The Magic of Math

Starred review from June 22, 2015
Pizza and poker hands, ice cream and “immortal” rabbits—these items aren’t typically to be found in math books, but Benjamin (The Secrets of Mental Math), professor of mathematics at Harvey Mudd College, welcomes them all with open arms in this positively joyful exploration of mathematics. His approach is simple and refreshingly practical. A look at number patterns introduces tricks for carrying out “fast mental calculations”; a chapter on the properties of the number nine reveals methods for easily calculating calendar dates. Without ever using the word “statistics,” Benjamin deftly covers the basics of calculating the odds of having a winning lottery ticket or poker hand. Whether figuring out compound interest, using trigonometry to determine the height of a tree, or employing calculus to work out a shortest possible walking route, each topic is presented in the clearest, simplest way possible. There’s even room for explorations of more abstract concepts such as pi, imaginary numbers, and infinity. Benjamin’s accessible book expands on video lectures on “The Joy of Mathematics” that were created for the Great Courses series, and its energy and enthusiasm should charm even the most math-phobic readers. Agent: Karen Gantz, Karen Gantz Literary Management.

July 15, 2015
An enthusiastic celebration of the beauty of mathematics. Benjamin (Mathematics/Harvey Mudd Coll.; co-author: The Fascinating World of Graph Theory, 2015, etc.) brings to this book the stage presence of a video lecturer who has contributed math programs to the Great Courses series. Indeed, the book is a distillation of one of those courses and is filled with the patter, puns, and occasional poetry of the stage performer. Presumably because he also loves magic and has learned tricks of the trade, the author compares the workings of math to magic. This is misleading because, as he well acknowledges, math is based on logic and proofs-not magic at all. Benjamin does a fine job of explaining the variety of proofs that math uses (by contradiction, induction, etc.). He begins with a chapter on numbers, number patterns, and tricks on doing mental arithmetic. He then moves on with what is essentially a high school syllabus on algebra, Euclidean geometry, and trigonometry, with a few chapters on Fibonacci series, pi, and probabilities. The author provides several different proofs of well-known results like the Pythagorean theorem. The going gets tougher as Benjamin moves on to more advanced math in the form of complex numbers, e, and calculus. Here, the author is more skilled at telling rather than showing as he introduces how e, for example, appears in odd places and amazing equations. He does a better job at explaining differential (but not integral) calculus, but he devotes much of that chapter to how to differentiate certain functions-a nice tutorial for a test crammer, perhaps, but not of interest to general readers. A final chapter on infinities is better articulated and interestingly shows how performing a few illegal tricks with infinite series can yield astonishing answers. Forget magic. Benjamin delivers a primer generously filled with insights and intuitions that make math approachable, interesting, and, yes, beautiful.

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September 1, 2015

Some mathematical theorems and proofs are so clever as to seem almost magical, and some properties of numbers can be the basis of magic tricks. Many teachers of the subject think about compiling their favorite examples in a book. Benjamin (Smallwood Family Professor of Mathematics, Harvey Mudd Coll.; The Art of Mental Calculation) has done exactly that in this well-written, entertaining volume. He starts, as most writers do, with results from arithmetic and number theory, including a very nice chapter on Fibonacci numbers. He then moves on to algebra, geometry, and trigonometry. Unlike many authors writing for the interested layperson, he is not afraid to show the necessary calculations and formulations, nor to go into more advanced topics including the calculus and transfinite arithmetic. VERDICT This solid reference for teachers seeking interesting classroom examples (and jokes) could easily lure a student into further studies in mathematics.--Harold D. Shane, Mathematics Emeritus, Baruch Coll. Lib., CUNY

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