Contents

• A Tour of Wolfram Research Accessing MathSource with Gopher MathSource on CD
• New! Mathematica for Students
• Low Prices for High School Teachers
• New Mathematica Applications
• Arithmetic in Mathematica

About MathUser

MathUser is published by Wolfram Research to provide news and information about Mathematica to registered Mathematica users. MathUser is also available free of charge to other people interested in Mathematica. To be added to the list of subscribers or to submit a change of address, send your postal address information to mathuser@wri.com, or call 217-398-6500. (In Europe, fax +44-(0)993-883800.) Note that MathUser is sent to your registration address, the same address where all other Mathematica information and mailings are sent.

Electronic copies of this and earlier issues of MathUser are available on MathSource. This issue of MathUser is MathSource item 0205-771. For printed copies of back issues, send an email request to mathuser@wri.com.

Your comments and suggestions are important to us. Send letters to the editor at the address below. We are always interested in hearing ideas for topics to be covered in MathUser.

How to Contact Us

Wolfram Research, Inc.
100 Trade Center Drive, Champaign, IL 61820-7237, USA
phone: 217-398-0700; fax: 217-398-0747;
user services: 217-398-5151; technical support: 217-398-6500

Wolfram Research Europe Ltd.
Evenlode Court, Main Road, Long Hanborough,
Oxon OX8 2LA, UK
phone: +44-(0)993-883400; fax: +44-(0)993-883800

Internet email addresses

General and sales information:	info@wri.com
European information:	info-euro@wri.com
Customer service:	orders@wri.com
User registration:	register@wri.com
Technical questions and support:	support@wri.com
European technical questions and support:	support-euro@wri.com
Mathematica bug reports:	support@wri.com
Mathematica suggestions:	suggestions@wri.com
MathSource:	mathsource@wri.com
This newsletter:	mathuser@wri.com

On the Cover

The cover shows the Riemann surface of w = (z^21)^1/4. You can see the four sheets and the branch cut between 1 and 1 along the real axis.

A more detailed discussion of the surface and how to produce it can be found in The Mathematica Guidebook by Michael Trott (TELOS/Springer-Verlag), to appear in the autumn of this year.

1994 Wolfram Research, Inc. MathUser (ISSN 1062-7030) is published quarterly by Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237, USA; email: mathuser@wri.com.

Mathematica, MathLink, and MathSource are registered trademarks, and MathUser is a trademark of Wolfram Research, Inc. Mathematica is not associated with Mathematica Policy Research, Inc. or MathTech, Inc. All other product names mentioned are trademarks of their producers.

A Tour of Wolfram Research

How the people behind Mathematica work together to deliver todays leading technical computing program to users around the world

From the initial idea for designing a new Mathematica feature to the moment you have your new Mathematica box in hand, there is a dedicated Wolfram Research staff member behind every step. Mathematica's development including every aspect of the design of the kernel and front end is the result of the combined expertise of scientists, engineers, mathematicians, programmers, and other specialists from around the world.

Even as you open your box to begin discovering the program, our work continues. You may have additional questions about loading the program, or perhaps want some technical guidance as you put Mathematica to work for you. As your involvement progresses, you may decide to use Mathematica to enhance the courses you teach or develop your own Mathematica program to get a specialized task done quickly. For these projects, we are also available to consult and share suggestions. And then somewhere along the way, you may have a suggestion for improving Mathematica, you give us a call, and the process begins again.

1. The team behind Mathematica has close to 200 members, most of whom work at the company's main offices in Champaign, Illinois. We invite you on a quick photo tour of what we do all day (and sometimes all night) and what it means to you as a Mathematica user.

2. The Electrical Engineering and Finance Packs and MathLink for Excel are the latest fruits of the labor in the Applications department. Mathematica specialists here continue to work in-house and with third-party developers to create more application-specific products for use with Mathematica, constantly expanding the contents of the Mathematica Applications Library.

3. The System Administration group keeps our 300 or more computers from desktops to workstations in perfect (well, usually) working order at all times! We rely heavily on email to share news throughout the company, and it is imperative that we keep every employee connected to the network.

4. From every manual you consult to the Mathematica box you keep on your shelf, the technical writers, proofreaders, and graphic designers in the Publications department have had a hand in their creation.

5. Have a question about Mathematica? Technical Support engineers have the answers, free of charge, for all registered Mathematica users. Their speedy and accurate answers often save the day when a user gets stuck during an important project.

6. Developers in Research and Development make Mathematica what it is, researching algorithms, writing and modifying code, and designing the Mathematica notebook interface to make Mathematica run compatibly on not only over 20 existing platforms, but on upcoming platforms and operating systems as they appear on the market as well. In addition, they are often invited to present Mathematica at conferences, universities, and companies around the world.

7. The company library houses hundreds of reference books and journals that are made available to the entire staff. The librarians tap far-reaching electronic resources to obtain all kinds of documents and information, and find virtually anything we might need to make the most informed company decisions.

8. The Software Quality Assurance team plays a vital role in delivering a top-quality product to our users. They constantly test the software as it is being developed, and identify, keep track of, and resolve any bugs that they or our beta testers discover.

9. Developer Support staff members provide support to Mathematica users who are creating and developing Mathematica-related books, packages, and courseware. In addition, they are often invited to present Mathematica at conferences, universities, and companies worldwide.

10. Production and Shipping personnel efficiently pack up the Mathematica boxes and ship them out. With over 300 different items in inventory, their attention to detail is vital as they assemble the right pieces for each package.

