Ebook: Programming in Mathematica - 3rd Ed.

The programming examples in this book serve two purposes. First, they help explain
concepts and show how things fit together to make up complete programs. Second, they are
designed to be more than mere toy programs and should prove useful in their own right. In
developing an example we always use the same method. We start out with a few commands
or definitions that could be entered directly into Mathematica. We then extract the parts
of the computation that are the same regardless of the input and define some functions or
procedures that automate these steps. Then we apply standard techniques to these functions
to make them into a package, adding documentation and certain programming constructs
that make such a package easier to use. The goal is to write a program that would be
useful not only to its author, who knows how it works, but also to other people. Finally,
we might add a few more functions to the package or look at alternatives to what we did so
far. In Chapter 1 these steps are described in full detail. Later on, when we concentrate on
other aspects, we assume that you are familiar with these basic concepts and we shall not
mention all the steps in detail. All the programs developed in this book are either part of
the standard Mathematica distribution from Wolfram Research, or they are available free
in electronic form.
This book is no replacement for the Mathematica manual "The Mathematica Book"
[40]. I do not expect that you have read everything in the Mathematica book, but you
should have some basic experience with Mathematica before reading this book. Single
commands are usually used without detailed explanation. You can use the index in the
Mathematica book to look up a description of a command that you did not know about. We
also give references to places in the Mathematica book where you can find explanations of
concepts that are particularly relevant to a topic in this book. You should always tum to the
Mathematica book for explanations of features that are assumed known here, but that you
have not used yet. The place to look for an explanation of all variants, defaults, or options
for a particular command is the reference guide in the back of the Mathematica book. All
this information is also available in electronic form and can be accessed through the Help
Browser of Mathematica.