I found that for the average student, a very useful (and free) alternative is SciLab. It's feature rich, it's language is almost identical to MatLab, it's toolboxes are open source as is the program itself and it has a fairly robust community supporting it.

I haven't used it professionally, but I would suspect it measures up quite nicely to MatLab in that respect as well, and it has enough similarities that making a transition to MatLab would be quick and painless.

The basic price of MATLAB is not unreasonable for a professional product, though some items which should in my opinion be included, are only available with the addition of toolboxes, which can cost more than the basic MATLAB. There is even a toolbox for curve fitting.

A professional user could easily need to spend $15,000 to get all the toolboxes they need. Often one toolbox requires several others to be installed too. The price rockets up.

The symbolic toolbox for MATLAB, adds symbolic capabilities, but it is clear this was not developed initially for MATLAB, but was sold as another product, and the company than acquired by Mathworks. It does not feel very nicely integrated into MATLAB, and although I have access to it, I soon gave up and use Mathematica when I want symbolic maths, as Mathematica is much stronger at symbolics.

For numerical work, this is an industry standard and well worth learning to use well. But there are alternatives someone should consider

1) Octave is a free Clone. It is not 100% MATLAB compatible, but is quite close. However, from a students point of view, I'd rather learn MATLAB as that's what employers want.

But if money is tight, Octave is a very viable alternative.

2) Sage - open source, and free, but too buggy. I would not trust any result from Sage.

3) Mathematica - more expensive, but more complete, but not as easy to use as MATLAB. There is a "home edition" of this too, which is excellent value for money if you want it for hobby use.

4) Maple - Like Mathematica, this is better at symbolics than MATLAB with the symbolic maths toolbox. But I feel Mathematica is better than Maple, so I don't really consider Maple worth bothering with.

5) R - for statistics this can't be beaten, and is free too.

The "Free demo" is only for registered users.

Other people have to fill a detailed request. Then they are told that "A MathWorks representative will contact you to discuss your needs and provide access to trial software."

I know what I need : a free demo not a discussant about my needs !

This software isn't for people looking for a shiny Cocoa-application. It's for people looking for a top-of-the-line mathematical and computational tool. I've yet to come across any software that can compare with Matlab in this regard, it's amazing.

Its language is very easy to work with, well designed. People with limited programming experience should be able to pick it up easily.

The built-in documentation is top class as well. I've compared it with Mathematica's documentation, and it blows it away. It's easy to search, comprehensive, and the examples work.

Matlab makes it painfully easy to manipulate and visualize data, and run various experiments. Its full capabilities are rarely tapped, as it can even integrate with various other languages. If you're looking for a product that makes it easy to do hard things, look no further.

Another suggestion is Octave. It's extremely close to Matlab (especially since version 3) and all the code I have written now runs in both. The best part is that it's free!