(Written 2008-07-25 10:30)
I'm writing this somewhere above Warsaw, halfway through our flight to Budapest. From Budapest we take a connecting flight to Sofia, after which a bus will take us 100km to the town of Blagoevgrad, where the American University of Bulgaria at Blagoevgrad is hosting the International Mathematics Contest for University Students 2008 for the nth consecutive year.
IMC is an indivitual competition but contestants are divided into teams originating from universities. We have a three-man team representing the University of Helsinki, whose participation has been intermittent at best. I wouldn't even know of the event if I hadn't overheard an acquaintance of mine talking about forming a team.
A word about my history with competitive math. I did pretty well in the national math competitions during school, often placing in the top 10 or 20. During high school I attended special training that aimed to produce a finnish team for the prestigious IMO (International Mathematics Olympiade, a high school level contest). In the process I attended multiple nordic and baltic competitions, but never did make it to IMO, partly because I attended the coaching only for two years while most do it for three or four, and partly because of seriously underperforming in the final selection tests.
Well anyway, I'm kind of looking forward to the competition. The problems are very different compared to IMO: gone are geometry and number theory, instead the problems focus on (basic univariate) calculus and linear algebra with some algebra hiding in the nooks. The competition requires only the very basics of undergraduate math but the problems offer opportunities for applying advanced techniques. Here's an example problem:
Let A and B be real nx_n_ matrices such that AA+BB=AB. Prove that if BA-AB is invertible, then n is divisible by 3.
On the other hand I fear my analysis and linear algebra have fallen into a state of disuse as I've mostly been meddling around with logics and algebra for the past year.
I'm finishing this at the airport in Budapest waiting for the connecting flight. Keep tuned for follow-ups.
... finally got an opportunity to post this. It seems our accomodation's all "IT services" are down. A kindly local internet cafe let me plug my laptop in. Rates are pretty low, 1 local currency unit (about 0.5€) per hour.