ChapterZero

My officemate and I have decided to take 30 minutes or so a week to inform each other about various mathematical topics– on the theory that teaching helps you to cement your own knowledge. I’ll be teaching him something relating to my research, and vice versa: he’ll probably be teaching me about Sobolev spaces, which I’ve wanted to learn about for a while now, so it should be an interesting experience. I’m debating between teaching him what I know of random matrix theory (which I’ve already gotten fuzzy on, despite having learned it last term), working my way through the Cauchy-Schwarz masterclass book (because I’m sure I’ll find those inequalities useful), or basic operator theory (which I know I’ll need down the road as my research becomes more theoretical).

Speaking of my research, I fell in love with the subject all over again. Remember my problem is to find bounds on the error in approximating a given matrix with a sparse matrix ; ideally, these bounds should be a function of only: the whole point of sparsification is to avoid making convoluted computations involving the original matrix ; if we had to make such computations to bound the error, we might as well just calculate it exactly. Anyhow, I saw anew how awesome it is that you *can* get useful bounds that are just a function of . I think it helped a lot that I got nice results

Possibly relevant posts:

• One interesting corollary of our error bounds (10/21/2008)
• Teaching styles (2/4/2008)
• I can finally move on (or, a deviation result proved) (11/5/2008)