The Mathematica GuideBook for Programming

Abstract

This volume is the first one in a series of four books on the Mathematicaprogramming language. It is best suited for those who already knowthe basics and want to learn the sophisticated tricks of the advancedprogramming and to use Mathematica up to its full capacity. The author'sphilosophy is to use the high level Mathematica commands (such asMap, MapThread, Apply, NestList, FoldList) whenever possible, avoidingthe do, while, for loops common to most languages. This leads tovery short programs and even one single command, which in many casesoccupies several lines of text, can carry out very involved tasks.In such cases, translation of the Mathematica programs into otherlanguages such as C may be a very time consuming task. The book addressesmany features of human-computer interaction. Obviously the basicquestion is how to make the computer work harder for the benefitof the user. Here I found discussions of essential mathematical questionsthat I have not seen elsewhere, such as printing of tables of basictrigonometric identities (e.g. \cos(π/2 +x) = - \sin(x), \sin(\arccosz) =\sqrt{1-z^2}) graphing Riemann surfaces of multivalued functionsand a careful analysis of branch cuts of functions, symbolic matrixalgebra etc. Quite fantastic was also to see how one can use a reservoirof strings to construct crosswords, for instance one could use thenames of built-in Mathematica commands. This book is one of the mostvaluable sources for the advanced users of Mathematica. Since Mathematicais now used in all mathematical institutes, all the science/engineering/computerscience/mathematics libraries should have this book and its companionvolumes.