By Dale Farris, Vice President
Golden Triangle PC Club
January 2005

General Overview

As both a highly readable tutorial and a definitive reference for over a million worldwide users of the renowned math software program, Mathematica, this book covers every aspect of Mathematica. It is an essential resource for all users of Mathematica, from beginners to experts. This expanded fifth edition presents Mathematica Version 5 for the first time and is important for anyone interested in the progress of advanced computing.

Included in this new edition are the following:

Visual tour of key features
Practical tutorial introduction
Full descriptions of 1,200+ built-in functions
Thousands of illustrative examples
Easy-to-follow descriptive tables
Essays highlighting key concepts
Mathematica language tutorial
Guide to symbolic programming
Introduction to document-centered interfaces
Guide to the MathLink API
Notes on internal implementation
Index with 10,000+ entries

"The software program Mathematica that this book is based on is a programming language, a calculator, a composite of subtle mathematical algorithms, and a program that is more powerful than any application that has yet been devised for it. Even to a user who has just begun to toy with its most accessible surface powers, it is uncanny." (New York Times)

At a technical level, Mathematica is widely regarded as a major feat of software engineering. It is one of the largest single application programs ever developed, and it contains a vast array of novel algorithms and important technical innovations. Among its core innovations are its interconnected algorithm knowledge base, and its concepts of symbolic programming and of document-centered interfaces.

Click here for a review of the software program Mathematica 5.1.

Scope of the Book

This book is intended to be a complete introduction to the program 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.

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.

The book describes the standard Mathematica kernel, as it exists on all computers that run Mathematica. Most major supported features of the kernel in Mathematica v. 5 are covered in the book. Many of the important features of the front end are also discussed.

The book serves its customer best when used in conjunction with the program it is based on, Mathematica 5.1. Author Wolfram includes super suggestions about learning Mathematica that will help those new to the program. These suggestions cover getting started with the program, solving a complete problem, the principles of Mathematica, how using Mathematic will change the way you solve problems, how to use the program to write programs, and suggestions regarding how best to approach learning the entire Mathematica system.

All the examples in this book, literally thousands, were generated by running an actual copy of Mathematica, v. 5. If you have a copy of this version, you should be able to reproduce the examples on your computer as they appear in the book.

Most of the examples in the book are chosen so as to be fairly quick to execute. Assuming you have a PC with a clock speed of over about 1GHz, then almost none of the examples should take anything more than a small fraction of a second to execute. If the calculations do take longer than this, there is probably something wrong. Section 1.3.12 of the book describes how to stop the calculation.

Table of Contents

The thirty-seven (37) chapters are organized into three (3) parts, and include the following:

Part 1 - Practical Introduction to Mathematica

Ch 1.0:   Running Mathematica
Ch 1.1:   Numerical Calculations
Ch 1.2:   Building Up Calculations
Ch 1.3:   Using the Mathematica System
Ch 1.4:   Algebraic Calculations
Ch 1.5:   Symbolic Mathematics
Ch 1.6:   Numerical Mathematics
Ch 1.7:   Functions and Programs
Ch 1.8:   Lists
Ch 1.9:   Graphics and Sound
Ch 1.10: Input and Output in Notebooks
Ch 1.11: Files and External Operations
Ch 1.12: Special Topic: The Internals of Mathematica

Part 2 - Principles of Mathematica

Ch 2.1:   Expressions
Ch 2.2:   Functional Operations
Ch 2.3:   Patterns
Ch 2.4:   Manipulating Lists
Ch 2.5:   Transformation Rules and Definitions
Ch 2.6:   Evaluation of Expressions
Ch 2.7:   Modularity and the Naming of Things
Ch 2.8:   Strings and Characters
Ch 2.9:   Textual Input and Output
Ch 2.10:  The Structure of Graphics and Sound
Ch 2.11:  Manipulating Notebooks
Ch 2.12:  Files and Streams
Ch 2.13:  MathLink and External Program Communication
Ch 2.14:  Global Aspects of Mathematica Sessions

Part 3 - Advanced Mathematics in Mathematica

Ch 3.1:   Numbers
Ch 3.2:   Mathematical Functions
Ch 3.3:   Algebraic Manipulation
Ch 3.4:   Manipulating Equations and Inequalities
Ch 3.5:   Calculus
Ch 3.6:   Series, Limits and Residues
Ch 3.7:   Linear Algebra
Ch 3.8:   Numerical Operations on Data
Ch 3.9:   Numerical Operations on Functions
Ch 3.10: Mathematical and Other Notations

