I think there have been a few interesting changes to my life lately. Perhaps the biggest change is that Labutin finally gave us some problems to do. It had been rather unclear to me what we were doing in that class. I think we proved two big theorems, but we didn’t have any proofs that seemed interesting or complicated in any way. For some reason, he was using derivatives yesterday. I don’t think that’s quite fair. We went through a lot of trouble to define an integral before we were allowed to integrate stuff, but he didn’t define derivatives with anything like the same rigor. I suppose we already knew how derivatives are defined but not how (Lebesgue) integrals are defined.
Finally we finished Chapter 0 in Hatcher and started fundamental groups. They’re much more interesting than the homotopy extension property.
I bought a bunch of pushpins yesterday for the sole purpose of putting up Riemann’s 1859 paper “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (“On the Number of Prime Numbers less than a Given Quantity”) on my wall right above my bed. Now I have something very interesting to read in case I ever suffer from insomnia. I can also put LaTeX stuff on my wall near my computer so that I don’t have to search for The LaTeX Companion every time I don’t remember a macro.
I wonder if professors could reach an agreement about who gets to define continuity and who doesn’t. It is rather annoying that three professors this year have given me the same definitions of continuity. A friend of mine jokingly told me that he thought that professors shouldn’t be allowed to talk about things that he has already been told by more than one other professor. Of course, different students take different classes, but I’m sure some agreement could be made so that only people teaching certain subjects (maybe real analysis?) are allowed to define continuity.
How strange. Right after I posted this entry, the second movement ended, and the key changed for c minor to E major for the third movement. I think that’s enough to wake anyone up.