From the reviews of the third edition:
The book is full of interesting things. The first half focuses on visualization and the math is relatively elementary (nothing beyond multivariable calculus). The second half works on much harder problems. —MAA Reviews
“Beginners will benefit from the book as will more experienced Mathematica programmers as the explorations build from simple introductory concepts … . The best feature of the book is that it teaches via interesting examples. … The writing is remarkably good. … The book contains a good number of color illustrations and is rich in Mathematica output. … interesting explorations with clear and engaging writing are hard to come by. I’m delighted to have this book in my collection.” (Playing with Mathematica, June, 2011)
From the Back Cover
Case studies ranging from elementary to sophisticated are provided throughout. Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, an illustration of the Banach—Tarski Paradox via hyperbolic geometry, new and surprising formulas for p, the discovery of shadow orbits for chaotic systems, and the use of powerful new capabilities for three-dimensional graphics. Visualization is emphasized throughout, with finely crafted graphics in each chapter.
Wagon is the author of eleven books on mathematics, including A Course in Computational Number Theory, named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of Mathematica, including the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory.
From reviews of the second edition:
"In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics."
—Richard Walker, The Mathematical Gazette
"The bottom line is that Mathematica in Action is an outstanding book containing many examples of real uses of Mathematica for the novice, intermediate, and expert user."
—Mark McClure, Mathematica in Education and Research