I’ve spent much of the past week trying to learn a bit of algebraic topology. Homology is good stuff — homology groups are not difficult to calculate, but they are powerful topological invariants. I was looking forward to cohomology more in fact, but I keep alternating between feeling that cohomology is a trivial dualization of homology and too difficult for me to grasp at the moment, but I think both of those are in fact false. Of course, cohomology has more structure than homology with the cup product and all that, but I’m not supposed to know about cup products yet. I’ve managed to come to terms with Hatcher’s book somewhat — I used to feel that he went to great lengths to explain all the geometric stuff that I could figure out on my own anyway while neglecting formalism with categories and functors and all that. Well, I still do, but now I don’t mind it so much for some reason.
I thought it was fine time for a break today, so I got myself a book on umbral calculus, a topic I have been peripherally interested in since high school. I didn’t get too far yet, but it looks like fun.