Yesterday morning, I went to school to participate in the Putnam Competition. This is a six-hour math exam (if you want to call it that), split into two 3-hour sections, with a lunch break in between. Each section has six questions that require college mathematics and a lot of creative thinking to solve. Each question is worth a maximum of 10 points, with partial credit given, and the median score is typically 1 or 2 points (out of 120).
I didn't really have time to go, but I didn't see how I could miss it. The competition is only for undergraduates, so this was my last chance, and I'd never done it before (nor had an opportunity to, that I was aware of, though you can take it four times overall and needn't be a senior nor a math major). I wanted to support our math department as well; I knew some people wouldn't show up, and I wanted to be able to say that, yes, we can at least field a Putnam team. (I wasn't on the actual team, which is three people from each school, in the end. But that's fine. You don't work together anyway - it's a purely individual endeavor.)
The morning session was fun. Of the six problems, one looked tractable, but I didn't get anywhere with it. I turned to another question that looked less tractable and ended up writing out an answer. (You have to write a full proof for the answer, not just solve the problem.) I am pretty sure a central assertion in my proof was wrong, though, but I haven't had a chance to check it yet. (It involved an 18x16 matrix, which I'm sure was not how the problem was meant to be solved.)
What was fun was that I was only trying to score any points at all. On a normal exam you're trying to get all of the points, or fall short as little as possible, but I was aiming to just get above 0, so it wasn't really stressful. I had three hours to work on as little as one problem.
The professor running the show bought us lunch - we all walked over to Old Chicago. It was actually pretty blissful. There were six of us students, of whom two are in my advanced calculus class, one is in my "senior seminar" next semester (but I hadn't met him yet), and the other two were unknown to me. (One I'm not so sure about - he argued on the way to lunch that irrational numbers can be accurately represented as fractions, using 22/7 - a classic approximation for pi - as an example.) We talked about the test, and other math topics, all through lunch. The professor kept quiet and just let us talk, which for all I know might have been out of peevishness at our annoying qualities, but felt gracious.
I found myself hoping that this is what grad school is like - that there are other people around and you can talk about math with them sometimes. I realize undergrad is like that for some people, but it hasn't been for me. I really enjoyed it. I also realized that I hope my graduate program does not have a competitive feel to it, because I wouldn't have enjoyed lunch nearly as much had we all been trying to one-up each other.
After lunch, we had six new problems. Several of them seemed tractable but I couldn't gain any traction for a long time. I was really tired from my week (I've been exhausted pretty much all week, and had to get up extra early for this thing), and that started to kick in, and I had had too much iced tea at lunch, so I had that nervous/sick kind of feeling, plus I kept having to pee. I finally did get an answer to one question. I now think that part of my answer was wrong, but I was really happy with the way that I approached it and the style of proof that I wrote for it. Still, I did not enjoy the afternoon session very much.
In the end, I am really glad that I went, and I'm hopeful that I might have scored 2 or 3 points on the exam. I'll post when scores come out.