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Maor (formerly, Loyola University Chicago) offers readers many stories about the pentagon and related shapes, and includes a plethora of beautiful, mathematics-inspired illustrations as well as some challenging puzzles and mazes (answers are provided in an appendix). The text also includes chapters that deal with the influence of the pentagon on the built environment--not limited to the Pentagon building in Washington, DC. This seasoned mathematics reader was pleased by actually learning something new from the text: if one shades the area of a pentagon, one obtains a "pentastar." Although pentastar is not a documented word, the denoted shape is seen worldwide, most especially in Christmas decorations. In another intriguing chapter, Maor discusses how a San Diego housewife uncovered four previously unknown types of pentagonal tilings. The chapter discussing the pentagram is also fascinating, including little-known facts about the history of the five-pointed star and how to draw it with a single stroke of the pen. As readers will learn, the pentagram's five points stand for love, truth, peace, freedom, and justice. This is a wonderful book for interested readers at any level.Summing Up: Highly recommended. All readers.

This is a thorough introduction to the subject for undergraduates. There are very few prerequisites (less than in most similar textbooks) because topics such as infinity, countable and uncountable sets, and even the principle of mathematical induction are discussed in an early chapter. Sedaghat (Virginia Commonwealth Univ.) keeps the notion of infinity at the center of his attention in all parts of the book. After covering sequences, he introduces real numbers as "equivalence classes of Cauchy sequences of rational numbers." He discusses infinite expansions of real numbers, illustrating this with Liouville numbers, focusing on several of their properties. Following this, Sedaghat covers the usual topics of differentiation, continuity, and integration. As an illustration of the leisurely, reader-friendly pace adopted here, the mean value theorem makes its first appearance on page 270. The book concludes with a chapter on sequences and series of functions. The main advantage this book offers is its reader-friendly style. Exercises conclude each chapter, but there could be more of them. Solutions are not provided, making self-study more of a challenge. However, the book should be warmly received by interested students of mathematics who have not taken a class on sets and logic.Summing Up: Highly recommended. Lower- and upper-division undergraduates.

In this sequel to The Art of Mathematics: Coffee Time in Memphis (2006), Bollobas employs the same format as in the earlier book. The text presents the reader with a list of 128 mathematical problems in an introductory section. Subsequent parts of the book provide the reader first with hints on how to solve the problems, and then a solution to each one. The problems range in difficulty, some being accessible to a reader with basic mathematical skills, others best left to the devices of a trained mathematician. As implied by the titles of these two books, the problems posed often arose in the context of a tradition that is well established in many university departments of mathematics, whereby the members of the department gather for afternoon coffee or tea and do what they like to do best: discuss mathematics. Such camaraderie among mathematicians can be felt by readers working through the problem solutions, most of which also include a fascinating account of the history of the particular problem and the mathematicians who were involved in discussing it. Bollobas signals the intended use of his book in the preface: "this is not a volume for systematic study, but a book to enjoy" (p. xi).Summing Up: Highly recommended. Lower- and upper-division undergraduates. Graduate students and faculty.

While a previously published book coauthored by Diaconis (Ten Great Ideas about Chance, CH, Jul'18, 55-4074) explores the history of chance in the development of probability theory, this book takes up the notion and runs much further with it. The book begins with examples of ways to shuffle cards, including photographs of the methods, then moves on to such topics as probability distributions, group theory, Markov chains, and hyperplanes. Diaconis (Stanford Univ.) and Fulman (Univ. of Southern California) aim to find card shuffling algorithms that result in a deck whose cards are arranged as randomly as possible. Many of the results in the book are asymptotic. The authors go so far as to suggest that magicians (especially, non-mathematically inclined magicians) would find chapters 12, 13, and 16 useful. The other chapters are presented as self-contained discussions that employ various mathematical techniques. The recommended companions to the text include high-level works such as William Feller's two-volume An Introduction to Probability Theory and Its Applications (1968), Stanley's Enumerative Combinatorics (1997), and more than 50 works written by the coauthors. Thus, certain chapters of this text can be used as scaffolding. Together with the references the book can provide either an introduction to the material or a jumping-off point for further study.Summing Up: Highly recommended. Upper-division undergraduates. Graduate students and faculty.

Wonderful surprises await readers as Abbott (Middlebury College) masterfully interweaves mathematical ideas and theatrical works, building a critical context reminiscent of G. H. Hardy's 1940 work A Mathematician's Apology. The mathematical ideas identified in the plays are from well-known mathematicians such as Euclid, Cantor, Euler, Newton, Russell, Bolyai, Lambert, Gauss, Lobachevsky, Zeno, Frege, Godel, Galileo, Mobius, Klein, Ramanujan, Peano, Turing, and Nash. In turn, the playwrights who have incorporated or modeled the mathematics in dramatic form include Tom Stoppard, Alfred Jary, Stanislaw Witkiewicz, Samuel Beckett, Friedrich Durrenmatt, Michael Frayn, Simon McBurney, Bertolt Brecht, and David Auburn. Abbott performs admirably as a knowledgeable guide, revealing the necessary mathematics as couched in a play's dialogue and/or characters, often in a disguised form that Abbott fleshes out. The only unfortunate aspect is that readers do not have simultaneous access to most of the plays, whether on stage or via video, an absence felt acutely by this reader, whose appetite was whetted by Abbott's descriptions of the mathematical richness in theatrical productions far beyond the accessible versions of Auburn's Proof or Stoppard's Arcadia. Extensive chapter notes, a bibliography, and helpful index support this text. A wonderful gem for anyone interested in mathematics or theater--or both. Encore!Summing Up: Highly recommended. All readers.