Budapest Math Program Challenges Tech's Best

July 2002

When David Eger started looking at study abroad programs two years ago, he found very little of interest. Surely there were programs that offered a good selection of Architecture and History classes, but he found that going abroad and learning proofs and theorems just wasn't a popular college diversion for most American Undergraduates. For an out-of-state math major, studying abroad needs to aid, not just delay, graduation.

"When I found the Budapest program, I knew immediately it was what I was looking for," remembers Eger. "Some mathematicians whose books I rely on grew up in Budapest--scientist including Pál Halmos, John von Neumann and Pál Erdõs. When I heard Don Knuth extolling the mathematical education system of Hungary, I really didn't have any doubts."

What David found in his travel served well to reinforce his expectations of high-caliber of mathematicians. Run over by the Turks, yoked by the Hapsburgs, being stripped scandalously of two-thirds of its land after the World Wars, doomed to playing along with its imperial neighbors Germany and the Soviet Union during the twentieth century, Hungary has had more than its share of rough times. However, those rough times have instilled in its people an interesting cleverness.

As explained by a Hungarian biomedical researcher, "When a laboratory test takes you two months to run, and your Western counterpart gets his results in two days, you learn to make every test count."

"Szabó Csaba, our professor for Galois Theory and Number Theory, was wont to rush through proofs at such a speed that only a couple of people could keep up -- and half of the time, in the end he would turn around, admit that he'd lied to us, and then ask us to find the mistakes - it was a wild ride," David recounts. "He was always scrawling madly and tossing his chalk at the board, trying to prove as many theorems as humanly possible while he had time."

As an example of some of the cleverness of Hungarian teachers, here is a theorem from elementary number theory. The sum of phi(d) over the divisors d of n is equal to n. Typically, this fact is proved using cyclic groups, or playing cleverly with products and the multiplicative property of the Euler phi function. Instead of either of these, Csaba wrote down the fractions of the form k/n where 1 <= k <= n. Then noted that, when written in reduced form, each of these became a fraction of the form j/d where j ranges over all of the numbers between 1 and d relatively prime to d, and that d ranged over the divisors of n. Voilá!

Entrance to David's Flat a Day of Class on Margaret Island Hungarian Parlament Keleti Train Station David's Home on Szent Istvan körüt

The mathematics programme in Hungary covers the equivalent to American Graduate school while the Hungarian students are undergraduates. Though the Budapest program is in English, targeted towards American undergraduates, the teachers are all native Hungarian professors. "It was certainly a humbling experience being surrounded by so many brilliant teachers," David says. But then, when kids talk math instead of baseball during elementary and secondary school, young mathematicians come to college ready for a challenge. "I'm really glad I was exposed to a taste of it--I mean, who really thinks there's a subset of the plane that maps into a proper subset of itself under isometry? The ideas that we tossed around on a day-to-day basis -- it's gotten me excited about going graduate school."

While taking grad level courses like Measure Theory, David got a chance to explore Eastern Europe with his American compatriates. From Transylvania to Bohemia and Croatia, they brought Putnam problems to ponder while sampling Romanian wine and Czech Beer. "I met some of the people who I'll be collaborating with in the future. These weren't you're typical college kids just studying abroad to party - they're the ones who are going to be teaching at the best American Universities and publishing articles in Journals and going to MAA and AMS meetings."

David received a scholarship from the Georgia Board of Regents for his Study Abroad. The Regents' scholarship is open to all University of Georgia students.

This summer, David is doing Undergraduate Research sponsored by the Mathematics Department's recently won NSF VIGRE grant. He is studying under Dr. Johan Belinfante and Dr. Olin Shivers, investigating symbolic computation and formal methods. While at Tech, David has been active in the Psi Upsilon Fraternity and the DramaTech Theater. He will graduate in the Spring of 2003 with Bachelors' degrees in Applied Mathematics and Computer Science.