Everyone reading these reviews will be (or at least should be!) familiar with the collections of mathematical essays penned by Martin Gardner. He is far from alone in this field, however, and some readers may be unaware of the other authors in this arena . Naturally, quality varies greatly. Happily, newcomer Brian Hayes has scored a hit with his first collection.

*Group Theory in the Bedroom* collects 12 essays that originally appeared in *American Scientist* , with one exception, which first saw print in *The Sciences* . For this edition, Hayes has added “afterthoughts” to each essay, supplementing the material with reader responses and/or bringing the coverage up to date. This was Gardner's custom as well, and it should be standard practice, as the net result is having a slew of experts review each essay.

Part of my expectation in picking up a book of mathematical essays aimed at a general audience is that I will find material outside of my own area of expertise that I can weave into the classes I teach, expanding my set of interesting examples, applications, and anecdotes. Hayes succeeded in meeting this expectation. Examples include

- how randomness plays an important role in Ethernet,
- the way in which the genetic code appears to be optimized,
- a reference to modeling an arms race with differential equations

[While I was a student at Franklin and Marshall College (and the Soviet Union was collapsing), Professor Bernard Jacobson presented these equations to us and showed how the end result was bankruptcy for the weaker economic power. This example may once again be timely as America’s expenditures for “The War on Terror” escalate.]
- an application of logarithms in measuring the wide range of “deadly quarrels” from a single homicide to WWII,
- using Farey addition to generate all rational numbers (some intriguing references are provided), and
- a way in which base 3 can be considered the most efficient.

[This chapter, entitled “Third Base,” was of great interest. The diverse examples for which base 3 is preferred will be worked into my discrete math class, where I only discussed base 2 and base 10 in the past.]

Roughly half of the essays appealed to me. This is intended as a positive comment. I don’t own any collections of essays (or short stories or even a CD) for which *every* piece is a joy. The ones that were duds were due mainly to my lack of interest in the topics. Another reader might find the other half appealing, but nearly all readers ought to find something of interest.

Mathematicians may well wish more equations were presented, as they are very rare and proofs are completely absent. However, ample references are provided at the end for those wishing for greater rigor. Hayes himself admits, “I’m not a mathematician, but I’ve been hanging around with some of them long enough to know how the game is played.” [p.232] Perhaps this is why a bias toward applied mathematics is present, with essays addressing topics in engineering, economics, biology, and geography. But a bit of pure mathematics does appear.

Stylistically, some of Hayes’s essays remind me a bit of Isaac Asimov’s columns for the monthly *Magazine of Fantasy and Science Fiction*. Few of Asimov’s pieces dealt with mathematics and when they did he complained that he nearly always received letters from mathematicians telling him how he blew it!

Based on Hayes’s first collection, I look forward to seeing more. It is both easily accessible to the layman and enjoyable to the professional. And for those of you intrigued by the provocative title, the titular final essay deals with the symmetry group for mattress flipping.

Craig Bauer is an Associate Professor of mathematics at York College of Pennsylvania. He also serves as the editor-in-chief of *Cryptologia* , a quarterly journal devoted to all aspects of cryptology.