Next week, graduate students will be taking qualifying exams. To me this means that people actually talk about math at tea, and so I can say things like “Is the Continuum Hypothesis equivalent to the statement that it is impossible to find an uncountable set with Hausdorff dimension 0?” without seeming out of place. (Cooper convinced me that the answer is no, although I think his construction was more complicated than it needed to be.) I wonder if I can take qualifying exams too. After all, I didn’t get to take the USAMO, so I think I should get some sort of compensation. The problem is that I don’t know anything and haven’t been studying for a few months for these tests. But our homework for differential geometry comes from old qualifying exams, and those problems seem rather easy.
and I will be giving a presentation on pseudospheres an hyperbolic geometry for our differential geometry class on Sunday. Perhaps since I know the material pretty well I won’t stutter and mumble my way through the presentation.
I occurred to me yesterday after topology that I have learned more this quarter in a differential topology class I’m not taking than I have learned from any class that I actually am taking. I suppose that is largely due to the fact that I have not yet convinced myself that just because I have something written in a notebook doesn’t mean that I actually know it, but I should also give Cooper credit for being a terrific teacher. I used to know everything in my notebooks, and so I didn’t take notes very often. I don’t know if I can’t do that now because I’m becoming old and my memory is fading or because there is more material now and I never would have been able to learn it from one exposure. But for some reason, I feel that the former is the more likely. Learning was definitely not difficult for me in middle school; if I read a book, I would know just about everything in the book by the time I had finished. But that doesn’t work now.
There are now two more weeks of classes, and I could really use a break from academic life for a little while before I return for nine more classes in the fall. I still don’t know when I will go home or what I will do with my stuff. That’s not good.