Mathematica 4.2

Rating:
Summary: My second most commonly used program
Review: I have been using Mathematica for years and spent over forty hours playing around with this version just to update my knowledge for this review. And yet, I still feel that I know only a small fraction of what it can do. Without question, it is the most awesome piece of software that I have ever used. With decades of personal experience and having seen and used many different types of software, I am not easily impressed, so this is saying a great deal.
In the past few months, I have used it to:

* Verify the solutions to exam and homework problems in advanced calculus.
* Perform calculations for several research projects that I am working on.
* Perform computations in my attempts to solve problems that have appeared in journals.
* Perform statistical operations on data for an algorithms class.
* Examine and verify the contents of manuscripts that were received in my capacity as editor of Journal of Recreational Mathematics.

In fact, I find it so useful that it is now the second most widely used piece of software in my arsenal, trailing only word processors. By my rough computations, I now use it more than e-mail.
While I have never used Mathematica in the classroom, it is very easy to learn. I doubt if even a half hour of instruction would be necessary to get a user already familiar with the Windows environment to the point where they could use it. The user interface is clean, although it takes a few passes through some examples before you remember what the specific commands are. I tend to keep a small note of the primary commands near my workstation in case I forget.
The speed of the computations is amazing, there is clearly some very powerful algorithms under the hood of this bad boy. In trying some test computations, one million digits of PI were computed in a few minutes and I used a lot of unusual summations, all of which were completed in a matter of seconds. A great deal of time was wasted in my trying to see how complex and unusual I could make the summations before Mathematica finally had to struggle. Quite frankly, I failed in that endeavor, it took the best I could come up with and always computed the correct answers in a short time. While I did not perform any explicit timing tests, my distinct impression was that many of the computations are indeed faster than in previous versions.
Given the rapid expansion in the use of XML for data exchange, the ability to store Mathematica expressions in XML form is useful. Exporting information in XHTML format also is another step in keeping Mathematica in tune with the advance of technology. The online documentation is great and while "The Mathematica Book" is large enough to serve as a piece of exercise equipment, it is thorough and it is never more than arms length from my computer where Mathematica is loaded.
While there are mathematicians whose work would not be benefited by Mathematica, they have to be a small subset of the population. For most of us, it is an indispensable tool, adding to the amount of different things that you can do and also shortening the amount of time it takes you to do them. It is the one piece of software that I would chose if I ever faced the "if you were stranded on an island with only one program" question.

Published in Mathematics and Computer Education, reprinted with permission.

Rating:
Summary: Oh, if only I'd had this years ago in college!
Review: Maybe I'd have been an astrophysicist if I'd have been able to grind my way through advanced calculus and differential equations . . . I'll never know, but I do know that if I'd had Mathematica 4.2 back then, I certainly would have improved my GPA in math!

M4.2 uses a combination of tables, algorithms, and an impressive kernel to process some of the most demanding equations you could throw at it, and it is *fast*. For example, it can calculate 1000! (1000 factorial) in under a second; 100000! in about 30 seconds; 999999! in a few minutes. [For comparison, the last two of these numbers are trillions of times larger than the number of atoms in the known universe!]

M4.2 offers a huge number of predefined functions and operators, and allows the user to define others on the fly. There is powerful, extensive support for calculus and D.E. equations, as well as number theory and probability. Most formulae can be entered in either standard mathematical form, or using keyboard-entered shortcuts.

Also available is powerful 2D and 3D graphing and plotting functionality. From simple trigonometric functions to extremely-complex data sets, M4.2 allows the user to generate beautiful graphical output. This is complemented by M4.2's use of style sheets to format your presentations: users can choose from predefined styles (white paper, overhead projection, web, textbook, etc.), modify the included styles, or create their own.

I would go so far as to say there are so many functions that I can't even intelligently comment on most of them -- they're way over my head. However, in researching this software, people who *know* have reported that M4.2 is the best there is, and with over a million academic and commercial users I can't disagree.