I can help out with things in the math/statistics vein. I can go over stuff commonly taught in schools but in a more fun way (maybe probability theory but I take requests), stuff that's particularly relevant to LessWrong (an intuitive explanation behind Occam's Razor), or ideas I'm interested in that are more current and rarely found in textbooks (sparse approximation, dictionary learning, diffusion maps).
I've thought about compiling a post or a few about "The Math They Didn't Teach You," as I've found that linear algebra courses don't teach the most useful linear algebra techniques & algorithms, probability classes don't teach the most useful theorems, etc. for very standard computational purposes.
ETA: I can take care of compression.
In a recent thread, SarahC said:
... so here's the place to float ideas around: is there an area you know a lot about? A topic you've been considering writing about? Here's the place to mention it!
From a poll on what people want to see more of, the most votes went to:
Some that got less votes:
... but there are certainly many more things that would be interesting and useful to the community. So what can you teach us?