I gave my numerical analysis students this week off to work on their projects (which they start presenting next week). I told them I would be available during class time for them to ask questions. The difference between doing this with upper level and lower level students is that the upper level students will actually do it. (I was actually a little surprised at how many people I saw.)
I'm actually really pleased with my numerical students right now. Most of them have been working hard on interesting projects. Most of my work in meeting with the students up to this point has actually been in getting students to scale down their proposals to a manageable size. One group of students was originally starting with an ambitious project of figuring out how to guide a robot through an obstacle course using GPS guidance. I initially got that scaled down to just working with the GPS, then got them to massively reduce the number of factors they include in their GPS model, and finally we have settled on doing linear least squares fitting, which is simpler than the non-linear least squares fitting that GPS requires. I'm relieved, and so are they. I knew at the beginning of the semester that this was simply too big, and I think it's finally something they can finish in a reasonable time. (Actually, they are almost finished now.)
Almost all of the projects are progressing nicely and look really interesting. I have student showing how calculators evaluate functions like sines and cosines, another student solving linear systems using iterative techniques, one studying efficient matrix multiplication for graphics applications, a pair of students working on Bezier curves and their use in graphics, a group of three presenting on a numerical simulation of the Tacoma Narrows bridge collapse, one doing arbitrary precision arithmetic, and one doing on the fly polynomial interpolation to compensate for lag in networked computer games. All of the presentations look good. I just need to make sure they don't run too long.
Sometimes I really like teaching.