11. Our Wolfram Research Europe Ltd. office maintains close contact with Mathematica users in Europe. Frequent electronic mail to and from the company's main office in the U.S. keeps communication lines open between the two sites.

New Versions

Power Macintosh
The Enhanced Version of Mathematica for the Macintosh now ships with an optimized version built to take full advantage of the Power Macintosh. One of the first native technical software products available for the Power Macintosh, this new version of Mathematica runs three to ten times faster than other versions of Mathematica run on 680x0-based Macintosh computers.

DEC Alpha
Mathematica 2.2 is now available for Digital Equipment Corporations 64-bit Alpha systems running OSF/1. Mathematica versions running under both OpenVMS and Windows NT for the DEC Alpha systems are currently in development.

OS/2
A native OS/2 port of the Mathematica kernel is now in testing. It will be available soon, and will feature full 32-bit addressing.

Hitachi
A version of Mathematica for Hitachis 3050RX Series workstations running the HI-UX/WE2 operating system is now available.

1994 Developer Conference for Advanced Users

Engineers, economists, biologists, mathematicians, physicists, software developers, chemists, computer scientists, financial analysts, and others recently gathered on the University of Illinois campus at Urbana-Champaign to attend the Mathematica Developer Conference for Advanced Users from April 20 to 23.

Practical and informative tutorials, forums, and attendee presentations helped participants gather the information they needed as educators, authors, and developers of Mathematica-related materials. Participants learned about the various ways Wolfram Research supports the work of developers on such projects as courseware, books, and application packages.

Many Wolfram Research staff members were on hand to answer questions about features in future versions of Mathematica. Representatives from several publishing houses were also available to discuss book projects with authors.

Royal Albridge, Vanderbilt University, commented, These conferences are great opportunities for us users to learn the latest from your company and from fellow users.

I foresee some very professional software being developed around Mathematica, said Leszek Sczaniecki, Vertical Applications manager at Wolfram Research. We also learned a lot from users, who offered valuable input for our development efforts both with Mathematica and upcoming products in our Applications Library.

Third-party developers are focusing their efforts in the areas of heat transfer and energy flow, statistics, group theory, actuarial science, circuit design, ecology, and financial risk management, as well as linear algebra, trigonometry, and physics courseware.

If you are developing or are interested in developing a Mathematica application for commercial distribution, publishing a book using Mathematica, or creating Mathematica-based courseware, we have many resources available to help you. For more information, contact Wolfram Research Developer Support at 217-398-0700 in the U.S., or send email to devsupport@wri.com.

Opportunities

Wolfram Research is expanding and we are looking for outstanding people to join our team. Positions are open in research and development, software engineering (particularly on Unix), and technical writing, editing, and translating. We are also looking for experienced Mathematica programmers to develop application packages in specific fields such as control theory, mechanical engineering, biomedical engineering, etc. Send applications for all positions to Personnel, Wolfram Research (resumes@wri.com). Wolfram Research is an affirmative action/equal opportunity employer.

Mathematica Days in Japan Reach Far and Wide

Wolfram Research to open office in Japan later this year Mathematica lecturers traveled over 3000 miles as they presented Mathematica at universities and companies throughout Japan earlier this year. University of Illinois materials science and engineering professor Richard Gaylord and University of Western Australia physics professor Paul Abbott introduced Mathematica to hundreds of Mathematica Days attendees around the country.

"The Mathematica Days tour gave us an opportunity to offer practical information face-to-face with people in areas of Japan that are somewhat removed," said Wolfram Researchs Bill Harris, who coordinated the events with one of the Mathematica software dealers in Japan. "Attendees gained a solid understanding of how to use Mathematica to enhance their productivity."

Mathematica is currently used by technical corporations, government research labs, and professors and students at all major universities in Japan. Waseda University and the Science University of Tokyo are two of the many schools that have also made Mathematica available campuswide. To provide local technical support to the rapidly growing number of Mathematica users in Japan, Wolfram Research will open an office in Tokyo later this year.

European Conference to Be Held this Fall

Register by July 15, 1994 for the reduced conference fee

A conference for intermediate and advanced users will be held at St. Annes College in Oxford, England from September 18 to 20, 1994. Tutorials are planned for advanced Mathematica users, in addition to sessions and forums for users interested in creating Mathematica packages, MathLink applications, and Mathematica books, courseware, and interactive texts.

To register, please contact:
Wolfram Research Europe Ltd.
Evenlode Court, Main Road
Long Hanborough, Oxon OX8 2LA
UNITED KINGDOM
telephone: +44-(0)993-883400
fax: +44-(0)993-883800
email: conf-euro@wri.com

Registration fee: £165 before July 15/£225 after July 15

Upcoming Workshops

• Mathematica Tutorials at DSPx
  "Introduction to Mathematica for DSP", and "Symbolic Computation for DSP", by Brian Evans and Wolfram Research staff. Moscone Convention Center, San Francisco, CA, June 1315. For more information call M.J. Quinn, Reed Exhibition, at 203-352-8459.

• Mathematica Workshop by Variable Symbols
  Mathematica training by Nancy Blachman, author of Mathematica: A Practical Approach. Washington, DC, June 1315, Boston, MA, August 1517. For information call 510-652- 8462; or send a fax to 510-652-8461.

• Mathematica in the Mountains
  A course on developing Mathematica skills at the intermediate level, by Stan Wagon and John Miller. At Colorado Mountain College, Leadville, CO, July 1824. For information contact Stan Wagon by email at 71043.3326@compuserve.com; or call 303-468-0977.

