Today began the same way Wednesday did. Witth breakfast (my breakfast habits get very fixed very quickly. Pretty much every morning it's been coffee and a muffin, usually chocolate chip) and then resarch seminar. (Beginning the morning with coffee, chocolate, and math. What more could I want?)
The research seminar today was a deepening of the introduction we'd gotten yesterday. In Dr. Farley's ideal plaan, he would have given us a brief but thorough explanation of what was going on in the paper, and get us started on thinking about how to extend this to groups with more than 2 generators before lunch. Then after lunch, we would have been free and eager to learn about the next project.
Things didn't quite work out that way. All of us had verified the existence of the paper, but none of us had read, or even started trying to read it. (Reading a math paper is hard enough under ideal circumstances. A mathematical paper in a subject you were only introduced to last week, and even then not very thoroughly, is not an example of ideal circumstances.) So Dr. Farley spent a decent portion of class trying to explain it.
The issue is that he was trying to explain the paper in exactly the same way he would have attempted to understand the paper himself. And what works really well on an individual basis learning math (working through the examples, making guesses as to how to get from step one to step three, making mistakes and correcting them) works much less well when you're trying to explain something to students. So by the time we finsihed for the day, we had a better idea of what the paper was proving and why this was important, we had no idea how the authors had achieved this for groups with two generators, let alone where to go from there.
We also have no idea what the other projects are. Which is a shame because he's told us there are others. And I'd rather have a general overview of the three problems and then narrow focus from there. Oh well. At least we know in general terms what one of the projects is about, and we have a paper to read and struggle to understand over the weekend, so we have no excuse to be bored.
During the seminar, it started pouring. The rain was still pretty heavy when the class ended, which most of the people I was with seemd to find discouraging. I thought it was nice and, when the rain stopped and I was able to walk around outside without fear of getting soaked, I found that it had turned into a beautiful day. Given how hot it had been the past few days, the coolness that the storm had brought with it was much appreciated.
Speaking of things that are increasingly appreciated... analysis. Today, we were discussing topology of the real numbers, and everything made so much more sense than it did during the research seminar. Not just because the real numbers behave so much nicer than some of the topological spaces we've been looking at, though that was certainly a factor. It was ust well-defined and explained, with theorems that we were able to prove and a pervading sense of logic and intuition.
One of the ideas that several of my classsmates have come up with is to replace the first week with just short courses. Though it would have a disadvantage in terems of introduction to the research problem, I think it would have some significant advntages. Mainly, it would allow us to learn the material in the short courses as opposed to relying on the definitions that need to come up to understand the research. I also think a short course in topology would be helpful. Not sure how doable it is (there's only much you can cover in 13.5 hours), but certainly I would be feeling a lot more comfortable right now if I thought I understood the foundations of topology.
I am glad we have the short courses, though. A lot of REUs don't. Even though so far it's been more review than new material, the review has been helpful. It think formal explanations like the ones from the algebra class have been necessary, especially for the students who haven't taken an Abstract Algebra class before. And Analysis has been a welcome break from incomprehnsible examples and hand-wavy proofs. So I'm very glad we have those, even though it's made for long days.
So that was the first week. It's been a strange week. Slightly overwhelming, which is a good thing. (I basically only have two modes- overwhelmed and bored. Overwhlemed is by far the better mode to be in.) Everyone's getting along well, which is good. (It would be a very long six remaining weeks if there were a couple of people who couldn't stand being in a room together.) 8 is a a nice, manageable number of students in the program. It's large enough that we can split into smaller groups easily and in a number of ways, but it's also small enough we can do things together as a full groupov Most years, SUMSRI is bigger but I think I'm glad that this isn't one of those years.
Today, I got paid for the first part of the program, which was exciting. Both because it's the largest paycheck I've ever had, and because it's the most closely related to what I want to be doing with my life. And when I'm not freaking out about this decently-large amounts of money, I find it amazing that I am actually getting paid for this.
At breakfast last Sunday, Griselda made a comment along the lines of not believing this was real. That without knowing anyone, or even that much of what we'd be doing, she'd shown up in the middle of nowhere (her words, not mine) to do math. Most of the others nodded in agreement, but I caught myself thinking “really?” This pales in comparison with the other times I've gone somewhere without knowing anyone, or having that good an idea of what I was doing.
Between the craziness htat was the end of last semester and the terrifyingly huge adventure that next year will be, I didn't spend much time thinking about SUMSRI until I got here. So I wasn't really sure what to expect. To be honest, I'm still not. I know our schedule for the next two weeks, but I have no idea what comes after that.And I'm surprisingly OK with that. I don't know what I'm doing next, but I know that so far, I'm doing fine, which is all I could really ask for.
I can't say how this compares to my expectations, but so far, I think I can say things are going about as well as I could hope. I'm looking forward to the next 6 weeks.
