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The Role of This Book

The Scope of the Book

This book is intended to be a complete introduction to Mathematica. It describes essentially all the capabilities of Mathematica, and assumes no prior knowledge of the system.

In most uses of Mathematica, you will need to know only a small part of the system. This book is organized to make it easy for you to learn the part you need for a particular calculation. In many cases, for example, you may be able to set up your calculation simply by adapting some appropriate examples from the book.

You should understand, however, that the examples in this book are chosen primarily for their simplicity, rather than to correspond to realistic calculations in particular application areas.

There are many other publications that discuss Mathematica from the viewpoint of particular classes of applications. In some cases, you may find it better to read one of these publications first, and read this book only when you need a more general perspective on Mathematica.

Mathematica is a system built on a fairly small set of very powerful principles. This book describes those principles, but by no means spells out all of their implications. In particular, while the book describes the elements that go into Mathematica programs, it does not give detailed examples of complete programs. For those, you should look at other publications.

The Mathematica System Described in the Book

This book describes the standard Mathematica kernel, as it exists on all computers that run Mathematica. All supported features of the kernel in Mathematica Version 4 are covered in this book. Most of the important features of the front end are also discussed.

Mathematica is an open software system that can be customized in a wide variety of ways. It is important to realize that this book covers only the full basic Mathematica system. If your system is customized in some way, then it may behave differently from what is described in the book.

The most common form of customization is the addition of various Mathematica function definitions. These may come, for example, from loading a Mathematica package. Sometimes the definitions may actually modify the behavior of functions described in this book. In other cases, the definitions may simply add a collection of new functions that are not described in the book. In certain applications, it may be primarily these new functions that you use, rather than the standard ones described in the book.

This book describes what to do when you interact directly with the standard Mathematica kernel and notebook front end. Sometimes, however, you may not be using the standard Mathematica system directly. Instead, Mathematica may be an embedded component of another system that you are using. This system may for example call on Mathematica only for certain computations, and may hide the details of those computations from you. Most of what is in this book will only be useful if you can give explicit input to Mathematica. If all of your input is substantially modified by the system you are using, then you must rely on the documentation for that system.

Additional Standard Mathematica Documentation

The following are available in printed form for all standard versions of Mathematica, and can be ordered from Wolfram Research:

FilledSmallSquareGetting Started with Mathematica: a booklet describing installation, basic operation, and troubleshooting of Mathematica on specific computer systems.

FilledSmallSquareStandard Add-on Packages: a book describing standard add-on packages available for Mathematica.

Extensive online documentation is included with most versions of Mathematica. All such documentation can be accessed from the Help Browser in the Mathematica notebook front end.

In addition, the following sources of information are available on the web (note that all of these are available at and as well as

FilledSmallSquare the main Wolfram Research website, giving extensive information on Mathematica and its applications.

FilledSmallSquare answers to frequently asked questions about Mathematica.

FilledSmallSquare corrections and updates to this book.

New in Version 3Suggestions about Learning Mathematica