• Mathematica Week by Oxford System Solutions
  Five courses for beginners to experts. Oxford, UK, July 1115. Oxford Systems Solutions will present another event September 2123, following the European Mathematica Conference. For information call +44-(0)865-784279, (in the UK (0)865- 784270); or send a fax to +44-(0)865-784004.

• Mathematica Tutorials at WESCON International Electronics Conference
  "Introduction to Mathematica for Engineering" and "Advantages and Uses of High-Level Math Programs for Electrical Engineering" by Alfy Riddle and Wolfram Research staff. Anaheim Convention Center, Anaheim, CA, September 2729. For more information call Amy Dario at 800-877-2668.

• Interactive Mathematics Text Project
  The Mathematical Association of America continues to offer introductory and advanced Mathematica-based workshops this summer as part of the Interactive Mathematics Text Project. "Using Mathematica to Create Interactive Texts" by Nancy Blachman, at Seattle Central Community College, June 2025. "Teaching Calculus with Calculus&Mathematica" by Juan Manfredi, at Los Angeles Pierce College, July 2530. "Using Mathematica to Create Interactive Texts" by Bill Davis, at University of Michigan- Dearborn, July 1123. For more information contact: Project Director, Gerald Porter, Department of Mathematics, University of Pennsylvania, 209 S. 33rd Street, Philadelphia, PA 19104-6395; or send email to gjporter@math.upenn.edu.

Accessing MathSource with Gopher

MathSource is the Wolfram Research online collection of Mathematica packages, notebooks, and documentation. It now has over 600 items by far the largest publicly accessible collection of Mathematica-related materials. Many of the items are the size of small books. The collection is accessible by email, Gopher, World Wide Web, anonymous FTP, direct dialup, and CD-ROM. This article focuses on the Gopher interface to MathSource.

*Gopher
You can reach the MathSource Gopher server at mathsource.wri.com (port 70). It contains the full contents of the MathSource collection, pointers to other Mathematica-related Gopher and FTP sites around the world, and search utilities for both MathSource and all of Gopherspace.

Developed at the University of Minnesota, Gopher is a highly flexible Internet tool for distributed document delivery. The latest version of the Gopher software for most computers can be obtained from the University of Minnesota FTP server at boombox.micro.umn.edu.

The information on MathSource is divided into four main categories:

• General--information of general interest to the Mathematica community
• Enhancements--items that extend Mathematica beyond the basic capabilities of the kernel
• Applications--subject-specific applicatons of Mathematica
• Publications--documentation, bibliographical information, and electronic supplements from Mathematica books and journals.

At the deepest levels in the directory tree, the MathSource items are identified by item number and title (e.g., 0202-194: Generating Feynman Graphs and Amplitudes with FeynArts). In each of these directories there is also a 00-Index file that contains the MathSource listings (including abstracts and subitems) for each item in that directory, plus a 00-SeeAlso file containing the listings and locations of related items in the MathSource collection.

Searching MathSource via Gopher is straightforward. Gopher users enter MathSource at the top level of the directory tree. From the top level of the MathSource Gopher menu, select the Search MathSource item. You get a menu of field-specific searches and a general search function. In most cases, the general search will return more matches than a field-specific search. After completing the search you get a list of matching files, a folder containing all the matching items, and a menu choice to narrow the list of matches by refining your search parameters. You can then select a specific item from the results of your search.

*World Wide Web
In a future issue of MathUser, we will discuss the MathSource interface on the World Wide Web. The MathSource Home Page can be found at URL http://mathsource.wri.com.

MathSource Now Available on Compact Disc

The entire MathSource collection is now available on a single CD-ROM. This is the first in a regular series of MathSource CD-ROM releases.

The MathSource CD is ideal for those who don't have electronic access to MathSource through email, Gopher, World Wide Web, anonymous FTP, or direct dialup. Even if you do have electronic access, having your own MathSource CD on hand can mean substantial savings in commercial online service fees or long-distance modem charges. And if you find yourself often searching through and downloading files from MathSource, as thousands of people have, you'll save time by having the complete collection right there on your desk.

The MathSource CD will can be used on any platform that Mathematica runs on, as long as you have a CD drive. Call Wolfram Research or your nearest software dealer to order today!

Macintosh-HFS/ISO-9660 with Rock Ridge format CD can be used on any platform that Mathematica runs on. Includes all files submitted to MathSource by April 1994.

To order call 1-800-441-MATH (6284) in the U.S. or Canada. In Europe call +44-(0)993-883400. $45.

Major Discounts Now Offered to High School Teachers

Its no secret that college students gain a better understanding of concepts when Mathematica is part of the curriculum. Now more and more high schools are also putting Mathematica in their computer labs and using it as a primary teaching tool for algebra, trigonometry, calculus, and other courses.

"For years, science teachers have had the luxury of a lab where students experiment with chemicals, plants, or animals," explains Sandra Dawson, a mathematics teacher at Glenbrook South High School. "Mathematica is like a lab where students can experiment with numbers and gain a better understanding in the process."

In response to hundreds of requests from high school teachers who want to incorporate Mathematica into their teaching, Wolfram Research now offers Mathematica for High School Teachers, a full-function version of Mathematica at a special price.

In addition, high schools can now purchase High School Packs of 5 and 10 copies of the student version for their computer labs at 60 percent off the price previously available to high schools. High School Packs are shipped with a complete set of documentation, including a copy of Mathematica: A System for Doing Mathematics by Computer, plus 5 or 10 license packs.