In addition, the book has thirteen (13) appendixes, including

Appendix 1 -  Basic Objects
Appendix 2 -  Input Syntax
Appendix 3 -  Some General Notations and Conventions
Appendix 4 -  Evaluation
Appendix 5 -  Patterns and Transformation Rules
Appendix 6 -  Files and Streams
Appendix 7 -  Mathematica Sessions
Appendix 8 -  Mathematica File Organization
Appendix 9 -  Some Notes on Internal Implementation
Appendix 10 - Listing of Major Built-in Mathematica Objects
Appendix 11 - Listing of C Function in the MathLink Library
Appendix 12 - Listing of Named Characters
Appendix 13 - Incompatible Changes since Mathematica Version 1

Target Readers

This book is essential for anyone new to Mathematica. Although the software program does contain a super guide to using the program, author Wolfram goes much further in describing and explaining the program in this supplemental book. All teachers of math who use Mathematica should seriously consider adding this sound reference to their library of materials. Students new to the program will also find this book to be a super resource, while those more experienced in using the program will appreciate the book's many advanced discussions.

Book Contents

1,488 pages; hardcover; about the author; about Mathematica; features new in Mathematica v. 5; the role of the book; suggestions about learning Mathematica; thousands of examples; tons of figures; tons of code examples; appendixes; extensive, detailed index

Author

Stephen Wolfram

About the Author

Stephen Wolfram is a well-known scientist and the creator of the premier math program, Mathematica, now in its 5.1 version. Mr. Wolfram is widely regarded as one of the world's most original scientists, as well as an important innovator in computing and software technology.

Born in London in 1959, Wolfram was educated at Eton, Oxford, and Caltech. He published his first scientific paper at the age of 15, and had received his Ph.D. in theoretical physics from Caltech by the age of 20. Wolfram's early scientific work was mainly in high-energy physics, quantum field theory, and cosmology, and included several now-classic results. Having started to use computers in 1973, Wolfram rapidly became a leader in the emerging field of scientific computing, and in 1979 he began the construction of SMP--the first modern computer algebra system--which he released commercially in 1981.

In recognition of his early work in physics and computing, Wolfram became in 1981 the youngest recipient of a MacArthur Prize Fellowship. Late in 1981 Wolfram then set out on an ambitious new direction in science aimed at understanding the origins of complexity in nature. Wolfram's first key idea was to use computer experiments to study the behavior of simple computer programs known as cellular automata. And starting in 1982 this allowed him to make a series of startling discoveries about the origins of complexity. The papers Wolfram published quickly had a major impact, and laid the groundwork for the emerging field that Wolfram called "complex systems research."

Through the mid-1980s, Wolfram continued his work on complexity, discovering a number of fundamental connections between computation and nature, and inventing such concepts as computational irreducibility. Wolfram's work led to a wide range of applications and provided the main scientific foundations for such initiatives as complexity theory and artificial life. Wolfram himself used his ideas to develop a new randomness generation system and a new approach to computational fluid dynamics, both of which are now in widespread use.

Following his scientific work on complex systems research, in 1986 Wolfram founded the first research center and the first journal in the field. Then, after a highly successful career in academia, first at Caltech, then at the Institute for Advanced Study in Princeton, and finally as Professor of Physics, Mathematics, and Computer Science at the University of Illinois, Wolfram launched Wolfram Research, Inc.

Wolfram began the development of Mathematica in late 1986. The first version of Mathematica was released on June 23, 1988, and was immediately hailed as a major advance in computing. In the years that followed, the popularity of Mathematica grew rapidly, and Wolfram Research became established as a world leader in the software industry, widely recognized for excellence in both technology and business. Wolfram has been president and CEO of Wolfram Research since its inception, and continues to be personally responsible for the overall design of its core technology.

Following the release of Mathematica Version 2 in 1991, Wolfram began to divide his time between Mathematica development and scientific research. Building on his work from the mid-1980s, and now with Mathematica as a tool, Wolfram made a rapid succession of major new discoveries. By the mid-1990s his discoveries led him to develop a fundamentally new conceptual framework, which he then spent the remainder of the 1990s applying not only to new kinds of questions, but also to many existing foundational problems in physics, biology, computer science, mathematics and several other fields.

