The Mathematica GuideBook for Programming [Hardcover]

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Now then - one of the advantages of Mathematica is that it is supported by extensive documentation - both online and in print. Trott's Guidebooks (set of four books - Programming, Graphics, Symbolics and Numerics) is an impressive addition to this literature. These books stand out among the rest of the literature in several respects:

1. The whole set put together must be the biggest Mathematica book around.

2. The books teach Mahtematica through examples. But unlike most other books, the examples are not toy-examples; they are applications of Mathematica to non-trivial mathematical problems. Not only do they teach you Mathematica, they also teach you mathematics!!

3. The above mentioned non-trivial mathematical problems and results are very well referenced. Each chapter ends with an extensive bibliography - usually several hundred references. This further enhances the value of the Guidebooks as books on mathematics, not just Mathematica.

4. Each book comes with a DVD containing the WHOLE SET (yup - you heard it - all four books) as Mathematica notebooks. You can open these notebooks in Mathematica, edit them and experiment with them.

5. There is a piece of Mathematica code on the web-page that incorporates the whole set on DVD into the Mathematica help browser. This feature is just brilliant!!

I purchased the Programming Guidebook with considerable hesitation; to all appearances the Guidebooks are intended for the discerning cognoscenti, whereas I am very much a Mathematica novice.

The Programming Guidebook turned out to be a pleasant surprise: while there is a vast amount of material that would benefit the expert, it is also a careful and patient instruction book for the beginner.

Mathematica is a complex system; at first acquaintance it appears to be a bewildering collection of expressions and ad hoc programming styles. This book is a pedagogical masterpiece: it brings order to this seeming chaos by revealing the underlying framework. Topics are organized into comprehensible groups and the author focuses on each in detail.

Some parts that particularly appealed to this reader:

The section in Chapter 1 on Solutions to "What you always wanted to compute". This is a wonderfully whimsical list of problems that the author has gathered over many years and each is backed up by several references. This section is an unexpected delight and following up on the references provides an education in itself. The very first paragraph in Chapter 2, where the author provides one of the keys to unraveling Mathematica. The section in Chapter 3 on lambda calculus, which clarifies the use of pure functions. The entire collection of topics in Chapter 4 on meta-Mathematica.

Chapter 5 deals with the topic that is probably most foreign to those like myself used to traditional languages, (Fortran, C, C++); the treatment in this chapter is outstanding. Chapter 6 shows how Mathematica uses lists as a unified approach for vectors, matrices and tensors. Be aware however, that the book does require a fair background in mathematics or physics, (bachelor's or above).

It is clear that this is a labor of love; the author is deeply excited by the capabilities of Mathematica, and does his best to share his enthusiasm with the reader. The result is an inspiring book that is richly deserving of high praise. To fellow novices aspiring to use Mathematica gainfully, I can recommend the Programming Guidebook without hesitation. With study and patience, this Guidebook will dramatically enhance your ability to use Mathematica successfully.

I still believe my path to skillful use of Mathematica is going to be a long one, but it does not matter - with a guide like this, I expect to enjoy the journey immensely.

Michael Trott's skill, knowledge and enthusiasm regarding the use of

Mathematica in scientific research is extraordinarily impressive, as I

have found to my considerable

benefit from some extended professional contact.

His infectious passion is manifested very strongly in this Guidebook

(devoted to programming, with the subsequent three volumes --- already

available --- being

concerned with the topics of graphics, symbolics and numerics).

Chapter 1 ("Introduction to Mathematica")

alone contains close to twelve hundred

references to the scientific literature (mostly physics, mathematics

and engineering

in nature), pertaining to one application or another --- many of an

engaging/intriguing nature.

Each chapter includes a set of exercises and a detailed solution

proposal for each exercise.

It certainly behooves each reader to peruse the Table of Contents and the

Index to find the topics of most interest to him or her. Much valuable time

for the computer practitioner

can certainly be spent with simple browsing of this impressive work of

devotion and erudition.

Desirably, some of the virtuosity in the use of Mathematica, abundantly

exhibited here by Trott, can be acquired by the reader.