Ebook: Mathematica in Action: Problem Solving Through Visualization and Computation

In this third edition of Mathematica® in Action, award-winning author Stan Wagon guides beginner and veteran users alike through Mathematica's powerful tools for mathematical exploration. The transition to Mathematica 7 is made smooth with plenty of examples and case studies that utilize Mathematica's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. Mathematica in Action also emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas. This material enables the reader to use Mathematica to solve a variety of complex problems.

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

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Stan Wagon's long awaited 3'rd edition of Mathematica in Action fulfilled all my hopes. Every page is filled with deep insight into both topic covered and the related Mathematica implementation. Here is just a small sample of some of the things you will read about and learn: 1) How to effectively plot unstable functions. 2) How to speed up animations 3) Techniques for getting the most out of Mathematica's 3D plotting functions 4) Practical advice and examples using Mathematica's dynamic interactivity features (Manipulate, Dynamic, etc.) 5) Beautiful ways to visualize the behavior of Differential Equations. 6) An entire chapter dedicated to optimization and another to computational geometry (I have only skimmed these at this time) Naturally the book revisits a lot material from the 2nd edition but there is enough new material to reward owners of older editions, especially with respect to the latest features of Mathematica 7. The book has a slight leaning towards pure mathematics (whole chapters on such topics as Prime Numbers, Penrose Tiles, Fractals, Pi, Banach-Tarski Paradox and Riemann Zeta Function). Readers whose needs are more firmly rooted in the practical (statistics, finance, image processing, audio processing, parallel processing) might look at some of the other recent Mathematica publications (yes, that is shameful plug!) to fill out their Mathematica knowledge. However, even within the theoretical coverage there is priceless gems of Mathematica know-how that only an author like Stan (who has spent a significant portion of his life using and teaching Mathematica) could provide. Two added bonuses: - Many full color images and plots - The notebooks containing the code (but not text) for every chapter. I wholeheartedly recommend this book!