Due to their ever-increasing capabilities, today’s computer algebra systems, such as Mathematica and Maple, play an increasingly important role in mathematical computing. To reflect this rising significance, the authors have written a series of books introducing the use of such systems to novices in the field. The first volume in this series [1], published in 2011, was devoted to Maple. Now the corresponding text about Mathematica has appeared.

The books are not introductions to the tools themselves. Rather, they are focused on mathematical computing using computer algebra systems in a generic way, with Mathematica and Maple as the means to this end. Therefore, it is not surprising to see that the books are very similar; in fact, in many sections, the texts are literally identical, except for the concrete examples that reflect the syntax of the tool in question. Unfortunately, this means that the authors have not used the opportunity to elaborate on each system’s strengths (and weaknesses). Rather, they have only concentrated on the basics, where both systems offer quite similar functionalities. This is certainly useful for novice users of such software packages, but limits the value of the book for more advanced readers.

Three main chapters form the core of the book. In the first chapter, the authors talk about using a computer algebra system like Mathematica for problems in number theory, with the term “number theory” used here in a very broad sense. At the same time, this chapter serves as a brief introduction to using Mathematica, including the basics of its command syntax and some fundamental programming techniques. Chapters 2 and 3 are devoted to calculus and linear algebra, respectively. A short fourth chapter describes some of the visualization capabilities of Mathematica and concludes the book. The mathematical content of the chapters is, for the most part, elementary and written in a style easily understandable by nonspecialists.

As the second volume of this mini-series, it is quite evident that the authors started with the manuscript of the first book and made small changes here and there where unavoidable, replacing all content specific to Maple with the corresponding statements about Mathematica. One can do that of course, but such an approach requires extremely careful proofreading of the final result. Unfortunately, in this case, it was not careful enough. There are still occasions where Maple is discussed instead of Mathematica, and there are plenty of misprints, particularly in the Mathematica code examples. None of the errors are really severe, but for inexperienced users, the main target group of readers, this can be most irritating. Regrettably, at the time of writing this review (February 2013), the joint web site devoted to updates and corrections for the series contained only a placeholder for this book, without any information whatsoever.

In summary, the concept devised for these books has the potential to produce a very good introduction for beginners to this interesting and important topic. However, the actual implementation of the concept leaves a certain amount of room for improvement. Readers will definitely hope for a possible future second edition, with all of these minor errors resolved.