Promotions - Choice's Outstanding Academic Titles 2021 -

Classifying mathematics as either serious or recreational makes sense only upon recognizing said designations as somewhat subjective, at best provisional, and--as is key here, not necessarily mutually exclusive. Indeed, the material in this book lives on the intersection: a chess book written in a similar spirit would contain fun, short brilliancies played by great masters and accompanied by sardonic annotations. Other books have packaged similar content as problems to be solved, followed by appendixes full of answers, and there is little doubt that the integrated presentation here actually makes spoilers nearly impossible to avoid. Indeed, by design, the book doesn't generally call on readers to solve any problems themselves. Stanley (Univ. of Miami) posits a dialogue in which a fictional, slightly pompous professor challenges his eight fictional, genius-level, and diverse students and rarely stumps them all. The amusing conversations that ensue teach valuable problem-solving tricks that mathematicians use constantly, yet rarely try to systematize. Although the answers here generally arrive immediately, they come tersely, sometimes more like hints, so that a careful reading--not so passive after all--will actually demand mental effort much like digesting any theorem/proof book. A few old saws recur in the text, but they serve as points of departure for genuine novelties.Summing Up: Highly recommended. All readers.

In this textbook Krantz (Washington Univ., St. Louis) provides a complete introduction to differential equations, but with an updated feel. The text covers the basic theory, and also includes chapters on Fourier analysis and wavelets, and a brief final chapter on partial differential equations. Although he presents the material in a traditional way, the author has taken pains to include plenty of current examples and visual aids likely to appeal to readers learning the subject for the first time. Supporting the book's use as a course text, Krantz provides many exercises at the ends of sections and chapters. The problems are identified as appropriate for use at three different levels: "basic," "challenging," and "discussion." One additional feature that students will surely find enjoyable are the "Math Nuggets" interspersed throughout the book. These are small boxed snippets of mathematical history, each corresponding to the subject matter of its surrounding text. This device allows for readers to take a quick break from the material at hand to consider it in historical perspective. Overall, this textbook offers a thorough introductory investigation of differential equations, emphasizing Fourier analysis and wavelet theory and addressing the needs of undergraduates.Summing Up: Highly recommended. Lower- and upper-division undergraduates, graduate students, and faculty.

Being a lover of mathematics and art, this reviewer found the work under review to be a wonderful and fascinating book. Each chapter features contributions from artists who attended an "Illustrating Mathematics" workshop program, as described in the book. Every chapter highlights the use of a different material and/or technology for the illustrations shown, and each contributor explains in detail the processes he/she used to create the illustration, as well as the mathematics involved. All told, the book shows the variety of materials and methods that can be exploited for illustrating mathematics. The illustrations are absolutely beautiful, while the math concepts illustrated include fractals, prime numbers, groups, the Klein bottle, and 3-manifolds, to name a few. The textual explanations are easy to follow, and contributors even include the mistakes that were made along the way, a wonderful gesture enabling readers to learn from their successes and failures, and try to create such illustrations on their own. Anyone interested in mathematics at any level will find this book captivating.Summing Up: Highly recommended. All readers.

In a nota bene at the beginning of this text, Sulzer (Columbia Univ. Medical Center), who also performs and composes music as David Soldier, asserts that this is not a "pop science" book of the easy-reading variety. What readers come to discover, however, is that it is exactly the sort of book that science written for a general audience should be--accessible on multiple levels from the neophyte to the expert, engagingly written, and informative in a way that stimulates curiosity and prompts further investigation. In addition to his main text covering the mathematics and neuroscience of music (especially the mathematics of pitch, how the brain processes rhythm, etc.), Sulzer includes an array of textboxes throughout the book, exploring the actual mathematical equations involved in a way that is comparatively friendly even for those who find higher-order mathematics intimidating or inscrutable. The book also features a "playlist" of relevant examples, in which Sulzer playfully crosses a variety of genres and traditions. Thus, listening to some of the recommended sources may enhance the experience of reading the work.Summing Up: Highly recommended. Lower-division undergraduates. General readers.

The Raven's Hat is a great book for readers who enjoy games and logic puzzles. Peters and Meinshausen present eight well-known games and explore why they appear as unsolvable problems, then cleverly use mathematics to reveal underlying structures that make the games solvable. Glimpses of the history of the games are provided, along with variations of some of them. The games presented--including identifying hat colors, finding IDs in boxes, the dovetail card trick, animal stickers and matching, the fallen picture, and common locations on two globes--are enjoyable to read about and can also be performed in front of audiences. The mathematics involved--Hamming Codes, permutations, sequences, cyclic groups, information theory, projective geometry, eigenvalues, and algebraic topology--is conceptually varied and ranges in difficulty from one game to another, but the authors make it accessible through a simplified format and by using minimal notation. To help the general reader, two appendixes in turn summarize the mathematical notation being used and discuss the key mathematical concepts. For the advanced reader, a third appendix provides the specific mathematical details behind some of the solutions. A helpful reference list and index are also included. Again, this is a fun--indeed fantastic--book for anyone who enjoys games, logic puzzles, and especially mathematics.Summing Up: Highly recommended. All readers.