Cambridge University Press: New York, 1998. xii + 564 pp. Paper: ISBN 0-521-57586-9. $29.95. Cloth: ISBN 0-521-57586-9. $74.95.

This is a comprehensive math workbook for anyone who needs to refresh his or her math skills. It is designed for individuals who have been exposed to these math topics but need additional help on techniques and methods for solving problems. The workbook starts out at a very elementary level: discussing basic algebra, "a + b means adding a to quantity b." But by the end of the workbook, the algebra of complex numbers is described with several examples and problems. Algebra and trigonometry, sequences and series, differential and integral calculus, and complex numbers are all covered. The table of contents and index are very detailed and thorough, allowing one to easily find selected math topics for review.

The value of this book, like that of all workbooks, to the reader depends on whether the reader is willing to complete the exercises. To encourage the reader toward this goal, the author uses a very informal writing style, a style that is referred to in the book as "friendly and gentle". To further enhance this style, many of the figures are hand drawn. As I read the discussions and worked several of the exercises, I found this approach likeable at times, but at other times it seemed to be unnecessarily wordy.

The workbook starts out with basic algebra, reviewing the number system and basic operations. Equations and graphs, including quadratic and simultaneous equations, are described next. The discussion on rearranging equations to solve for different quantities is particularly clear. Graphs are employed throughout the workbook as an integral part of the development. Functions, what they are, and how to work with them are described, and a detailed summary of exponential and log functions is included.

Trigonometry, sequences, and series are considered next. Common trigonometric relations such as the sine and cosine rules, sines and cosines of a sum and difference of two angles, and inverse trigonometric functions are described well, and whenever appropriate, figures are used in the explanation. Straightforward descriptions of arithmetic and geometric progressions and binomial series are supported with several examples.

A review of differential and integral calculus starts with the basics and ends with implicit differentiation and solving differential equations by the method of separation of variables. These and other topics are covered with an applications-oriented emphasis. Only background that is essential in understanding calculus is covered; the bulk of the discussion consists of examples of differentiation and integration of real functions.

The final topic of this workbook is the algebra of complex numbers. It is concise, and understandable, suitable for someone who has never been exposed to complex numbers.

This book is intended to be either a refresher workbook or a supplement to a course. Considering the thoroughness of the explanations and solutions to the exercises, this book is particularly useful for the practical individual who is interested in the mechanics of solving problems. For example, while working through the problems, I reviewed the method of partial fractions, which I have not used in quite a while, and found both the discussion and the problems helpful. Individuals who consider themselves intimidated by mathematics and who learn best by repetitive practice and seeing several complete solutions to examples will benefit the most from this book. The author has admirably accomplished her stated intentions.