My own research

I'm currently working with Todd Arbogast on using his idea for upscaling to form accelerators for solvers. (You can read some papers about my work and his.) One of my ideas is to use the upscaled approximation as a substitute for a coarse-scale approximation in a multigrid V-cycle. I'm also working on using the upscaling as the inner step in a nonlinear Uzawa-like scheme; the iteration has superlinear convergence on linear problems! You can read about these ideas in my dissertation. It's not the best writing, but the introduction is very accesible and gives a good flavor for what all the hullabaloo is about. There's also some slides that I wrote for a SIAM student conference, and also my slides from my defense.

Various and sundry teaching stuff

I have accumulated various notes and problems from classes I've taught. There're first and second semester calculus classes at MIT: 18.01 and 18.02. A TAR-ball of stuff from a first semester calculus - 408C - at UT. Diff EQs - 427K at UT.

For spring '08 I'm teaching the second semester of an undergraduate numerical analysis sequence, M368K. I've devised my own homework assignments for the class rather than use textbook problems. The class web site is here.

Recently I was trying to devise an exam problem for a linear algebra class. I was looking for a simple matrix with repeated integer eigenvalues, but I can't seem to find any.

Here's a list of projects I'm thinking about using for a math/science club at a local high school. I may ask to give demos during regular classes. If you like the ideas or have some to share of your own, let me know.

I wrote up a solution for my mom for an elimination style problem from a book of logic problems. Some day I'll scan in the original problem sheet.

Neat science articles

I tracked down some of Michelson and Morley's original papers on their experiments refuting the existence of the ether (the purported medium whose vibrations trasmit light). I've found three so far:

• ``The relative motion of the Earth and the Luminiferous ether'' by Albert A. Michelson. In the American Journal of Science, third series, volume 22, issue 128, August 1881 on pages 120--129. (Note that the volume and series together are sometimes referred to as ``volume 122.'' Also, this is a copy of the microfilm copy of the original journal --- it's only an OK quality.) This paper describes the proposed experiment.
• ``On the Relative Motion of the Earth and the Luminiferous Ether'' by Albert A. Michelson and Edward W. Morley. In the American Journal of Science, third series, volume 34, issue 203, November 1887 on pages 333--345. (The volume and series are sometimes referred to together as ``volume 134.'' This is a copy of the microfilm.) This paper discusses the set-up, results and data, and conclusions of the experiment.
• ``On the Relative Motion of the Earth and the Luminiferous AEther'' by Albert A. Michelson and Edward W. Morley. In the Philosophical Magazine, fifth series, volume 24, issue 151, December 1887 on pages 449--463. (This is a copy directly from the original journal article --- it's a little better quality.) This article is very similar to the second one above.

• Feynman, R. P.; Leighton, R. B.; and Sands, M. The Feynman Lectures on Physics, Vol. 1. Redwood City, CA: Addison-Wesley, pp. 15-3-15-4, 1989.
• Fowler, M. "The Michelson-Morley Experiment." http://www.phys.virginia.edu/classes/109N/lectures/michelson.html.
• Lorentz, H. A. "Michelson's Interference Experiment." In Lorentz, H. A.; Einstein, A.; Minkowski, H.; and Weyl, H. The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. New York: Dover, pp. 3-7, 1952. Reprinted form Lorentz, H. A. Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern. Leiden, 1895.

An article from PNAS about flying ants. One from Proceeding of the Royal Society about the giant squid. (Yes, Ian, they finally found them!)

Useful stuff

Here are some reference documents on LaTeX that I've found useful.

organism