Putinar almost gave us another proof of zeta(2)=pi^2/6 on Tuesday using the Fourier series of x^2. He moved on right before deriving it, but he didn’t manage to fool me. I (naturally) started thinking about what would happen if we consider the Fourier series of x^3, but after thinking about it for a while, I realized that we could only find out something like 1/1-3^3+1/5^3-1/7^3+…, which is known to be equal to pi^3/32. Apparently this proof that zeta(2)=pi^2/6 is well-known, but I hadn’t seen it before, so it was exciting to me.
At the end of algebra on Tuesday, Agboola mentioned a paper about card shuffling and told us we could talk to him if we were interested in reading it, so after class, Jeff and I went to his office and asked him about it. Yesterday he gave us each a copy of the paper. That was very nice of him. It looks like a tough paper; I hope I can understand it.
After that, Jeff and I were outside South Hall talking, and Putinar saw us and made Jeff promise with a witness (me) present that he would learn Fourier series, either by going to class or by reading the book and solving problems. Putinar is such a friendly professor as well as a good teacher and a talented and highly-respected mathematician. I hope that after I learn a reasonable amount about analysis, he’ll let me do some research.
I found out today that Putinar’s special topics in math (functional analysis) and the graduate differential geometry class next fall will be at the same time. Now I have to make choices. I hate choices. I was really hoping to take both of them. What shall I do? Perhaps the conflict will save me from taking way too many classes next year (no, nothing will really stop me from taking too many classes, but at least it will be one fewer class) and is thus a good thing, but right now I’m annoyed about having to choose.