Overview

Mathematica is a computing environment described by its publisher as the world's only fully integrated technical computing solution. Mathematica can perform many types of mathematical procedures; for example, calculus, algebra, statistics, and geometry. The program will evaluate just about anything, display the output in numerical or symbolic format, and allow the user to format the data produced in a publication-quality layout. Mathematica is also able to generate eye-catching 2-D or 3-D plots, and to import files in several graphic formats for display within a document. Mathematica 4.0 introduces a number of new features relative to its 3.0 predecessor, varying from advanced data structures that speed calculation to spell checking. The user base of Mathematica is very diverse, ranging from the Patent and Trademark Office to scientists in disciplines such as biology, engineering, mathematics, and physics.

How Long Did It Take to Learn to Use It Productively?

After spending three hours with Mathematica, while not proficient, I did obtain a basic working knowledge. Using Mathematica as a calculator is quite easy and basically depends upon using proper syntax for the calculations. The shift-plus-return-key combination (Evaluate Expression) will become second nature as more time is spent with the program. Becoming comfortable with the program will take about 2 to 3 weeks.

Product Quality

Customizability

Nearly every aspect of the program can be tweaked to suit the user. Editing, calculation, and text formatting options are just a few of the areas that can be quickly adjusted via the menus. Infinite customization is possible because Mathematica is a programming language. For example, object-oriented and string-based programming are both possible within Mathematica. If it seems like something is missing from the program - just build an add-on package (not trivial, but possible for users with a programming background). Ultimate compatibility of Mathematica code can be obtained with the help of MathCode C++, a third-party application that allows export of Mathematica programs to C++.

Ability to Program in Scripts, Add Extension Modules, etc.

Excellent.

Ability to Import and Export in Different File Formats

Very good.

Useful or Unusual Features

Mathematica is composed of three programs, the front end, kernel, and Mathlink. The front end is the platform-specific part of Mathematica and the part of the program that the user sees. The kernel is the portion of the package that accomplishes all calculations. Mathlink allows external programs to call Mathematica or be called by Mathematica. The multipart system allows a user of the front end to send commands to multiple kernels running locally or over a network. Sending jobs to multiple kernels is very useful for running several computationally intensive tasks in parallel.

The Mathematica kernel contains many built-in functions. A plug-in architecture (similar to Photoshop or Web browser plug-ins) called "add-on packages" allows a great deal of expansion of the Mathematica system. The add-on packages generally are geared toward specific applications or the extension of built-in operations available in the Mathematica kernel. Mathematica ships with standard add-on packages for algebra, calculus, geometry, and statistics (plus 7 more). Of interest to life scientists are the protein-DNA interaction, evolutionary-ecology, and channel-kinetics add-ons (to name a few) available at Wolfram's page on Mathematica in the Life and Medical Sciences. More add-on packages can be found on the Mathsource Web site.

The basic document created by Mathematica is the "notebook." A Mathematica notebook contains all the formulas, calculations, text, sound, and graphics entered or created by the user (see figure 1). Mathematical symbols such as alpha, pi, the integral symbol, and others are entered into the program with the aid of floating palettes (see figures 2, 3, and 4). The notebook file format of Mathematica documents is plain ASCII text. Therefore, Mathematica notebook files are truly cross-platform. Notebooks can be viewed by your colleagues or students, who many not have Mathematica, with the help of Mathreader (similar to Adobe's Acrobat Reader in function).

Mathematica 4.0 introduces a new data structure called packed-array technology. Wolfram describes the technology as "a fast and efficient method for storing and performing repetitive operations on large lists, matrices, and tensors of numerical values - integer, real, or complex . . ." A significant increase in the speed of calculation is realized by those that take advantage of packed-array technology. Another major improvement in Mathematica 4.0 is the addition of a spell checker (no more writing your text in a word processor and then dropping it into Mathematica). More in-depth information about features new to Mathematica 4.0 can be found at Wolfram's Web site.

While the layout capabilities of Mathematica are admirable, and certainly adequate for the majority of users, they are not up to speed with industrial-strength publishing packages such as Adobe InDesign and Quark XPress. Wolfram has realized this weakness and is currently developing a scientific DTP application called Publicon. A free beta version of the program is available.

The minimum system requirements are unrealistic. Ten Mb RAM for Macintosh and 16 Mb RAM for Windows are just enough to open the application. During testing with my Macintosh, Mathematica froze a number of times when complex notebooks were opened, requiring me to force-quit the application. Manual allocation of 25 Mb of RAM to the Mathematica front end on the Macintosh fixed the problem. The freezes didn't occur on my PC because of Windows' dynamic allocation of RAM. I did notice that the program was using about 25 Mb of RAM when I had the problematic notebook open. If I were running a machine with the minimum-recommended amount of RAM, it's likely I would have encountered problems. My recommendation is that you have at least 32 Mb of RAM to run Mathematica properly if you are creating complex notebooks.

Upon completing the online registration process, I noticed it was not executed via a secure Web page. It would not take much work to implement a secure online-registration process.

Comparisons with Similar Software

No other single program can handle calculations, generation of graphics, and layout better than Mathematica. Version 4.0 of Mathematica continues the tradition of powerful features and tight integration set by previous versions of the product.

Technical Support

The technical documentation included with Mathematica is very good. Three books are shipped with Mathematica: a getting-started reference, a standard add-on package guide, and the 1,500-page hardcover Mathematica manual. The paper manuals are well organized and helpful. A digital version of the paper manuals is available in Mathematica's online help browser. The online help is very effective and includes a complete tutorial covering the main features.

Wolfram encourages users to contact technical support via email. However, telephone support is available for Mathematica from 8:30 A.M. to 5:00 P.M. Central time (long-distance fees apply). After fixing the RAM allocation issue with the Macintosh version of Mathematica, I called tech support to test their abilities. The technician I spoke to was courteous and quickly came to the same conclusion I did: increase the RAM allocation to the front end. Since I'm the type of person who only resorts to manuals when all else fails, out of curiosity, I checked the Mathematica getting-started manual for information about this problem. Sure enough, on page 34 there was a note about complex documents and RAM allocation for the Macintosh application.