The first edition of Roger Cooke’s *The History of Mathematics: A Brief Course* sits on my bookshelf amid many other general history of mathematics texts designed for the college audience. It is a good, standard text, much like most, but not all, of its shelf mates. When asked to review the second edition of this book I was concerned over what to say about a second edition. After all, how different could it be? The short answer is *very* different. The second edition of Cooke’s *The History of Mathematics: A Brief Course* is a jewel. It is notable for what it includes as well as what it does not. But most importantly, it is a jewel for its presentation.

The majority of history of mathematics texts are ordered chronologically. And to be honest, it is nearly if not completely impossible to present an historical topic without some chronology. But this text is organized first by theme. The text is made up of seven parts broken into chapters. The first part consists of chapters on the origin and prehistory of mathematics, mathematical cultures, and women in mathematics. Part two is on numbers, from counting to combinatorics. Part three is on space up through point-set topology. Parts on algebra, analysis and finally mathematical inferences follow, as well as a section of beautiful color images. Given this organizational structure, several themes, cultures, and people make numerous appearances in different sections. I found this approach refreshing as well as informative.

Of the items included that I found interesting were discussions of Japanese, Australian, New Zealand and Mexican mathematics. These cultures are rarely or only briefly mentioned in typical history texts. Cooke takes pains to explain some of the dead ends taken by mathematicians as well as how the process of mathematics from an earlier era is different than current practices. At times Cooke goes into great detail in order to show the reader the thought process used by the individual in question. He gives information on those individuals who made concurrent or prior discoveries along with information on the individuals traditionally given credit for a discovery. Information about original sources is included in places as well. The references are a combination of new research and old classics now often ignored. These attributes are not commonly found in mathematical history texts and are what make this volume stand out.

What is not included are some of the traditional stories and biographical sketches of big names. This is a history of the process and development of western mathematics, straightforward and honest. It assumes a higher level of readership than the average college math history text, which left me feeling that the author respected my intellect. This text is an excellent choice for an undergraduate history of mathematics course, as well as for anyone wishing to learn about the history and development of mathematics.

Amy Shell-Gellasch is a Faculty Fellow at Pacific Lutheran University in Tacoma, WA. She is actively involved with the MAA and its History of Mathematics SIGMAA as chairperson to several committees. She enjoys researching and promoting the use of history in the teaching of mathematics through editing books and organizing meetings. She received her bachelor’s degree from the University of Michigan in 1989, her master’s degree from Oakland University in Rochester, Michigan in 1995, and her doctor of arts degree from the University of Illinois at Chicago in 2000.