After more than ten years of highly concentrated work, Wolfram finally described his achievements in his 1,200-page book "A New Kind of Science." Released on May 14, 2002, the book was widely acclaimed and immediately became a bestseller. Its publication has been seen as initiating a paradigm shift of historic importance in science.

In addition to leading his company to break new ground with its innovative technology, Wolfram is now developing a series of research and educational initiatives in the science he has created.

ISBN

2003 - Fifth Edition
1-57955-022-3

List Price

$49.95 (hardcover)

About Wolfram Research, Inc.

Through innovation and progressive growth, Wolfram Research, Inc. continues to thrive as the world's leading technical software company. Wolfram Research products maintain a reputation for innovation, power, quality, and elegance. The company's aim can be summarized: "Pushing the Envelope of Technical Computing."

While remaining privately held, Wolfram Research has been continuously profitable, and it has thus been able to fund unusually long-term R&D projects and to port Mathematica, its flagship product, to a wide selection of operating systems.

The Wolfram Group consists of four companies: Wolfram Research, Inc. and Wolfram Media, Inc. in the United States, Wolfram Research Europe Ltd. in the United Kingdom, and Wolfram Research Asia Ltd. in Japan. The UK office coordinates the sales, marketing, and support of all European distributors and customers, and the office in Japan is a direct sales and marketing liaison to distributors and resellers.

The Wolfram Group has employees in research and development, marketing, sales, support, and customer service. An Executive Committee of six long-serving Wolfram Research members, representing each division of the Group, reports to the president and CEO, Stephen Wolfram. The creator of Mathematica, Wolfram maintains close involvement with the development of Mathematica and the overall design of its new features.

Wolfram Research's leadership in technical computing stems from its ability to set the direction for new technology. The Wolfram Group is characterized by an individualist approach, a "no compromises" attitude to design, the welcoming of innovation, a deep respect for the Mathematica user base and users' suggestions, and the constant search for good general approaches rather than quick fixes or purely cosmetic solutions. Management fosters a lively, informal atmosphere with a flat organizational structure more like a research department than a typical company and recruits from a wide range of backgrounds. The selection of candidates to join the company is decided more by raw ability than by traditional qualifications in that field.

Wolfram Research sponsors both the academic and the corporate communities with direct contributions to education-related programs and scientific research. These programs range from the Mathematica Academic Grant Programs, which award grants to select academic institutions and educators showing outstanding creative promise in using Mathematica to enhance their education and research activities, to the Mathematica Author and Publisher Program, which provides support and tools for authors and publishers of Mathematica-related books. The Student Intern Program recruits talented students who would like to gain real-world experience and offers internships in all departments of the company each summer.

Stephen Wolfram, the founder of Wolfram Research, is widely regarded as the most important innovator in technical computing today. A distinguished scientist particularly known for his fundamental discoveries in complex systems research, Wolfram has been a leading user and developer of tools for scientific and technical computing for over 20 years. In 1987, Wolfram founded Wolfram Research to provide an organizational environment in which software of the highest quality could be produced and distributed.

Mathematica Version 1.0 was released on June 23, 1988, and was immediately lauded by the scientific and technical community, as well as the media, as a dramatic advance. Within months, there were tens of thousands of users around the world, and today Mathematica's reach has grown to several million enthusiastic users around the world.

Mathematica has been adopted in an unprecedented range of fields both in industry and in academia. In fact, Mathematica has been responsible for bringing advanced mathematics and computing to fields that were traditionally less technical, and in so doing it has substantially increased the market for technical software in general. A growing industry of applications, consulting services, books, and courseware serves the international community of Mathematica users.

As Wolfram Research continues to grow and as Mathematica's use continues to expand into a variety of fields, Mathematica's influence will be seen in the products of the future, in significant research findings, and in classrooms worldwide.

Contact Information

Wolfram Research, Inc.
100 Trade Center Drive
Champaign, Illinois 61820-7237
217-398-0700
1-800-WOLFRAM (965-3726)
1-800-441-MATH (6284) (U.S. and Canada only)
Customer service: 217-398-5151
Technical support: 217-398-6500
Fax: 217-398-0747

info@wolfram.com
support@wolfram.com
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www.wolfram.com