Mathematica for High School Teachers and High School Packs are available directly through Wolfram Research or through distributors who specialize in the elementary and high school markets. To order from Wolfram Research, customers may call 1-800-441- MATH (6284). For European orders call +44-(0)993-883400.

Mathematica for High School Teachers is available for Macintosh, MS-DOS, and Microsoft Windows for $175. High School Packs are available for Macintosh and Microsoft Windows. Pricing for the High School 5- and 10-Pack is $744 and $1488, respectively. Valid for North and South America.

Tell Us How You Teach with Mathematica

Mathematica Courseware Directory will be a valuable resource for educators. Have you written courseware based on Mathematica or Mathematica notebooks to teach your students? If so, you are among the rapidly growing number of educators at colleges, universities, and high schools around the world who use Mathematica in the classroom.

Wolfram Research is compiling a Mathematica Courseware Directory so that teachers can share this information. If you have written Mathematica-based material, we would like to include a description in the directory.

To be included, please send email to course@wri.com, or fax a message to Mathematica Courseware Directory at 217-398-0747 as soon as possible. We will contact you for a detailed description of your project after we get your response.

Mathematica for Students

The Essential Tool for Math and Science Learning Mathematica for Students is a full-function version of Mathematica for currently enrolled students, available at a price thats perfect for the student budget. Its specially developed documentation--including a student user manual and Mathematica: The Student Book (an adaptation of Stephen Wolfram's Mathematica: A System for Doing Mathematics by Computer)--makes the system easy for students to learn and use.

To order call 1-800-441-MATH (6284). For European orders call +44-(0)993-883400.

More Schools Are Bringing Mathematica to Campus

Flexible site licenses make it cost effective for universities of all sizes The number of schools taking advantage of flexible Mathematica site license purchase programs continues to grow. These are some of the schools that have joined the list of worldwide Mathematica site license locations in the last six months.

In Europe:
Manchester University (UK) -- University College (UK) -- University of Odense (Denmark) -- Chalmers University of Technology (Sweden) -- Stockholm University -- KTH (Royal Institute of Technology, Sweden) -- Eindhoven University of Technology (Netherlands) -- University of Vienna -- Technical University of Graz (Austria) -- ENSAM (France) -- Ecole Centrale (France) -- ENSAE (France) -- Catholic University of Leuven (Belgium) -- University of Liege (Belgium) -- University of Amsterdam -- Wilhelms University of Muenster (Germany) -- University of Stuttgart (Germany) -- University of Clausthal-Zellerfeld (Germany) -- University of Trier (Germany) -- University of Leipzig (Germany) -- University of Lausanne (Switzerland) -- Universitat Autonoma de Barcelona (Spain) -- Koc University (Turkey)

In Asia:
Waseda University (Japan) -- Kobe University (Japan) -- Hokkaido University of Education (Japan) -- Shokugyo Kunren University (Japan) -- Shimane Polytechnic College (Japan) -- Tokyo Denki University -- Tokyo Institute of Technology -- Hong Kong University of Science and Technology -- Hong Kong Polytechnic

In North America:
University of Texas System -- Rice University -- University of Northern Colorado -- University of Maryland -- Carnegie Mellon University -- Columbia University -- City College of New York -- DeKalb College -- University of Michigan -- Michigan State University -- Wright State University -- University of Notre Dame -- Los Angeles State University -- University of Guadalajara (Mexico) -- ITESMMonterrey (Mexico)

In Other Countries:
University of Otago (New Zealand) -- Olimpiada Matematica Argentina -- Balseiro Institute of Argentina -- University of Tasmania (Australia) -- University of Natal (South Africa)

New Books

*English-Language Books

Calculus&Mathematica
Bill Davis, Horacio Porta, and Jerry Uhl (Addison-Wesley)
ISBN 0-201-58461-1 (Windows version)
ISBN 0-201-58153-1 (Macintosh/NeXT version)
Completely interactive courseware package covering the standard calculus course. Contains Mathematica notebooks on diskette and printed material. Appropriate for structured, partly supervised, self-paced, or independent study.

Calculus Labs Using Mathematica
Arthur G. Sparks, John W. Davenport, and James P. Braselton
(HarperCollins College Publishers)
ISBN 0-06-501196-1
A series of 39 topical labs structured as a supplement to any traditional calculus text. Designed to enhance and broaden the students understanding of calculus by incorporating Mathematica's numerical, symbolic, and graphical capabilities. Each lab introduces appropriate Mathematica commands, illustrates these commands by numerous examples, and provides exercises.

Calculus Laboratories with Mathematica, Volumes 1, 2, & 3
Michael G. Kerckhove and Van C. Nall (McGraw-Hill)
Vol. 1: ISBN 0-07-034220-2
Vol. 2: ISBN 0-07-034252-0
Vol. 3: ISBN 0-07-034253-9
Collection of computer-based laboratories exploring the basic concepts and techniques of a standard calculus course series. Emphasizes a level of experimentation, visualization, and computation that cannot be duplicated in a traditional classroom setting.

Computer-aided Analysis of Electric Machines: A Mathematica Approach
Vlado Ostovic (Prentice Hall)
ISBN 0-13-068859-2
Textbook designed for electrical engineering students and professionals. Demonstrates the application of Mathematica in the analysis of electric machines.

*Non-English-Language Books

Das Mathematica Arbeitsbuch
(The Mathematica Workbook)
Elkedagmar Heinrich and Hans-Dieter Janetzko (Verlag Vieweg)
ISBN 3-528-06528-1 (in German)
Explores Mathematica as a means of solving relevant mathematical problems typically encountered by students at a technical high school or university.

