MATLAB WAS a wrapper around commonly available libraries.
And in many cases it still is. When you get to larger
datasets, it has many additional optimizations, including
examining and special casing common problems (reducing to
sparse matrices where useful, for example), and handling
edge cases. Often, you can submit a problem in a standard
form to a general function, and it will determine the best
underlying algorithm to use based on your data. For small
N, all algorithms are fast, but MATLAB makes determining the
optimal algorithm a non-issue.
This is written by someone who hates MATLAB, and has tried
to replace it due to integration issues. From your
question, you mention getting MATLAB 5 and using it for a
course. At that level, you might want to look at
Octave, an open source implementation with the same
syntax. I'm guessing it is up to MATLAB 5 levels by now (I
only play around with it). That should allow you to "pass
your exam". For bare MATLAB functionality it seems to be
close. It is lacking in the toolbox support (which, again,
mostly serves to reformulate the function calls to forms
familiar to engineers in the field and selects the right
underlying algorithm to use).
