Documents that don't fit into any other category
See the research section for papers, etc related to any research I've done.
In the Student Combinatorics Seminar on 10 February I presented a quick overview of Maple and Mathematica. For your enjoyment: the basic Maple usage worksheet and the basic Mathematica usage notebook. I've also produced PDF versions: basic Maple, PDF and basic Mathematica, PDF. The Maple version mildly assumes you've read the Mathematica version, but they're fairly independent.
What's the size of SL(n) over a finite field?
Annuli in the complex plane are conformally equivalent iff the ratios of their radii are the same.
What's the size of a conjugacy class in the symmetric group S_n? Those notes also include conjugacy class sizes for the alternating group A_n. The A_n stuff closely follows an argument from a tutorial at the GAP website which I found helpful, but confusingly written.
I've typed up our department's algebra prelims from 1988 (when they switched to the current format) to now. Get them as a 1.3MB tarball of PDFs. Or, even better, see them done in MathML. UPDATE: I took those down, sorry! Note that these are unofficial copies and may contain mistakes (although in at least one case, I've corrected a problem that, as written, was outright wrong).
Similarly, I have a few complex prelims and the fall 2002 real analysis prelim.
If you have taken (or are taking) a multivariable calculus course such as 2374, you might want to see fifty ways to find the volume of a torus. Mmmmm, doughnuts.
Some initial work on the B_2 MacDonald identity. This is exercise 9 from these notes by my advisor, Dennis Stanton. I'm working on a proof of the general B_n case.
The chameleon problem. I've always wished this problem would show up on a prelim. I heard it from Catalin Turc:
On a (nearly) deserted island there are 10 red chameleons, 15 blue chameleons, and 20 green chameleons. When a red and blue chameleon meet, they both turn green; when red and green chameleons meet, they both become blue, and so on. When two like-colored chameleons meet nothing happens. Is it possible to arrange meetings between these chameleons so that they all end up one color?
A good solution should precisely classify all triples of numbers (x, y, z) so that with x red, y blue, and z green chameleons it is possible to get them all one color.