School begins...
Classes have started, so life feels as if it has returned to some sense of normalcy, except that everything is new.
I have been showing up to quite a few classes. Among other things, I like the "numbering" system for classes here.
NUT (Topics in Number Theory) is the more advanced of the number theory classes, but I've actually seen almost all of the topics listed as prerequisite in a combination of discrete math and algebra classes. We've been reviewing complex numbers and quadratic reciprocity. I'll probably take it, in the hopes that applying complex analysis to number theory sounds as awesome as I think it is. One of the professors for the beginning number theory class is apparently extremely quirky and hilarious and in love with Diane already. I guess I'm missing out.
TOP (Introduction to Topology) is the only course that obviously breaks from the CS-themed math that I planned to take here, though I'm sure some of you could tell me about cool applications to CS. There's a more advanced algebraic topology class that claims only to have real analysis as a prerequisite, but I looked at the first homework assignment and was completely lost. So introductory it is for me. It looks like most of the course is setting up the groundwork for sexier courses later, but at the same time it'll probably put to use (and then, the professor claims, throw away) all the metric spaces that I suffered through in real analysis. I might take it in the hopes that I get to learn about manifolds.
HAM (Historical Aspects of Mathematics) is actually a humanities class. This was apparent, well, first from the schedule, and second from the presence of (gasp) non-math people in the class. That's right, it's cross-registered with McDaniels College, a school whose Budapest program takes up an entire floor of College International. The non-math people consisted of three heavily made-up girls who sat together in the back of the class and talked non-stop, and one isolated hipster-looking guy off to the side. If their presence wasn't obvious enough from the distinctly different aura they gave off (or perhaps it was just the make-up), they piped up immediately to ask the professor if there was going to be any... math... in the class.
As for the professor, he was hilarious. He told us he came from the best university in Hungary, three hours from Budapest. Then he explained why we should stay in the class: 1. "You can learn a lot from me. If a young guy says that, he's just trying to sell himself. But me, I'm 60. I'm old, so it's the truth." (this was actually the answer to the afore-mentioned question) and 2. "In the US, they gave me a salary 12 times more than my salary in Hungary. So I decided I will help however I can. At my home university, of German students, 20% will fail. Of English students, 40% will fail. Of Hungarian students, 30% will fail. But you, 100% chance you will pass. Last year, 100% of students get an A."
The lecture itself was on the origin and history of measurement, which he told us was the inspiration for mathematics and scientific discovery. It was interesting, but I was suffering in a three-hour lecture after four straight hours of math lecture, and left halfway through. I don't think I need an easy-A humanities course. Apparently the last hour tied together the random threads he had begun in the first one (Fahrenheit, Celsius, Kelvin, the origin of the word meter, Babylonian miles and measurements of hours and minutes, our base-60 time system, and the shifting of the Roman calendar) into an awesome conclusion.
GTT (Graph Theory) contained a lot of proofs by picture. Right now it's all basic definitions and theorems on trees. I feel like a lot of the topics will either be review from CS courses (basic notions, Hamiltonian cycles, cliques, bipartite matchings, network flows, probabilistic method) or last summer (chromatic number, planarity, Ramsey theorems). I could use a more formal treatment of a lot of these topics, and it's certainly fun, but at the same time it will be much less new than some other courses. Waffling. I'll need to try the homework.
C&P (Conjecture & Proof) is the classic "only in Budapest" class. The syllabus: proofs of non-existence, proofs of existence. The class is two to three times larger than any other of my classes, about 30 students, or more than half the entire program. The first couple lectures, we did: 1. you can't remove diagonally opposite corners of a chessboard and tile it with two-squre dominoes, 2. the "standard" proof, an analytic proof, and a geometric proof of the irrationality of root 2, 3. two proofs of Sperner's Lemma, 4. using Sperner's Lemma to prove Brower's Fixed Point Theorem, and 5. Gallai's proof of Sylvester's problem (if you have finitely many points which are not all co-linear there is a line which contains exactly 2). Totally awesome. The homework isn't due until next Thursday, but it was the first one I started.
HUN2A (Hungarian Language, focus on reading and writing). Not many people are continuing on with a language course. In this one, we're supposed to keep a diary in Hungarian and translate a short book.
I wrote a summary of my experience with Hungarian so far in an email to Hixie:
> Sixteen cases?!?!?! Good god. Give up now. :-P
Yeah, so there's your standard nominative, accusative, genitive, dative, and so on... and then there's a whole system of directional suffixes corresponding approximately to {from, at, to} x {in, on, by}, except that in addition these all correspond to our normal prepositions like "about" or "with" as well. Plus there's random other suffixes for stuff like time. These are complemented by whole systems of prefixes for verbs, leading to such fun direct translations of sentences as "upsoar (I) the businto" (I got into the bus). Oh, did I mention that they usually delete personal pronouns, too?
The only (and I mean only) saving grace is that there's no gender. Of course, when I say no gender, I really mean no gender. The third person singlar pronoun is genderless. Which means that sometimes Hungarians learning English screw up the whole he/she thing when talking about men and women.
However, since only one form of each suffix would be far too few, there's this whole notion of "vowel harmony" which effectively takes the place of gender for complicating the endings. For the most part, if a word has the vowels a, o, or u in it, it has one kind of ending, and if it doesn't, it has the other. Except sometimes if there's an umlaut there's a third form for umlaut-words. And also, some words with the letter i act like the aou words, but not all of them.
CO2 (Combinatorics of Set Systems) is a pretty uniquely Hungarian subject. It is the more advanced of the combinatorics classes, but after looking through the course notes for Combinatorics 1, I think my CS experience in combinatorics is more than adequate. The lectures launched straight into hypergraphs, discussing dual graphs and Steiner systems. I was glad I've at least seen a Fano plane before. The whole subject seems to inspire yawns of "who cares?" from people hoping for different kinds of combinatorics, but *I* think it sounds like fun.
The biggest surprise of the week has been that I seem to have actually taken more math classes than the average student here. The answer, of course, is that I'm on my way to grad school while most kids here are juniors, but that doesn't quite work, since I'm less than halfway done with the number of required courses for a pure math major at Berkeley. This has led me to the realization that Berkeley actually does seem to be a pretty good school. Amazing.
The second biggest surprise of the week has been that I've started to hear back from graduate schools already. I wasn't expecting much until the end of the month. The news so far has been almost uniformly excellent. Among other things, I will be in New Jersey between Feb. 24 and 27.
It's been dumping snow all morning. We were planning to go to the city park to ice skate before going back to the Szechenyi baths. Hot tubbing in the snow.
The construction next door begins work at 8 am on Saturdays doing something that involves a lot of metal crashing into things.
I have begun sleeping with my radiator. It's my new favorite friend. It has solved the problem of me being too cold to sleep at night. The new bed arrangement has broken the feng shui of the room, but I think it's a worthwhile sacrifice.
The addition of internet access to our home has broken the quiet monotony of our evenings. The combination of the sun setting at 4:30, nearby stores being closed by 8, a lack of clocks in our apartment, and only each other and books to keep company made time seem to progress slowly at night. I would check the time, expecting it to be past midnight, and discover it was 9:30. This problem is no more, thanks to the advent of per-minute modem access and grad school anxiety which leads to the constant and excessive checking of email.