Learning Mathematics with Mathematica: Introduction
Ryoji Moriya (Kaibundo)
ISBN 4-303-72780-6 (in Japanese)
The first book in the "Learning Mathematics with Mathematica" series. Shows how Mathematica can be used in learning elementary algebra. Each chapter provides explanations of theoretical concepts and related problem sets that can be solved with Mathematica.

Learning Mathematics with Mathematica: Linear Algebra
Ryoji Moriya (Kaibundo)
ISBN 4-303-72800-4 (in Japanese)
The second book in the series, providing a practical introduction to linear algebra. Each chapter describes topical concepts and shows how Mathematica can be applied to related problems. Assumes little prior knowledge of linear algebra.

Mathematica
Enrique Castillo, Andres Iglesias, Jose Manuel Gutierrez, Elena
Alvarez, and Angel Cobo (Editorial Paraninfo)
ISBN 84-283-2017-9 (in Spanish)
A basic introduction to Mathematica. Also shows how symbolic computation is revolutionizing science and mathematics education. Includes both Macintosh and DOS diskettes.

*Translations

Exploring Mathematics with Mathematica
Theodore W. Gray and Jerry Glynn
(Addison-Wesley/Toppan)
ISBN 4-8101-8045-X (in Japanese)

Partial Differential Equations with Mathematica
Dimitri Vvedensky (Addison-Wesley/Toppan)
ISBN 4-8101-8069-7 (in Japanese)

*Forthcoming Books

MathTensor: A System for Doing Tensor Analysis by Computer
Leonard Parker and Steven M. Christensen (Addison-Wesley)
ISBN 0-201-56990-6
Introduction to the authors MathTensor software, which extends Mathematica's capabilities to include tensor analysis. Includes an introduction to MathTensors commands and functions along with information on how to apply MathTensor to specific problems.

Applied Electronic Engineering with Mathematica
Alfred Riddle and Samuel Dick (Addison-Wesley)
ISBN 0-201-53477-0
Shows how to use Mathematica to solve a wide range of problems in electrical engineering. Presents an overview of electrical engineering problems and solution methods. Also shows how the abilities of Mathematica combine to make it easier to solve electrical engineering problems. Includes diskette containing a demo version of the Nodal package and code for the book's examples.

Engineering Mathematics with Mathematica
John S. Robertson (McGraw-Hill)
ISBN 0-07053171-4
A supplementary text for junior/senior-level college courses in applied mathematics where Mathematica is used in a laboratory setting. Covers topics found in courses on ordinary and partial differential equations, vector analysis, and applied complex analysis.

The Joy of Mathematica: A Point-and-Click Way to Use and Learn Mathematica
Alan Shuchat and Fred Shultz (Addison-Wesley)
ISBN 0-201-59145-6
The Joy of Mathematica is a software program for the Macintosh that adds menus and dialog boxes while running concurrently with Mathematica. The book is both a software manual and an introduction to Mathematica. It teaches readers how to use the Joy of Mathematica software to solve problems in ways that reveal the extent of Mathematica's abilities and that are interesting in their own right. Software diskette included.

Mathematica Graphics: Techniques and Applications
Tom Wickham-Jones (TELOS/Springer-Verlag)
ISBN 0-387-94047-2
Book/diskette combination that provides a complete and detailed description of the mechanics and applications of Mathematica graphics. Mathematica programs demonstrate a vast range of carefully chosen and organized examples that can be adapted by readers to solve their own problems. Also includes 32 pages of full-color demonstrations.

Computer Simulations with Mathematica: Explorations in the Physical and Biological Sciences
Richard J. Gaylord and Paul R. Wellin (TELOS/Springer-Verlag)
ISBN 0-387-94274-2
Introduces computer simulation to students and professionals in the sciences. Emphasizes programming as well as visualization and numerical analysis. Topics include random walks, DLAs, spreading, percolation, Ising model, evolution, self-organized criticality, various cellular automata models, Mathematica programming, and using MathLink. Includes CD-ROM.

Linear Algebra with Mathematica
Eugene Johnson (Brooks/Cole)
Suitable for those who want to automate calculations, or for a student learning linear algebra. Mathematica is used to illustrate the theory of linear algebra and to provide example applications and exercises.

*Other Books of Interest to Mathematica Users

Cellular Automata and Complexity: Collected Papers
Stephen Wolfram (Addison-Wesley)
ISBN 0-201-62716-7 (hardback)
ISBN 0-201-62664-0 (paperback)
A new collection of scientific papers by Stephen Wolfram from the five years before the creation of Mathematica. The papers describe Wolfram's ideas about computational models of nature, and reflect the methodology of computer experimentation that in part led him to develop Mathematica. Some of the papers in the book are widely known in the scientific community; others are now being published for the first time.

Probability, Statistics and Queueing Theory
Arnold O. Allen (Academic Press)
ISBN 0-12-051051-0
Contains an appendix of Mathematica programs.

Visualization of Natural Phenomena
Robert S. Wolff and Larry Yaeger (TELOS/Springer-Verlag)
ISBN 0-387-97809-7
Accompanying CD-ROM contains Mathematica notebooks on computer graphics and image processing.

Digital Processing of Random Signals: Theory & Methods
Boaz Porat (Prentice Hall)
ISBN 0-13-063751-3
Includes an extensive Mathematica software package, suitable both as a study aid and as a working tool for practicing engineers.

