The Magic of Math is yet another addition to the popular mathematics literature.  There is no magic, really, but lots of fascinating, well-founded results.  General topics include number patterns and operations, algebra, the number 9, counting, Fibonacci numbers, proofs, geometry, pi, trigonometry, the irrationals i and e, calculus, and infinity.  Unlike many books of this type that become esoteric, this one is aimed at an advanced high school/beginning college-level audience.  For example, Benjamin (Harvey Mudd College; The Secrets of Mental Math, coauthored with Michael Shermer, 2006) suggests a very few practical mental math calculation techniques and avoids presenting those that are more difficult than they are worth.  The topics seem to be those often hinted at in courses for these students, but often not explored for lack of time.  The title would be perfect reading for the gifted and talented as a supplement to other course work.  Of course, self-motivated individuals interested in mathematics will enjoy the book too.  It would be a good resource for mathematics teachers seeking some additional spice for their presentations.  The book is well written; graphics are particularly clear; physical format is excellent. Summing Up: Highly recommended. All general readers, high school students, undergraduate students, and mathematics educators.

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

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. (Sept.)