Tuesday, September 22, 2009

Real Analysis

Class was especially thrilling last night.

First, we got our first exams back. I got a 98.5% (only points lost were for forgetting a quantifier in a logical statement), and apparently the median was 70%, which was lower than I expected it to be. (Of the people I know in the class, the girl who is in both of my classes did not tell me her grade, the smart but unmotivated guy got a D, the scatter-brained gay guy got a 79%, and the guy who sits behind me and seems dim got an 87%, and would have had an A had he not mixed up "converse" and "contrapositive." So much for expectations.)

But, seriously, that wasn't the exciting part.

I won't get into all this math, but this past weekend, Ed and I were arguing about the real numbers. (We were actually arguing about the real numbers in a restaurant. I think people who sit near us must really regret it. It's bad enough listening to an argument at another table about politics or religion, but math? Of course we weren't fighting, just talking, but still.) And at some point, late in the conversation, I made some observation (relating to a hypothetical process for generating a real number), and Ed said, "Well, as long as it's Cauchy."

"What's Cauchy?" I asked. "Something like convergent?"

"Something like that," he said. "I forget exactly."

Anyway, I was sitting in class last night, thinking, my god, this class is really showing me where Ed's math genius comes from. I seriously feel like it is unlocking all of the little bits that Ed has that I do not have.

The following is not quite true, but you know how sometimes, someone seems to know a lot about an esoteric field, but then you learn just a few terms, and suddenly you can talk to them all about it? And it turns out that really very little knowledge separates you? Well, it's kind of like that. There are a lot of little backgroundy things that Ed can toss around (like, in case you want an example, "strictly increasing") and use comfortably that I've always had to think about a lot and process whenever they've come up, but that are now becoming background for me as well.

So, here I was, sitting in class, and noting in my margin (where I write personal notes) that I now know where Ed's math genius comes from, and the next topic that comes up is...Cauchy.

And I am so ready. As soon as Dr. P starts talking about what makes a sequence Cauchy, I know just what it has to be, and of course that's equivalent to convergence. And I was just thrilled. It was almost a sexual thrill, and I'm not sure if the almost-sexual part was towards Cauchiness or towards Ed or what.

It was a little bit funny, because I felt extremely thrilled on the inside, but on the outside, I was quite tired, leaning slumped over on one arm, and probably looked like every bored student in the history of bored students. I marveled a bit at the contrast between my feelings and how I must look, if the prof was paying attention. (People around me were groaning a little at each new thing - lemma, proof, theorem - that arose. It was late.)

So, that is how it is for me these days.

And oddly, I came home and Mosch was online and I told him about convergence, and monotonicity (if that's a word), and Cauchy, and he got all excited and wired. So obviously it is just good stuff.

1 comment:

Sally said...

Nah, it demonstrates nothing - Mosch just responds to your emotions. Um, so I guess I'm saying he's like a dog, only he can also talk human. Hmmm.