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Book review

Author(s) Kaufmann, S.
Title MATHEMATICA als Werkzeug
Publisher Birkhäuser
Year of publication 1992
Reviewed by Bazil Pârv

Together with DERIVE from Soft Warehouse Inc., Maple from Waterloo Maple Software, and the newcomer AXIOM from IBM and NAG, Mathematica (produced by Wolfram Research) is one of the most well-known computer algebra programs. The Mathematica software is a commercial one, and there exists several books and documentations related to it.

This book, with the sub-title "An Introduction with Examples of Application" can be considered as a good Mathematica tutorial for native German readers.

The book is structured in three parts, covering basic aspects, structural aspects and programming in Mathematica's own programming language. Two lists of references (first dedicated to computer algebra, second on Mathematica literature) and two indexes (Mathematica predefined objects and general terms) can be found at the end of the book. Every section ends with a review of Mathematica concepts discussed, given in table form, and with proposed exercises.

First part, the basic Mathematica concepts and skills contains: introduction, help, pocket calculator, symbolic computer, graphics, list processing, graphic programming, other tools (more graphics and sound; complex numbers; sums, products, series; data analysis and interpolation; mathematical functions; polynoms; linear algebra and programming); files, resources and configuration.

The second part of the book, dedicated to syntactic and semantic aspects in Mathematica covers: expressions; patterns; transformation rules and definitions; evaluation; local and global variables, contexts and packages; text, formats and messages.

The last part, programming in Mathematica, discusses: procedural, recursive, functional, and rule-based programming; program development, testing and debugging; numerical aspects; an example of large computing: RSA-Algorithm.

Computer algebra programs are now modern tools for studying and solving various problems which use mathematical modelling. This book, well produced, with various illustrations, and many examples gradually presented, can be very useful for computer algebra users: engineers, researchers in pure and applied mathematics, students. The price, also very convenient, can be a major argument in achieving it.