The Real Projective Plane, Third Edition
H.S.M. Coxeter (Springer-Verlag)
ISBN 0-387-97889-5 (PC version)
ISBN 0-387-97890-9 (Macintosh version)
Mathematica scripts that generate illustrations and animations are provided on an accompanying diskette and described in an appendix by George Beck.

CRC Standard Curves and Surfaces
David von Seggern (CRC Press)
ISBN 0-8493-0196-3 (book)
ISBN 0-8493-0761-9 (diskette)
Companion diskette is a complete electronic version of the hardbound book in Mathematica notebook format.

Projects in Scientific Computation
Richard E. Crandall (TELOS/Springer-Verlag)
ISBN 0-387-97808-9
Includes Mathematica support code on diskette and printed in the appendix for many of the projects explored.

Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems
William J. Thompson (Wiley-Interscience)
ISBN 0-471-55264-X
Contains 26 Mathematica notebooks in text and on diskette that create many of the images and solve many of the problems used in the book.

*Periodicals

Mathematica in Education
The highly successful quarterly Mathematica in Education, previously an independent publication, has been acquired by TELOS/Springer-Verlag. The journal, which covers the use of Mathematica in academia, now has an expanded editorial board, a semi-annual programming competition, and an increase in the breadth and depth of material. Mathematica in Education comes in paper format or electronically via MathSource. For subscription information contact:

Mathematica in Education
TELOS/Springer-Verlag Publishers
3600 Pruneridge Avenue, Suite 200
Santa Clara, CA 95051, USA
MathInEd@telospub.com

Mathematica World
Mathematica World is a monthly electronic Mathematica notebook magazine, published and distributed on 3.5" diskettes for Macintosh, Microsoft Windows, NeXT, and X Windows. This electronic publication combines tutorials, examples, application-specific packages, solutions to problems that have been posed recently through Internet news and mail groups, and a showcase of user applications from around the world. For subscription information, contact:

Mathematica World
Ormond College
The University of Melbourne
Parkville Vic 3052, Australia
+61-3-349-2001
email: mathematica@matilda.vut.edu.au

*Recently Released Books Previously Described in MathUser

Animating Calculus: Mathematica Notebooks for the Laboratory
Ed Packel and Stan Wagon (W.H. Freeman)
ISBN 0-7167-2428-6

Mathematica by Example
Revised Edition
Martha L. Abell and James P. Braselton (AP Professional)
ISBN 0-12-041530-5

Mastering Mathematica: Programming Methods and Applications
John Gray (AP Professional)
ISBN 0-12-296040-8

The Mathematica Programmer
Roman Maeder (AP Professional)
ISBN 0-12-464990-4

Quantum Methods with Mathematica
James M. Feagin (TELOS/Springer-Verlag,)
ISBN 0-387-97973-5

New Mathematica Applications

Application packs and third-party packages help you better apply Mathematica to tasks in your own field.

Whether you are a veteran Mathematica user or fairly new to the system, there is always room to improve the way Mathematica helps you work. Mathematica applications products are packages that extend Mathematica with specialized tools for particular fields. They also demonstrate how to apply Mathematica to daily tasks you encounter, and how to easily customize the system for your needs.

Electrical Engineering Pack
Engineers, for example, use the Mathematica notebooks in the Electrical Engineering Pack to see practical examples of how Mathematica is used to solve real problems in such areas as circuit analysis, transmission line theory, and antenna analysis.

Finance Pack
The Finance Pack puts a new set of powerful functions at users' fingertips for many kinds of financial analysis. Both the Electrical Engineering Pack and the Finance Pack were developed by Wolfram Research.

Optica
Optica is a fully customizable design and analysis tool for optics systems intended for both researchers and educators. It gives users easy access to hundreds of components-- including lenses, mirrors, gratings, baffles, pinholes, and more--in addition to flexible modeling capabilities. Optica was developed by Donald Barnhart (University of Illinois). It will be available later this year.

Live
Live provides real-time visualization of three-dimensional graphics generated by Mathematica, letting users adjust viewpoints, surface color, material properties, shading, and texture mapping, as well as convert objects to wire frame or scatterplot graphics. Live was developed by True-D Software Limited.

The EE Pack, Finance Pack, and Optica run on Microsoft Windows, Macintosh, the X Windows System, and NEXTSTEP. Live runs on Macintosh, Power Macintosh, and Microsoft Windows. A Sun version of Live is in development.

Other existing and upcoming Mathematica-related products focus on mechanical engineering, statistics, tensor analysis, signal processing, visualization, geometry, and control systems. See the description of the Mathematica Products Catalog later in this newsletter.

The Electrical Engineering Pack, Finance Pack, Optica, and Live are available directly from Wolfram Research or your local software reseller. For ordering information, call Wolfram Research at 1-800-441-MATH (6284) in the U.S. or +44-(0)993-883400 in Europe.

Arithmetic in Mathematica

There are many ways to do arithmetic. Considering that we teach arithmetic to children in the first grade, this statement probably sounds strange. Of course, there is only one mathematically "right" result in arithmetic, but compromises must be made if computers are to be able to provide answers efficiently. For example, if we want to do something as simple as divide 1 by 3 we have to decide whether we want the rational number 1/3 or a decimal expansion such as 0.333333... . The rational number is correct, but less efficient for use in further computations. The decimal expansion is efficient (because it allows all numbers to be represented in the same simple format), but can only be correct if it is not terminated, a condition that is clearly impractical. A similar problem arises with things like the square root of 2, where the choice is between a symbolic expression and a finite approximation. The point is that computers can do arithmetic correctly, but they are usually designed to do it "incorrectly." The errors come from compromises made to achieve efficiency, and different compromises result in different types of arithmetic.

