## Budapest Semesters in Mathematics - Student Experiences

**Daniel Crow '10,** a Middlebury mathematics major, just came back from his Budapest Semester in Mathematics, a program in English for American and Canadian undergraduates. Through this program, mathematics and computer science majors in their junior or senior years may spend one or two semesters in Budapest and study under the tutelage of eminent Hungarian scholar-teachers. The instructors of Budapest Semesters in Mathematics are members of Eotvos University and the Mathematical Institute of the Hungarian Academy of Sciences, the two institutions known for having educated more than half of Hungary's highly acclaimed mathematicians. There is an optional intensive language course offered about two weeks before regular classes begin, but the mathematics courses are taught in English.

During his spring semester at Budapest, Danny studied complex analysis, combinatorics, functional analysis, topics in geometry, and Hungarian, a required language course for Middlebury students who are studying here. According to him, the courses are definitely harder than the courses offered at most American colleges, but the efforts are worthwhile. Among all the math courses he took, functional analysis is conceptually harder than the rest, while complex analysis is a little bit easier. As for Hungarian, says Danny, it is an extremely difficult language, but the instructor knew they were there to study mathematics, so she did not put lots of pressure on them.

Danny further explains the setup for classes: for each course, they met twice a week for two hours each time with brief breaks in between. There was also an office hour during class time, and he says he found it extremely helpful. As for homework, there was usually a moderate amount of required homework to finish each week, but they also had really difficult extra-credit problems, and those problems could be very time-consuming. "There was one problem from combinatorics II, "says Danny, "only very few students from the past several years worked it out; it took me almost an entire day and I finally got it, using the techniques from functional analysis, interestingly enough."

The class sizes, adds Danny, are small. Class size is limited to 12; in his complex analysis class, there were only 5 people, and the same for functional analysis. He believes that small class sizes encourage direct interaction between students and professors, and discussions and office hours are more effective than ever. The program enrolled about 40 student in total this spring semester, but they usually have more, and fall semester is slighter larger. Surprising enough, Danny tells us that contrary to past trends in mathematics, there were almost as many girls as guys in this program.

Danny speaks highly of the professors at Budapest: they are all Hungarians, but since each has studied or taught in North America, they speak very good English and are awesome teachers. They are brilliant, helpful and make the class so much fun. His professor for combinatorics II was actually a good friend of Paul Erdös, one of the most prolific mathematicians of all times, and has published many papers with Erdös, an honor that most mathematicians covet.

Danny goes on to talk about life at Budapest. When asked whether he had any problem communicating, he says since English is widely taught in Hungary, most people can speak some, and with his limited Hungarian and their English, they could sort of communicate. "My level of Hungarian...hmm...I can count, to any arbitrarily large number," explains Danny. "Night life at Budapest is also great," he adds. "Strangely enough, Hungary doesn't have very good beer, but people can get good ones from other places easily as well. It *does* have good wine, though." Danny also traveled a lot in Europe, having described to have breathtaking landscapes and spectacular architecture.

In the end, Danny suggests people who are interested in studying at Budapest to take abstract algebra and real analysis before going there. Although these courses are not strictly required, they would be really helpful to prepare the students for other classes that they will be taking at Budapest. "Start applying soon," adds Danny, "Also, when you go there, take combinatorics and graph theory because they are what Budapest is famous for. Work hard, but also enjoy your life there."

In addition to Danny, several other Middlebury College student were previously enrolled in the Budapest program. **Greg Petrics 06**, went to Budapest in 2005. He graduated with honors of Summa Cum Laude, Phi Beta Kappa, and received 2006 Dr. Francis D. Parker '39 Mathematics Prize. He is now pursuing his Ph. D at Dartmouth College, working on a project involving minimal surfaces in the roto-translation group equipped with a sub-Riemannian metric. He published *Closed Geodesics on Orbifolds of Revolution *in the *Houston Journal of Mathematics* when he was an undergraduate student.

**Anna Blasiak '07**, a Mathematics and Computer Science double major, went to Budapest in the spring of 2006. She graduated Summa Cum Laude, earned both departments' highest honors, and achieved an appointment to Phi Beta Kappa. She also won the Dr. Francis D. Parker '39 Mathematics Prize and the Hazeltine-Klevenow Memorial Trophy for excellence in academics and athletics. Now she is a second-year Computer Science Ph.D student at Cornell University, currently working in the area of network coding, graph algorithms, and optimization problems. She published *Degree Sum Conditions in Graph Pebbling* with Middlebury College Professor John Schmitt in 2008 and has one other publication as well. The link to her webpage is, http://www.cs.cornell.edu/~ablasiak/

By Ying (Daisy) Zhuo