Since a bunch of you seem to be future high school math teachers, I thought you might be interested in the Hampshire College Summer Studies in Mathematics for mathematically talented high school students (HCSSiM). If you end up having any students who are really interested in math (maybe even interested enough to want to be a math teacher), this is a good program to tell them about. My brother did it this past summer and he really liked it. They do short modules on various advanced topics in math. My brother said that he learned how to solve a cubic equation using origami. There's also stuff like non-euclidean geometry, group theory (like what we've been doing), and other stuff. It's also really fun because the people who run the program are somewhat odd. They apparently are obsessed with yellow pigs, and the number 17. They have a huge collection of facts about 17, some of which are interesting, some of which are kind of useless (e.g. 17 is the only prime divisible by 17). For more info, check out their website, and here's an alumna's website which has more info about 17 and yellow pigs.