Mathematica is different from many computer languages in that it allows you to use a variety of different arithmetics: you can do arithmetic with exact numbers with no errors, with the fast, low-precision arithmetic provided by the hardware, or with high-precision arithmetic. You can mix these arithmetics and you can do interval arithmetic with any of them. Here are some of the types of arithmetic available in Mathematica.

Exact arithmetic--the arithmetic is exact so there are no errors, but it is often inefficient and there are no canonical forms. For example, 2 GoldenRatio Cos[2 Pi/5], which is mathematically equal to 1, will not be simplified to 1.

Machine-precision floating-point arithmetic--the arithmetic is provided by the machine and is very fast. The basic model is to do each individual addition and multiplication exactly and then round the result to the nearest machine-representable number before proceeding to the next operation. Addition and multiplication are neither commutative nor associative and the distributive law does not hold.

Arbitrary-precision floating-point arithmetic--the arithmetic is done in software and can be arbitrarily precise. The precision of the result is whatever is justified by the precision of the arguments. The arithmetic is analogous to interval arithmetic with very short intervals.

Interval arithmetic--the "numbers" are really sets of numbers; for example, the sum of two intervals is the set of all numbers that can result from adding a number from each of the given intervals. Multiplication is defined similarly. Addition and multiplication are commutative and associative, but the distributive law does not hold. Moreover, squaring an interval is different from multiplying it by itself. Because of outward rounding, rigorous computation can be performed even in the presence of rounding errors. The underlying arithmetic can be any of the previously discussed arithmetics. Interval arithmetic is a new feature in Version 2.2.

ComputerArithmetic--this is defined in the package NumericalMath `ComputerArithmetic`. This package is designed primarily for learning about machine arithmetic in various bases and with various precisions. It is not intended for serious computation.

Start with the expression for q.

In [1]: = q = (18601 + 168970 x - 356410 x^2 + 170400 x^3)/
                                (2394324 - 4807055 x + 2394324 x^2)

                                                              2
3
Out [1] = 18601 + 168970 x - 356410 x  + 170400 x
               ---------------------------------------------------

2
                    2394324 - 4807055 x + 2394324 x

Evaluate q using exact arithmetic.

In [2]: = q /. x -> 1091608/1000000

Out [2] =   401
             -(--------)
              336250

Use N to see what this is numerically.

In [3] : = N[%, 8]

Out [3] = -0.0011925651

Evaluate q using machine arithmetic.  On a different machine this
may give a different result.

In [4]: = q /. x -> 1.091608

Out [4] = -0.00119277

Evaluate q using arbitrary-precision arithmetic.  Notice that the
result has much less than the 20-digit precision with which we
started.

In [5]: = q /. x -> N[1091608/1000000, 20]

Out [5] = -0.0011926

Evaluate q using exact interval arithmetic.

In [6]: = q /. x -> 1091608/1000000 +
                   Interval[{-10^-20, 10^-20}]

Out[ 6] = Interval[{-(
 
              34225151000155330986666675067500400000000000071
              --------------------------------------------------), 
              28693291523410558399999999900236500000000000000000
 
            102636546999534007040000025202501199999999999787
           -(--------------------------------------------------)}]
             86080125429768324799999999700709500000000000000000

Use N to see what this is numerically.  Notice that the endpoints
of the interval differ in the seventh decimal place, which is the
last place in Out[5].

In [7[: = N[%, 8]

Out [7] = Interval[{-0.0011927928, -0.0011923373}]

Evaluate q using inexact interval arithmetic.

In [8]: = q /. x -> Interval[N[1091608/1000000, 20]]

Out [8] = Interval[{-0.001195, -0.0011901}]

Read in the package for ComputerArithmetic.

In [9]: = << NumericalMath`ComputerArithmetic`

Set the arithmetic to be 10 decimal digits with mixed-mode arithmetic
allowed.

In [10]: = SetArithmetic[10, 10, MixedMode -> True];

Evaluate q using ComputerArithmetic.  The problem is so ill-conditioned
that 10 digits are insufficient to get a good approximation.

In [11]: = q /. x -> ComputerNumber[1091608/1000000]

Out [11] = 0

Wolfram Research Announces Formation of Mathematics Advisory Board

Building upon the excellent relationship between Wolfram Research and the mathematics community, Wolfram Research has announced the formation of a Mathematics Advisory Board. The Board will assist the company in evaluating its technical and business directions to enhance the use of Mathematica in mathematics education and research.

The Board is chaired by Paul Wellin. Questions about it should be directed to him by email at wellin@wri.com.

The Board includes the following mathematicians:

Sheldon Axler, Michigan State University
Bill Barker, Bowdoin College
Linda Boyd, DeKalb College
Bill Davis, Ohio State University
Keith Devlin, St. Mary's College of California
C.T.J. Dodson, University of Toronto
Steve Dunbar, University of Nebraska
David Fowler, University of Nebraska
Silvio Levy, The Geometry Center (Minneapolis)
Debra Lewis, University of California at Santa Cruz
Keith Stroyan, University of Iowa
Stan Wagon, Macalester College
Sha Xin Wei, Stanford University

Mathematica Miscellany

Napoleon's Russian Campaign of 1812
Here is an interesting application of Mathematica to visualize history. Mathematica's extensibility allows you to solve problems beyond the scope of most off-the-shelf data analysis and visualization tools. Shaw and Tigg applied graphics primitives such as Point, Line, Polygon, and Text to data to re-create a famous graphic, first drawn by the French engineer C.J. Minard in 1861.

