I now have textbooks! My new friend, Walter Rudin’s Real and Complex Analysis, has been coming with me most places that I go. It’s quite an awesome book. I love the way he defines pi. “Since cos 0 = 1 and cos is a continuous real function on the real axis, we conclude that there is a smallest positive number t_0 for which cos t_0 = 0. We define pi = 2t_0.” It seems so unnatural but yet so brilliantly in the style of analysis. It made me laugh when I saw it first. I hope he has a lot more definitions like that.
We had a meeting for CCS today, where today is defined as some time less than 24 hours ago since I’m writing this after midnight. That’s all very well, but it’s not so good when someone *cough*Daniel*cough* insists that he take me on a campus tour around 1:20AM. That is, if I’m supposed to have eaten breakfast and be ready to leave for the meeting at 8:15. So I set my alarm clock for 7:00 (I’m sure my roommate was thrilled about that considering his sleep hours are about 3AM to 1PM), woke up at 7, turned off my alarm clock, fell asleep again, and woke up at 8:30. That wasn’t good. No breakfast for Simon. At least the group hadn’t left, although I wouldn’t have had any trouble finding the CCS building considering how many times I have been there since I got here last week. The beginning of the CCS meeting was boring (roughly, we stood around for an hour doing nothing; how disorganized!), so I got through a few pages of Rudin. The math submeeting was more interesting. The professors talked to each other (more or less) for about 20 minutes about algebra and number theory classes. Then Prof. Ryavec had one of the students (not a freshman) present a proof that he had come up with. The problem was to prove that if there are n points in a unit square, then there exists a point P inside the unit square such that the sum of the reciprocals of the distances from P to each of the n points was less than c*n*log(n) for some constant c independent of n. Apparently a very messy proof of this was used in a proof of a more difficult theorem, but Prof. Ryavec wasn’t satisfied with that proof and asked this student if he could come up with a better proof. He presented his proof in five or ten minutes, and it was clearly correct, and it was remarkably simple. It’s hard to believe that this proof wasn’t known before, but I guess it’s possible. If not, congratulations to him! He should publish it. After that problem, Prof. Ryavec presented some unsolved problems and told us not to work on them too much since they were hard.
In the evening I went to my first service at the UCSB Hillel. There were three separate services: orthodox, conservative, and reform. I chose to go to the conservative one, and it was a nice little service. I can definitely see myself going to the services weekly, as I enjoyed it greatly. Unfortunately, I had no idea how to get back from the synagogue, so I just tried to retrace my vectors as best as my inattentive memory could. I was quite lucky to find a little pathway from Isla Vista into the campus, and then I walked along a path for a while, still without any idea of where I was. Then I saw Snidecor Hall, and that was one of the stops on my first campus tour, so then I knew where I was, and I quickly returned to my dorm.