From the reviews of the third edition:
This book is a pleasing potpourri of Mathematica showpieces, picked to show the value of Mathematica for mathematics teaching and investigation... Although there is an introductory chapter explaining Mathematica, it is just enough to get you oriented and the examples go far beyond anything in this introduction. This book may motivate you to learn Mathematica but it won’t teach it to you.
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)
Mathematica in Action is not a guidebook nor a reference manual. It is best described as a project book full of ideas and inspiration for research projects for anyone from high school students to professional mathematicians. It combines real mathematics with sophisticated coding… I highly recommend Mathematica in Action, both for its mathematical content and for its Mathematica content. You don’t have to be a serious Mathematica user to enjoy this book or even use it. You can read it for mathematical ideas and inspiration without touching a keyboard, or, if you are a devotee of a different software system, you might be inspired to translate the examples into your favorite language. —The Mathematical Association of America, September, 2011
“This the third edition of the famous book ‘Mathematica in Action’ in which the author guides beginner as well as veteran users alike through Mathematica’s powerful tools for mathematical exploration … .” (T. C. Mohan, Zentralblatt MATH, Vol. 1198, 2010)