The Mathematica book. Version 3.0. 3rd ed. (English) Zbl 0878.65001

Cambridge: Cambridge Univ. Press. Champaign, IL: Wolfram Media. xxiv, 1403 p. (1996).
[For the 1st edition (1988) see Zbl 0671.65002).]
The software program Mathematica combines symbolic and numerical calculations, plots, graphic programming, list calculations and structured documentation into a unified, interactive environment. This book written by the creator of Mathematica, is intended to be a complete introduction to Mathematica and covers Mathematica version 3. It describes essentially all the capabilities of Mathematica and assumes no prior knowledge of the system.
This book is divided into three parts followed by a formula gallery, graphics gallery and an appendix. In Part 1, a tour of Mathematica package is presented. The purpose of the tour is to show a few of Mathematica’s capabilities concentrating only on general features: Some of the topics covered are: Running Mathematica, symbolic and numeric mathematics, functions and programs, lists, graphics and sound, and files and external operations. The internals of Mathematica are also discussed.
Part 2 describes the basic structure of Mathematica language, with which one can extend Mathematica, adding one’s own functions, objects or other constructs. This part shows how Mathematica uses a fairly small number of very powerful symbolic programming methods allowing to build up many different kinds of programs. The topics covered are: Expressions, functional operations, patterns, transformation rules and definitions, modularity, strings and characters, textual input and output, the structure of graphics and sound, manipulating notebooks, files and streams, mathlink and external program communication and global aspects of Mathematica sessions.
Part 3 discusses more advanced Mathematica topics and goes through the various mathematical functions and methods that are built into Mathematica. Topics like numbers, mathematical functions, algebraic manipulation, manipulating equations, calculus series and limits, linear algebra, numerical operations on data and functions are discussed here.
The formula gallery shows a few examples of the output from Mathematica. The graphic gallery displays a few images that are generated by Mathematica.
Finally the appendix gives a definite summary of the complete Mathematica system and is intended for reference purposes. Details of every feature of Mathematica are described here. The index is very exhaustive and includes not only specific phrases and words from the text, but also concepts and topics related to them.
This book is well written and is highly useful to all users of Mathematica.
Reviewer: T.C.Mohan (Madras)


65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
68W30 Symbolic computation and algebraic computation
68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
65Y15 Packaged methods for numerical algorithms