This book has two primary uses, as a reference for the Combinatorica extension to Mathematica or as a textbook in a course in combinatorics and graph theory where Mathematica is extensively used. In both cases it is the best resource on the market. Combinatorica is an extremely powerful package that allows for very sophisticated operations to be performed in combinatorics and on graphs. However, there is no coverage of other areas of discrete mathematics.
The structure of the book is that it is split up into sections. For each section, there is a short textual description of the operation, a section of code illustrating the appropriate function(s) and the output from that code. The output is sometimes in the form of a textual listing and at other times an actual diagram. A complete listing of the functions and their actions is given in an appendix.
While this book is not one that could be used in a general course in discrete mathematics, it is an exceptional example of one that fills a niche to perfection. If you have any interest in doing combinatoric or graphing operations with Mathematica, then you have to look no further.
Published in Journal of Recreational Mathematics, reprinted with permission.
