Mathematica. (mathematical software) (Software Review) (Evaluation)
by Richard C. Leinecker

I've seen hundreds of software packages, and at times I've been thoroughly impressed. But I have to tell you: Mathematica transcends the category. It's a complete solution for performing mathematics by computer. I won't be able to tell you everything about the program; even its 958-page textbook left plenty of room for personal exploration. But I can give you a short tour, and I hope you're as impressed as I am.

The easiest and possibly most useful way to use Mathematica is as a numerical and symbolic calculator. Type in a question, and out pops an answer. Sure, you can get answers to problems like 5 * 7 + 4. But more important, you can get answers to problems like ArcTan[Sin[45]*Cos[12]] without breaking a sweat.

You can develop your own functions, too. If you need something special, all you have to do is define exactly what the function does. It can be as many lines as needed and as complex as necessary. And the most surprising feature is the graphical plotting of practically any mathematical function that can be represented graphically.

The strongest reason to use Mathematica is for scientific applications. You can use the program to generate solutions for a wide range of problems. I'm involved in medical research on facial expressions. The data I have is in the form of captured pictures. Plugging formulas that were developed for this purpose into Mathematica and instructing the program how to read the data from disk, I was able to reduce the picture files to simple outlines of the major facial features.

Of special interest for analyzing facial expressions are the eyebrows. When they're reduced to simple outlines, they're easy to quantify. Once this is done, tables of data for different pictures allow the people doing the analysis to have nice, convenient sets of data for comparison.

If you run a business and want more numeric help than your spreadsheet can provide, think about using Mathematica. It'll let you easily create special functions for anything you can image. Financiers can design special amortization schedules. All that's necessary is entering the formula, typing in the numbers to process or reading them from an ASCII file on disk, and then letting the program work its magic. Before you know it, you'll have your table.

I ran Microsoft Works and loaded in my personal budget spreadsheet. I then saved it to disk as an ASCII file. After running Mathematica, I used the function that loads a list of numbers from an ASCII file into a variable list. Then, the Barchart3D function gave me a graphical display of my budget. You can also view pie charts, 2-D bar charts, and line graphs.

These graphs are great for business presentations. The program saves to a Postscript file that can be converted to film or 35-mm slide. You can also use a capture program that saves as PCX.

If you're in the education field, I'd also recommend Mathematica. In a classroom situation you can generate endless illustrations of your subject matter. I taught geometry for six years. During that time, I got proficient at creating examples at the chalkboard. If I'd had Mathematica, I could've simply prepared the formulas in advance and then typed in sets of numbers during class. There would've been no down time for the students while I created examples on the board.

Before you rush out and buy the package, let me warn you of a few things. First, you won't learn how to use it overnight. For me, it was about as difficult as a course in mathematics. This program is so powerful that there's a lot to learn.

Second, even though the documentation is good, it's not adequate for novices. It doesn't walk you through the program step by step. Besides the large, well-written, textbook-style manual, I would've liked a thorough tutorial that did some handholding.

Lastly, the interface for the version I have is a bit primitive. It's a simple, command line-style interface. If you can order the Windows version, do so. There's even a Macintosh version that uses a graphical interface.

Even with the caveats mentioned, I'd recommend this program to all those who need to do math on their computers. You won't find anything else that's as complete as this. For its technical merits and worthiness I can only say, "Bravo! Well done!" IBM PC or compatible, 4MB RAM, hard drive with 12MB free (additional 16MB recommended for swap space)--$595, $895 for enhanced version (requires a math coprocessor) WOLFRAM RESEARCH 100 Trade Center Dr. Champaign, IL 61820-7237 (800) 441-MATH (217) 398 0700 Circle Reader Service Number 366