Saturday, December 06, 2003

Still Alive

Sorry for the lack of posting. I have much to say, but little time before Finals start. Of course, I just used 6 hours of that prep time on the William Lowell Putnam Exam, a completely voluntary national undergraduate math competition. What was I thinking, you ask?

Good question. I woke up at 7:30 today and headed to the math building. PS2 handed out the test envelopes. He warned us that the mean on this test is a couple points out of 120, and the median score is zero (in other words, at least half the students who take the Putnam get no points). We had 3 uninterrupted hours to work on the first 6 problems, then 3 more hours in the afternoon for 6 more problems.

Example: Let n an integer and take the sequence 1, 1/2, 1/3, ... , 1/n. Then average the adjacent terms, resulting in the sequence 3/4, 5/12, ... , (2n-1)/2(n)(n-1). Repeat this process of averaging neighbors until only one term remains; call this x. Show that x < 2/n.

I was rather proud of that problem, by the way. I know I didn’t make the papers, but I believe I scored in the low 30s, and that makes me feel good. Now if I could only understand Burnside’s Theorem in time for my Monday final...

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