminiscences from other teachers with their valuable insights and experiences (who could write with such expertise as he does) would make a fine addition to the education literature.

— James Tattersall, Providence College

Steven 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. Steve 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 you, but they ought to make you think. They should spark needed debate in our community. Ultimately this is a human tale with rough parallels to Hardy's Apology; replace "Mathematician's" with "Teacher's" perhaps. Every teacher will sympathize with Steve's frustrations and empathize with the humanity and compassion that animated his life's work and that beat at the center of this book.

Order your copy today in the MAA eBooks Store.

(PDF: $11.00,  POD: $18.00)

More Fallacies, Flaws and Flimflam

More Fallacies, Flaws and Flimflam by Edward J. Barbeau is now available in the MAA eBooks Store. A paperback version will be available in the MAA Store soon.

Here is another collection of Fallacies, Flaws and Flimflam, mostly drawn from the column of this name in The College Mathematics Journal between 2000 and 2008. As in the first volume, there is a variety of items ranging from howlers (outlandish procedures that nonetheless lead to a correct answer) to errors that are deep or subtle often made by strong students. While some are provided for entertainment, others offer a challenge to the reader to determine exactly where things go wrong.

There are many proposals to improve the quality of mathematics education, but they seldom address the need for students to pay careful attention to what they do and to check their work. It is through an engagement with meaning that students can avoid the pitfalls that come too naturally. Accordingly, this volume should be useful to teachers at all levels by giving them examples of flawed work they can use in the classroom. Encouraging students to find where someone else went wrong may help them avoid similar errors in the future.

The items are sorted according to subject matter. Elementary teachers will not find much of use beyond Chapter 1, while middle and secondary teachers will find items in Chapters 1, 2, 3, 7, 8 that they might use. College teachers should find material in every part of the book.

The mathematical topics covered include arithmetic, algebra, trigonometry, geometry, combinatorics, probability, and calculus.