So this is my last quarter as an undergraduate. I feel that I am now completely ready to move on with my life and begin graduate school in the fall (at Stanford). Stanford has outstanding offers for two senior faculty positions in algebraic number theory for next year; I really hope that at least one of them is forthcoming, or else I may find myself looking for another thesis topic. They already have two analytic number theorists, so that would be a reasonable place to start; other possible areas are algebraic K-theory, ergodic theory, and algebraic geometry.
I expect this quarter to be much more manageable than the last in terms of courseload. I have only four course, but then I’m also teaching one. I think I should allow myself a lot of time for preparing lectures so that I don’t do (too many) really stupid things while speaking. So far preparation time hasn’t been too significant, but that’s because I spent a lot of time last quarter thinking about what I’d talk about at the beginning. I think my first two lectures went pretty well. I found myself having slight difficulties coming up with the best possible wordings for the rules for the games we will be concerning ourselves with (mostly Nim, Hackenbush, and Domineering). But the people taking the class at least pretend to enjoy it (and I hope that they aren’t just pretending!), so I imagine it’s going pretty well. We’ve more or less finished chapter one of Winning Ways, but I’m not exactly following the book, and I didn’t talk about some other (non-Hackenbush) games at all.
Now for the classes I’m not teaching… Quantum computing. I don’t know anything about quantum mechanics, so presumably I’ll pick something up along the way. So far not much has been new to me; we spent the last lecture discussing Turing machine computations, but I did that sort of stuff all last quarter, so it was just review. The next class is “Hilbert space formalism” and other stuff, so that will probably also be mostly review except the stuff on quantum information. But the lecture this coming Wednesday is on stuff I know nothing about, so that should be exciting.
Number theory and cryptography. All the number theory he has talked about so far is extremely basic stuff that I knew in high school. But some of the cryptographic stuff I hadn’t seen before. (What? Number theory has applications to the real world? How dare they!) So at least I’m getting something out of it.
Elliptic curves. This was going really well for me last quarter; I was understanding just about everything we did, but then a two-week break sort of messed up my memory. But I think I’m back on track now after a bit of review. We’re doing elliptic curves over local fields, which are fine, but I’m really excited about elliptic curves over global fields, which will be the next topic. It would be extremely interesting to see a proof of the Mordell-Weil Theorem, for instance.
Distributions, Fourier transforms, and Paley-Wiener theory. This class is tough. I’m a bit rusty on this sort of analysis to begin with, and Mihai’s lectures are notoriously speedy in general. Unfortunately, the textbook for the class (Lars Hörmander’s The Analysis of Linear Partial Differential Operators, I) is out of print, so we have to rely on photocopies, which have the annoying tendency of making me not want to read them. I must overcome this bad habit. So this class is going to be difficult if I really want to stay on top of things, which I think I do.
I ran into Ibarra (my professor from my computation and complexity course last quarter and the automata theory course the quarter before) in the hall of the compsci department last week. I think he was disappointed in my performance in his class last quarter. He said that my final was “good, but it wasn’t the top.” I told him I accepted Stanford’s offer, and that pleased him. I don’t think he thought it was even worthwhile to look at other places after Stanford accepted me, and given some of the people on the computer science faculty (and particularly theory people) at Stanford (for example, Knuth (emeritus) and Ullman), that might be reasonable, but of course I’m not in the computer science department.