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!