Preface to Second Edition

I was much gratified by the reception of students and teachers to the First Edition of this Math Study Guide. In response to your many suggestions, I have made several improvements and additions. A number of Problems have been added to help solidify the student’s understanding of some of the more complex concepts. I have also clarified the coverage of several topics and added a Chapter on Group Theory and a Section on Hypergeometric Functions. The figures in the Second Edition are now being rendered in full color. Finally, in the first example in Chapter 1, I have updated the format of the NCAA basketball tournament to reflect its expansion to 68 teams.

A (translated) quotation attributed to Leibniz states that “It is unworthy of excellent men to lose hours like slaves in the labor of calculation …” With modern computer software, it is now possible to perform, with remarkabke facility, not only numerical but also symbolic calculations involving algebra and calculus. I am an enthusiastic user of MathematicaTM as an indispensible aid to my mathematical and scientific work. Other symbolic mathematical programs which will provide many of the same befefits are Maple™ and Mathcad™.

A useful adjunct to this book is the Wolfram Demonstration Project. This has been available on the Web at since 2007 and contains a growing collection, approaching 10,000 Demonstrations, mostly on scientific and mathematical topics. This should prove very instructive to the same audience to which this book is addressed. I feel privileged to have been associated with this project. I would also like to acknowledge the assistance of my colleagues at Wolfram Research for their unfailing assistance and encouragement.

Since this little book is simply an introduction to several useful mathematical concepts, the reader will undoubtedly need to seek other sources for more exhaustive coverage of specific topics. There exist, of course, thousands of excellent textbooks and references on mathematics, but I have found it very useful to refer to two online sites as a starting point. One is Wolfram MathWorld at The second is the continually expanding online encyclopedia: Wikipedia, at

My sincere thanks also to my Elsevier editors, Dr. Erin Hill-Parks and Ms. Tracey Miller, for their unfailing cooperation in getting this Second Edition into production.


Ann Arbor

Setember 2012

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