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
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:
Insofar as I know, the copyright to each of these articles has expired. Also, I
claim no copyright to the scans I've made (nor can I --- unoriginal works cannot
be copyrighted). You're free to copy these articles as you please. ScienceWorld
has a few other references:
- ``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."
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!)
Here are some reference documents on LaTeX that I've