Wow, I hope I didn't try to ram too much into an hour and a half.... Sorry if I went a bit fast, but I had a lot to share with you! Believe it or not, I only just scratched the surface of Scientific Computing. Many colleges are starting departments in this new field which is a merging of Applied Math and Computer Science used in real-world math and science applications on super computers. BTW a super computer can be a single PC with multiple cores setup to use all cores on one problem. Also, a super computer can be Linux Cluster with several PCs linked together to solve one problem. Or, a super computer can be like Shadowfax (avatar below), a mix of both (25 compute nodes, each dual-core) known as a hybrid cluster!
If this is all too new to you, don't feel bad. I've been teaching programming since 1975, I've been perfecting Room 429 (aka Shadowfax) since 1985, I've been using Graphing Calculators since 1990, I've been using Linux since 1995, and I've been trying to get a Scientific Computing Lab course in place at BSHS since 2005. You guys just have to play catch up!
If you are interested in any of this, you should google Scientific Computing, Computing Sciences or Computer Algebra Systems in general as well as the Mathematica, Maple, MATLAB or S-plus programing environments in specific. Also, you can get tutorials on SAGE at http://www.sagemath.org and work online with SAGE at http://www.sagenb.org where you can create your very own free account in seconds or just use your SAGE liveCD!
BTW, remember FLOSS (Free Linux Open Source Software)? SAGE, Octave and R are FLOSS equivalents to Mathematica, MATLAB and S-plus respectively.