For some reason my math homework was somewhat hard this week. It was on automorphisms of groups, and conceptually it's pretty straightforward material, at least at the level at which we're working at. An automorphism is just a one-to-one and onto homomorphism of a group to itself, and everything falls out from that. Most of the homework problems were straightforward, except for two of them. Those two fell into the evil category of exercises which are hideously frustrating to work on, as what they assert is intuitively 'obvious', yet each attempt at a rigorous proof falls apart in a flurry of tautologous algebra and definitions. Until that magic moment when a light goes on in my head, and I see _exactly_ how to do it. Then I feel conflicted, as on the one hand, I did it, yay, and on the other, the answer looks so simple that I feel stupid for not having thought of it much faster.

Anyway. I'm trying to decide what to take next semester. If I was King and I had superpowers, everything would be simple and I'd just sign up for all the classes that I want - miraculously, they don't even conflict with each other, time-wise. Unfortunately, that would make for a 21 credit semester, where 15 of those credits would be in rather serious upper-level math and physics courses, and 6 in a japanese course. That would be really, really hard, as I don't actually have superpowers. But oh, it's so tempting.

The trouble started when I found out that the university's offering a course on Differential geometry in the spring, with a special focus on differential forms and whatnot. This is nominally Part II of the two-semester differential geometry sequence, and since I haven't taken part I, normally I wouldn't care. This time, though, the flyers for the course take pains to point out that the Diff. Geometry I course is really only a 'mathematical maturity' prerequisite, and you don't actually need to have taken it to enjoy the course. If you've had some other upper-level math courses, you should be fine, or so the leaflet claims. This is very tempting. Also, I've asked around, and the guy teaching it is supposed to be fantastic.

On the other hand, I'd planned to take statistical physics/thermodynamics in the spring. It's a required course, and generally useful, though I can't say I'm especially excited about it - but people tell me it's pretty cool. Also, the guy teaching it next semester is reportedly good. All the other courses I'm considering are lock-ins for various reasons, so it's between thermo and diff. geo. It's a tough choice. Next week, I'll try to find who's teaching thermo next fall, and I'll go chat with the diff. geo. professor, to see if he thinks my background is appropriate for his course.

I'm beginning to have fun in school for a change. It feels pretty good.

(And I hope this doesn't jinx it, knock wood and plastic)