Classes!

I've been in Budapest for 11 days now, meaning this is now the longest I've ever lived in a large city. The adjustment has not been as difficult as I thought it would be--although there are tons of people here, I've found a number of nice green spaces that feel more open than the city hubs, and my apartment provides a good space for me to be alone when I need it. I've definitely been experiencing some culture shock over the last week or so, but overall I'm feeling pretty happy in Europe.

Classes at BSM started last Monday, and I've spent most of this week attending as many of them as I can. We don't register for classes until three weeks into the semester in this program, so that students have time to shop around and find the classes best suited to them. I had a tentative schedule prepared before classes started, and after this week I feel fairly confident that I'm going to stick to it. In case anyone is curious, I'll describe each of the classes below:

1. Beginning Hungarian: I'm living in Hungary, which is a great opportunity to learn some Hungarian! Although I'm mainly here to study math, I'm also interested in linguistic anthropology, and Hungarian is interesting to study because it is one of the few non-Indo-European languages spoken in Europe. For the first week we focused on learning pronunciation and some basic phrases, but I hope to learn as much as I can before the semester ends. 

2. Discovery Learning (The Pósa Method): Hungary is famous worldwide for its methods of math education, and this is one of the primary techniques. I don't know much about it yet, but the basic idea is that the teacher creates "problem threads" for the students. These sequences of exercises lead the students to independently rediscover important mathematical results. It's a unique way of teaching math, and I'm excited to learn in the very place where it originated.

3. Algebraic Topology: I've wanted to take a topology class for years, and now I finally have the opportunity to do so! Topology is a sort of "rubber-sheet geometry" that examines the ways in which different objects can or cannot be transformed into one another, and algebraic topology aims to do this by establishing connections with group theory and other areas of abstract algebra. It's a little bit difficult to explain but it's awesome.

4. Commutative Algebra: Commutative algebra is an important branch of modern algebra, and it is very closely related to algebraic geometry, the field in which I did research this summer. This class is rumoured to be hard, so I expect to be collaborating frequently with my classmates, which is another important part of my mathematical education. :)

5. Functional Analysis: To be honest, I know very little about what functional analysis is. It combines some different ideas from linear algebra and real analysis and involves infinite-dimensional vector spaces I think? Mathematics can be roughly divided into algebra (which mostly considers discrete things) and analysis (which mostly considers continuous things), and I know much more about algebra than analysis. The professor for this course seems great though, and I'm hoping it will help balance out my schedule, since the other two courses I'm taking are on the algebraic side.

In addition to these five courses I plan to take, I also attended two courses that I won't have time for later in the semester. One was an introduction to topology, and the other was a problem-solving course called Conjecture and Proof. Both seem great, but sadly they don't fit with my schedule, so I cannot take them.

In addition to all of the credit courses here at BSM, there are four non-credit courses, all of which are interesting. The only one I've attended so far is Classical Algebra, which covers some techniques for working with polynomials and complex numbers that aren't usually taught in American schools. The professor is absolutely hilarious, and it's worth going to lecture just to observe his teaching. The other three non-credit courses are a GRE prep course, a Putnam prep course (the Putnam is a very hard math test undergraduates can take for fun), and a Hungarian culture course, and I hope to attend all of them as long as I have time.

Although this week has been dominated by taking classes and adjusting to the pace of school life again, I did find some time on Friday to explore. I took the subway to Fővám tér, which is right in the middle of the city, and then walked north along the Danube towards the parliament building. I meant to visit St. Stephen's Basilica, but I got distracted watching the boats on the river and somehow missed it. I did see a lot of statues and the parliament building though. After walking for a while, I crossed a bridge onto Margaret Island, which is a huge park in the middle of the city. I walked the whole length of the park, seeing lots of interesting statues, gardens, and fountains, before crossing back over to the Pest side of the city. At that point I realized I had walked roughly eight miles, so I found a bus back to Fővám tér and then caught the subway back to my apartment. It was a great time!

I had planned to go on more explorations this weekend, but I came down with a bad cold and decided to lie low for a few days to ensure I'm healthy enough to go to classes again on Monday. I did go out to Market Hall with Mykhaylo on Saturday morning though, and we bought some bread and spices to liven up our cooking in the apartment. Market Hall is huge and kind of touristy, but it's also a lot of fun to explore, and I loved seeing all of the produce, spices, cheeses, and textiles that people were selling in the stalls! Overall everything is going very well here, and I'm excited to see what the next few weeks have in store now that I'm becoming more comfortable with the city!

Pictures to follow immediately.