A History of Mathematics; Brief Version, Victor J. Katz, 2004,560 pp., $85.33. ISBN 0-321-16193-9. Pearson Education, Inc.(800)-947-7700, http://www.aw-bc.com/
Victor Katz’s goal was to write a book which “concentrates on the history of those topics typically covered in an undergraduate curriculum or in an elementary or high school.” Although difficult choices had to be made in downsizing his excellent book, A History of Mathematics: An Introduction, the result is a very fine book that serves its audience well.
The first chapter examines the contributions of the Egyptians and the Babylonians. Each culture is studied separately, allowing an opportunity to compare and contrast their accomplishments. Chinese and Indian mathematics each receive a separate chapter in this book. Together with the chapter on the mathematics of the Islamic world, these three chapters provide a very strong introduction to non-western mathematics.
Three chapters are devoted to Greek mathematics and another three chapters to those topics in high school mathematics that might be classified as precalculus mathematics. Chapter 11 introduces the calculus of the seventeenth century. The remaining nine chapters of the text carry the history of mathematics into the twentieth century. Most of this material would be more appropriate for those who plan to teach on the college level, although selected topics could be incorporated into a course for pre-college teachers.
I integrate problem solving into my course through the use of historical problems. This book contains a large and varied collection of problems. Answers are given to selected problems. The author also includes a short appendix to facilitate the use of the textbook for teachers of mathematics including a list of topics and the relevant sections of the text where they are covered.
I mourn, as I am sure Dr. Katz does, the disappearance of all of those wonderful pictures of stamps with mathematical themes that he used in his previous book. However the final product is a truly useful textbook about the history of mathematics for teachers.
Robert McGee, Professor Emeritus, Cabrini College ,Radnor, Pa. 19087