Sunday, December 5, 2010

Putnam 2010 Solutions are up!

So it turns out on three of the problems (A1, B2, and B3) I had a pretty good argument for each, and now I just have to wait until March to see if I got any points.  The solutions are posted here.  I would be interested in hearing from any of you, your ideas about the other solutions as I didn’t come close to any of the others. 

A little bit of history on the Putnam:  only three have ever achieved a perfect score on the Putnam exam.  David Moews in 1987, it having been a highly difficult year for the test.  Two in occurred in 1988, although I can’t pin down who they were.  Although the top five, had been fellows at least once, often several times before.  You can read up on a little bit of history here

As for other mathematical competitions there is the International Mathematical Olympiad, which if you look at the problems these high-schoolers have to complete, you’ll be impressed.  Then there is the Mathematical Contest in Modeling which a professor here in BYU-Idaho is very interested in registering some of us students for, although it has been hard to pass by the administration because the actual contest takes four days, and we pretty much have to eat, sleep and not shower at school.  It’s heavily programming oriented and has had some very interesting problems to model in the past including “finding the sweet spot on a baseball bat” (2010), finding the location of serial criminals, among other things.  Here are some other competitions. 

Putnam Competition

Yesterday was the nationwide 71st William Newell Putnam Mathematical competition.  (More info here).  It started at 8:30 am here in the Rocky Mountains, and it was off to a riveting start:  opening the manilla envelope with the first set of six questions, and then reading…rereading, stopping for a minute for a breather, then reading again.  Then drawing some pictures to try and see if we were understanding…

So the problems were pretty hard, I expected that.  Somewhere around half of the participants actually don’t score a single point.  I did feel like I understood and gave a good effort at a few of the problems.  A1, B2, and B3 specifically.  We’ll see what they tell us in March though. 

I’m excited for the time being to see what the solutions are, they should be posting them tonight. 

Tuesday, November 16, 2010

Intermediate Value theorem

I was fascinated the other day by my teacher's description of the fixed point theorem:

By taking two identical pieces of paper, crumpling up one and placing it anywhere on the second piece of paper you are guaranteed to have some point in the crumpled up mess that is over the same point on the flat piece of paper if you unfolded it again. Another explanation is here.

So I wanted to post my findings on the intermediate value theorem! You have to scroll down a little bit, but I found really interesting the part about the world having two antipodal points exactly the same temperature.