Friday, November 28, 2008

upsc update

Since I made a post earlier about the undergraduate problem solving contest I figured I might as well do an update post now. As it happens the first problem is the only one that I didn't turn in a solution for (the second one was about efficient encodings and the last one was a relatively easy question about squares) As it happens that actually puts me in third place. As the prize for winning the upsc (thats Undergraduate Problem Solving Competition, I like to pronounce the shortened version as oopsie=upsc) is an expenses paid trip to mathfest 2009 I certainly hope that I continue to pull up in the ranks (an all expense paid nerd vacation awesome). Hopefully at least one or two of the questions posted next semester will be really hard. Otherwise I doubt it will be possible for me to pull into the lead.

More urgently though the Putnam exam is going to be December 6th. It will have been 1 year and 5 days since I took the 2007 exam. It is hard to believe that it has only been one year since then. I have learned a great deal in that time. Looking at the putnam problems now I feel at least somewhat prepared for the test. Last time I took the Putnam I got a score of 1 point out of a possible 120. Which I am eager to say is above the average score. I have a book with some of the old putnam exams in it and perhaps if I have a spare 6 hours tomorrow I should administer one of them to myself and see how I do. Hearteningly if I get 40 points on the test then I would be in the top 100 of test takers (a few thousand mathematics undergrads and assorted others take the test every year, what can I say doing well on the exam looks good). Realistically I am shooting for 20 points. The 2007 test was a little harder than usual and encouragingly I now could solve 3 of the 12 problems from that exam. before I finish this post off and run away I will give you some example putnam exam problems.

(A1-1976) P is an interior point of the angle whose sides are the rays OA and OB. Locate X on OA and Y on OB so that the line sexment XY contains p and so that the product of distances (px)(py) is a minimum.

A1 and B1 are traditionally the easiest problems and A6 and B6 traditionally the hardest.

(A6-1976) Suppose f(x) is a twice continuously differentiable real valued function defined for all real numbers x and satisfying |f(x)| <= 1 for all x and (f(0))2 + (f '(0))2 = 4. Prove there exists a point x0 such that f(x0) + f ' ' (x0) = 0.

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