Niaboc: I was actually on PF today to ask a question about a personal project. Namely, orbital simulation using polar coordinates. If you've ever heard of a game named "Kerbal Space Program", it's about that - I'm interested in what the optimal ascent profile for a given rocket is. My 1D models work (emulating a rocket going straight up, with dynamic gravity and drag), but I'm having trouble implementing vectors correctly... never took vector calculus.
An old project of mine was using search algorithms (and the Quine McCluskey algorithm) to find the minimal representation of truth tables as digital circuits (logic gates including ANDs, ORs, XORs, etc...). I didn't completely solve the problem to my satisfaction, but I got a number of interesting results. For example, you can use that method to generate gate-minimal circuits, like a seven-segment-decoder in 27 logic gates. The closest thing I've seen to this is superoptimization, where you iterate through every possible machine instruction until you find the shortest that matches your specified function. The problem with both is that proving optimality is NP. Also, the generated circuits are completely incomprehensible to a human.
Then there was that time I compiled a list of 'mathematical cheat codes'... things like defining a function such that f(x) = 1 when (x==5) but f(x) = 0 when (x!=5) using only the operations we normally use in math. This turns out to be f(x) = 0^abs(x-5). If you wanted a function such that it outputs 1 iff x > 5, you could use (tanh(1000(x-5))+1)/2. There's a bunch like that, but it isn't too useful unless you have to bound functions within their expressions for some rare reason. And of course, when you do need to do it, you will forget how.
There's a few others things I've done. This is all stuff done of my own volition, though. The things a college (or business) will ask you to do are much less interesting. That would consist of writing a few template-based classes in C++ to demonstrate knowledge of object-oriented nonsense.
I hope I answered you question, and didn't bore you!
PS: Oh, you're the guy from the other thread too. That's the second thesis you've evoked from me.