One of the students requested pointers for some assignments or mini projects he could do in Matlab. Here was my reply:
Since I'm not familiar with abstract math problems with Matlab, I'll have to suggest what I know about, and also what is got by googling. So, please take these only as vague pointers, discuss with your concerned teacher before proceeding further.
1. Visualizations. Matlab has got very nice built in plotting tools. Visualizations of fractals, chaotic system equations, other differential equations etc could be done. The Mandelbrot function is already implemented, you could play around with it to learn more, and implement other fractals.
If you make high-resolution circularly symmetric movies, you could also help the planetarium,
All sorts of value-added stuff can be done with visualizations - making guis for varying parameters, interactive graphs, etc etc.
2. Matlab has got a Symbolic Math toolkit. All sorts of higher level math can be modelled using this, like
3. Linear Algebra problems, Manifolds and such are very much solvable with Matlab, so taking up some problems with these might be useful, eg.
http://www.manopt.org/and many more,
4. Scilab and Octave are open source Matlab clones. If you are looking at the programming side, there are many small functions which can be written for Scilab and Octave for better Matlab compatibility.