[Graphic deleted. See notebook version of this newsletter (MathSource item 0206-907-0022.]

MathLink Developer Kit for Microsoft Windows

MathLink for Microsoft Windows is now available. It enables Windows users to link the Mathematica front end to a Mathematica kernel on a different computer (or the same computer), or to link Mathematica to external programs such as Microsoft Excel or to programs written by the user.

MathLink for Microsoft Windows is a set of DLLs (dynamic link libraries) that can be used from any Windows development environment that supports DLLs. With the MathLink Developer Kit, many kinds of programs can be adapted to exchange data and commands with Mathematica. The kit includes MathLink documentation and sample MathLink applications: a small Mathematica front end and programs written in C and Visual Basic.

Registered users of Mathematica 2.2 can get the MathLink Developer Kit for Microsoft Windows by calling Wolfram Research at 1-800-441-MATH (6284) in the U.S. You can also request the kit by email at orders@wri.com. (In Europe, send email to info-euro@ wri.com.) Be sure to include your postal address and Mathematica license number.

SQL MathLink Development

Wolfram Research is developing a MathLink-based tool that will allow users to query and manipulate databases directly from within Mathematica. Among other things, it will allow data to be imported directly into Mathematica, where it can be analyzed, plotted, and presented. The program will provide a common SQL-like syntax for all databases, even if they do not support the SQL standard.

If you are interested in beta testing this product, or if you have any requests or suggestions concerning its design and implementation, we want to hear from you. Send email to mathlink@wri.com or a fax to 217-398-0747, attention MathLink Applications.

Q&A

Q: How can I use the results from Solve in further calculations?

A: The output from Solve, NSolve, DSolve, or NDSolve always has the same form. It is a list in which each element is a list of rules. Each of the inside lists represents one of the possible solutions.

In [1]: = a = Solve[{x^2 + y^2 == 25, x + 2 y == 5}, {x, y}]

Out [1] = {{x -> -3, y -> 4}, {x -> 5, y -> 0}}

You can substitute all the solutions into an expression by using
the replacement operator /.  ("slash-dot" or ReplaceAll).  Here
is the complete list of ordered pairs that are solutions of the above
equations.

In [2]: = {x, y} /. a

Out [2] = {{-3, 4}, {5, 0}}

To be consistent, when there is only one solution there are still
two levels of lists. Note that you can use the same unknowns in
this new pair of equations because Solve and its relatives don't
set any variables.

In [3]: = b = Solve[{x + y == 25, x + 2 y == 5}, {x, y}]

Out [3] = {{x -> 45, y -> -20}}

To see {45, 20} instead of {{45, 20}} you replace by First[b] or
b[[1]] instead of by b.

In [4]: = {x, y} /. First[b]

Out [4] = {45, -20}

Keeping the unknowns variable lets you evaluate expressions by
substitution. This is better than having to name and remember a
parade of constants.

In [5]: = x + y /. First[b]

Out [5] = 25

Q: How do I get a plot of the solution to a differential equation using NDSolve?

A: NDSolve returns a rule that involves a function rather than a number. The symbol < > indicates information that is not printed to save space.

In [1]: = result = NDSolve[{y'''[x] 
        + 8 y''[x] + 17 y'[x] + 10 y[x] 
        == 0, y[0] == 6, y'[0] ==-20, 
        y''[0] == 84}, y, {x, 0, 1}]  

Out [1] = {{y ->
        InterpolatingFunction[{0., 1.}, < >]}}

You can assign a name to the function. 

In [2]: = g = y /. First[result];

Evaluating it at a particular value shows that all is well. 

In [3]: = g[.5]

Out [3] = (y /. {10 y[x] + 17 y'[x] + 8 y''[x] + y'''[x] == 0, 
 
     y[0] == 6, y'[0] == -20, y''[0] == 84})[0.5]

Plotting the function is easy.

In [4]: = Plot[g[x], {x, 0, 1}];

Q: When I start Mathematica for Windows on my computer, I see a dialog box with the following message: General Protection Fault in module GROWSTUB.EXE. It has an OK button, so I click on that and then everything works fine. What is going on?

A: This harmless but annoying error is caused by a small memory-resident program called POINTER.EXE. This program gives you the ability to change the mouse pointer size during your Windows session, and therefore it is attempting to read one of Mathematica's resources. Most users have no use for this program and are usually unaware of its presence.

To avoid the conflict, you need to prevent POINTER.EXE from being loaded. To do this, edit the WIN.INI file, which is found in your main Windows directory. Find the line that begins:

load=

Technical Support Addresses
U.S. and non-European technical support
email: support@wri.com
fax: 1-217-398-0747
telephone: 1-217-398-6500

Monday, Tuesday 8:30am-5:00pm
Wednesday 9:00am-5:00pm
Thursday, Friday 8:30am-4:00pm
U.S. Central Time (GMT -6) email: register@wri.com
telephone: 1-217-398-5151

Monday-Friday 8am-5pm

European technical support
email: support-euro@wri.com
fax: +44(0)993-883800
telephone: +44(0)993-883400

Monday-Friday 9:30am-5:30pm
(GMT -0)

Look for the Mathematica Products Catalog in Your Mailbox Soon

You'll find more details about the applications described on page 12 in the new Mathematica Products Catalog, which you will receive in the mail soon. You will also find a broad selection of Mathematica-related books, courseware, MathLink applications, MathSource information, and Mathematica miscellanea.