Lim (maths)

And now, the descent into math classes…

As part of BSM, the first three weeks are allotted as shopping weeks for classes, so students can sit in on as many as they care for and then decide between them (registration after the third week). Everyone agrees this is a great setup because we can take in all the maths we want in the first three weeks and then dive further into fewer subjects after. Everyone agrees this is a terrible setup because we will take in as much maths as we can in the first three weeks. In that vein, it’s recommended to take about 5-8 maths for now then narrow it down to 3-6 once favorites become clear. The problem arises when they all are.

On Monday (with all classes in 2-hour blocks), I attended differential geometry, mathematical problem solving, and classical algebra. I quickly realized that with little topology and no analytic geometry in my background, differential geometry would not work. Mathematical problem solving was loads of fun, though; the first few problems we spent time on just push the boundaries of most students’ problem solving abilities. the professor is childlike and plays an ocarina to reconvene the classroom. It’s going to bring in some combinatorics, some number theory, some geometry, and some college algebra to hone students’ problem solving skills (good for the Putnam?). As for classical algebra, it’s an interesting concept; this American professor (the only American in the program) is going to teach an ungraded, 12-hour (total), 3-week “catch-up” course for students to make sure they have all the prerequisite algebra that a Hungarian entering this math program might have (“Everything Gauss knew when he was 19”). The first two sessions have been entirely on complex numbers, which I have never studied more than in passing, so I was attempting to focus, but…it seems the professor makes mistakes that I even notice, and jumps from one topic to the next so fast that if I’m going to understand complex systems, it’s not going to be his doing. And it follows four hours straight of math, so focusing is hard.

On Tuesday, I sat in on an intro combinatorics course (big in Hungary), complex analysis (taught by the only female professor), and topics in geometry. Combinatorics was cool because the professor seemed like such a nice guy, but I think I will definitely despise counting problems by the end, e.g. how many different permutations of the letters in the word “optimization” are there? I liked complex analysis because the professor actually laid out the structure of the class by giving us some theorems we were going to cover; it meant a lot of different areas in a short amount of time, and I know most of the class didn’t quite follow the proofs yet, but I genuinely think she’d be a good professor. And topics in geometry was awesome. The professor moves at just the right pace inbetween too challenging and too comfortable. He began by saying, “nobody likes Euclidean geometry. We’re going to skip over Euclidean geometry.” Twenty minutes later, we were looking at Euclidean planes. But next week, I think, we’re going to begin spherical geometry (from a spherical perspective rather than a flat one), then we’ll do projective geometry (looking at transformations), and then hyperbolic (negating the fifth postulate about parallels).

I was starting homework for that class in a communal study room, and trying to find a shape which would give me a certain isometry. A BSMer who I recognized but did not know walked in, asked what I was working on, and then the two of us spent the next 15 minutes coming up with a single shape to fit the criteria. This is why I’m part of a fantastic program.

And Wednesday was all about Geometry, Topics in Analysis, and Hungarian language. I’m glad I decided to go with “topics in analysis” rather than “real functions and measures,” which is the advanced version, because we are moving very fast as it is in the topics class, which is supposedly intro-level. Although I’ve taken a Real Analysis I class, it mostly spent more than enough time on every definition and theorem, so we moved slowly; i.e. I think we’re going to cover the majority of that semester-long analysis course within two weeks of this one, and throw in a lot of new information/perspectives in that time. As for the afternoon (3-hour long) Hungarian class, it was with Erika, who I had for the intensive language course, so it was great. We sang a song about whales eating rasperries, and it’s probably good that there was no writing on the first day, because my brain was shot.

On Thursday, I returned to Complex Analysis, Real Analysis, and Classical Algebra, and Friday, I was back in Combinatorics and Mathematical Problem Solving. I really like all these classes; I think it’s going to come down to Complex Analysis vs. Real Analysis and Mathematical Problem Solving vs. Combinatorics…but I don’t want to make this choice. Could there be a problem in combinatorics here? Anything to keep me from deciding.