#### A Fairly Objective Overview, Until The Last Part At Least

Budapest Semesters in Mathematics is a program whereby American and Canadian undergraduate students can spend a semester or two in Hungary, taking courses from eminent Hungarian professors. All classes are taught in English^{1}, and unlike in many other undergraduate study abroad programs, the workload is intense and the material quite difficult^{2}. Much of this comes from the simple fact that any way you look at it, math is hard. But BSM is an incredibly rewarding experience for those who persevere. Donald Knuth has said, "The Hungarian educational system has been the most successful in pure mathematics," and even in a single semester there is a lot of math to be learned here^{3}.

The program was initiated by Pál Erdős, one of the greatest and most eccentric and prolific mathematicians of the 20th century; László Lovász; Vera T. Sós; and László Babai. The first semester of BSM was in the spring of 1985, with fourteen students attending^{4}; after the near-death of BSM a few years later when Babai had to turn his attention to other things (the class size dipped as low as 3), word started getting out in America and the program has been steadily growing ever since. The program is currently run by Paul and Bonnie Humke, with St. Olaf College, on the American side of the Atlantic, and by Dezső Miklos and Klára Kerpely on the Hungarian side.

Currently, the average number of students participating in BSM in any given semester is around fifty or sixty, with a few each year opting to stay there for a full two semesters^{5}. According to the BSM website, over 170 colleges and universities have sent students to participate in BSM, and by the pigeonhole principle some colleges have sent several students.

Courses offered include number theory, combinatorics, analysis, algebra, topology, graph theory geometry, Conjecture and Proof^{6} and many others, covering basically all the most well-known fields of mathematics^{7}. Advanced courses in some of the more popular subjects such as combinatorics are usually offered too, as well as occasional slightly "fringe" courses like theory of computing, set theory and logic. Finally, most weeks feature a colloquium lecture by a prominent Hungarian or American mathematician.

As for the practical stuff... students can choose to live either in an apartment (usually with other BSM students) or with a host family. Living costs are very cheap compared to those in America and, in fact, most of the rest of Europe.^{8} The public transportation system is robust and fairly reliable^{9}. The most unsettling thing is probably the language barrier, but you'll learn to get by even if you don't learn Hungarian^{10}.

And then there's the city. The only complaint I can make about Budapest is that it's not the cleanest city, but it is beautiful nonetheless, there's no question about that. The Danube River slices right through the middle of it, separating it into urban Pest on the east side and hilly, calmer Buda to its west; the two sides are connected by eight different bridges all of which have their own unique design. The architecture is magnificent. From the huge Parliament building to the palace in the castle district, it is possible to take a walk starting virtually anywhere in the city and come across something stunningly attractive, and more verdant regions can be found in Városliget (City Park), Népliget (People's Park) and on Margit Sziget (Margaret Island). Statues of famous Hungarians, after whom most of the major roads in Hungary are named, are to be found in abundance too. The famous statue of the monk Anonymus resides in Városliget, and that of Szent Gellért, overlooking Pest from Gellért Hill^{11} (from atop which the whole city can be seen in all its splendour) is remarkable as well.

There's little bad to say about BSM. It was difficult and strange for me, but people who study mathematics know that the difficult and strange things are often the most rewarding and beautiful as well.

#### My Totally Subjective Annotations, Since I Did It And All

- It's a good thing the courses are taught in English, because Hungarian is a notoriously tough language. Nevertheless, I encourage anyone considering BSM to learn what they can. Hungarian is a beautiful and unique language, and on the practical side, relatively few Hungarians speak English.
*I* found the material quite difficult. Others seemed not to. Classes are taught at a fast pace, and you are expected to know the prerequisite material well. You may be well-advised to bring your class notes for background material with you, or to review it beforehand if you happen to be rusty on it.
- The emphasis is very heavily on creative problem solving. Gone are the problems where you can just hack away and eventually get them; many of the problems you'll encounter here require real ingenuity and cleverness to solve.
- BSM was originally going to be a graduate program or a four or five year undergraduate program. Babai, who gave a colloquium lecture while I was in BSM, didn't commit fully to the idea until one of his friends suggested making it a "semester abroad."
- The caliber of the students who attend BSM is amazing; the stereotype of math students as social rejects who stay in all the time could not be borne out less. One of my friends was applying to law school during her time in Budapest, one fenced and juggled, one was a classical music afficionada and had won a few violin competitions, several knitted or crocheted... the list went on. These were all exceptionally diverse and talented people, and they could talk math as well. I was surprised I could even have a normal conversation when I got back home.
- Conjecture and Proof is only offered as a BSM course, and I recommend it highly. It focuses almost exclusively on interesting mathematical concepts, problem solving, and elegant solutions to difficult problems. Lectures happen only occasionally; the course is mostly taken up with student-presented solutions to the homework problems, with the professor chipping in when he sees a way to shorten a solution or offer a more elegant one.
- The areas in which Hungarian mathematics excels are generally considered to be combinatorics and number theory. My Galois theory professor once asked who was taking either number theory, combinatorics, or the BSM-exclusive course, Conjecture and Proof. "Why are you here?" he asked the people who didn't raise their hands.
- A nice, spacious one-bedroom apartment cost about $425 per month, with utilities. That was for me, though, and I was one of the very few people without a roommate; I'm fairly sure most people paid less. When grocery shopping, I bought as much as I could carry and never managed to spend more than about $15 for roughly a week's worth of groceries. The exchange rate hovered at just over 200 forint (the Hungarian currency) to the dollar during my stay.
- My Conjecture and Proof professor said "Please do not rent a car in Hungary." I'm inclined to agree with him. Hungarian drivers are psychotic, and the roads are weird, not orderly like in a lot of American cities. Buy the hugest public transportation pass you can find and learn to love the metro. It's like a lifeline running through the city; memorize which stop is nearest to you and no matter where you are, all you need to do is find a metro stop to get home.
- My friends and I agreed, for the most part, that it takes about two months to get comfortable with life in Hungary, by which point you'll be gearing up for the end of the semester. That's the way things go, I suppose.
- Budapest has a lot of culture to offer as well, but that's a topic for another node, maybe. I would, however, venture to recommend that any visitor to Budapest go to Gellért Hill and the Castle District; the views from either are breathtaking.

#### Reference

The BSM web site. `http://www.stolaf.edu/depts/math/budapest/`