At the International Mathematical Olympiad held in Tokyo this past summer, two Madison high school students, Daniel Kane (Madison West High School) and Po-Ru Loh (Madison Memorial High School) were the two top scorers on the USA team, earning them Gold Medals again (see last year's Van Vleck Notes). The hardest problem (so we are told) in the competition was a problem in analytic number theory, and Daniel Kane was the only USA team member with a complete solution. In spite of these two excellent competitors, the USA team only took third place (behind Bulgaria and China). Po-Ruh's sister, Po-Ling Loh, another very talented high school student, was also among the top 12 high school students in the IMO qualifiers, who later competed for the 6 spots on the USA team. Daniel is now a freshman at MIT, and Po-Ru is a freshman at Cal Tech where his brother Po Shen Loh is also a student. You can read more about the ``Loh dynasty'' in the August/September issue of FOCUS (page 17) published by the Mathematical Association of America.
Dani Kane & Sen. Feingold
|Daniel Kane has won a prestigious $50,000 scholarship by the Davidson Institute for Talent Development for his project ``Two Papers on the Theory of Partitions'' as a representation of ä prodigious achievement in the field of Mathematics." He was awarded this special honor at a ceremony at the Library of Congress (see the accompanying photo with Senator Russ Feingold of Wisconsin). Daniel was accompanied by Ken Ono who has been his research mentor.|
Daniel has written 3 research papers. One, ``On an elementary approach to partition asymptotics,'' will be appearing in the Ramanujan Journal. Another paper proves a famous conjecture of George E. Andrews and Richard Lewis on Freeman Dyson's crank function. This paper has been accepted for publication by the Proceedings of the American Mathematical Society. He was also the focus of a CNN Headline News feature story in October 2003 which was partially filmed in Van Vleck Hall. Ken Ono was his research mentor on all three papers.
Our annual Student Awards Ceremony was held on May 7, 2003 in the 9th floor conference room of Van Vleck Hall. We have some truly excellent undergraduate mathematics majors, some of whom received awards at this ceremony.
An ``Integration Bee'', arranged by Jim Reardon of the Physics Department and sponsored by the ``Wonders of Physics'' program, was held in Sterling Hall recently. The competition was in two parts: A written qualification round, 50 integrals to evaluate in 60 minutes, and a week later a second round ``live'' at the board. The second round had pairs of contestants (from the 14 top finishers in the first round) going head-to-head working out integrals at the board: The first to circle a correct answer won the round, and two losses resulted in elimination. The answer had to be correct up to an additive constant and could include complex arithmetic so long as it would evaluate to a real value. If neither contestant got a correct answer within the available time, the same pair would have to try a new integral.
Both graduate students and undergraduates were eligible to participate: The overall winner got a $100 gift certificate for the UW Bookstore, and the top undergraduate got $100 cash. (If the winner had been an undergrad he/she would have gotten both prizes.) The contest excited a lot of interest among math grad students, whether for the money or the thrill of competition not being clear ... Five math grad students took part in the second round, and there was a large contingent of supporters from Van Vleck cheering them on. Sometimes it took four integrals to decide which of a pair was the winner. Boian Popunkiov, a student of Alex Nagel, emerged as champion and was crowned ``Grand Integrator of Madison.'' Other grad students participating were Jackie Anderson, Adam Berliner, Debraj Chakrabarti, and Jeremy Rouse, and all placed highly in the results.
While some of the integrals on the written test were more tricky than
difficult (e.g. expressions which evaluated to constants if looked at the
right way) some of the integrals were distinctly non-trivial.
In case you want to test yourself, here are a couple of sample
The hardest problem on the written test was probably