Thursday, April 05, 2007

A Well Spent Day

Today was the first time in about a month that I have actually had the time to do math problems that I actually find interesting. When I say I have time I mean that there was not a test that I needed to be studying for, or an assignment that must be completed. Sure I have a differential equations test on Friday, but it's going to be easy so no need to waste time with studying for that.
I started off the free time by solving this problem;

If you are unable to read the above problem then just click on it and it will be displayed in a larger format.
The problem did not require too much insight. It was basically a routine exercise with Lagrange multipliers. Also if you did not know any calculus the problem was still solvable thanks to the Cauchy-Schwartz inequality. This about two minuets to think up the solution and then another five to write it all down.
The next three hours were spent doing problems that were more challenging and took a little more insight. However, there was one problem that took the majority of the time. The disappointing part is that I was not able to solve the problem.

I was able to develop a recursion formula and initial conditions but after this point i was not able to generate a closed form. My answer is split into cases depending on the parity of n and then it has the solution in the form of a product of terms.
Hopefully, I will be able to solve this problem, and the other problems on the three sheets (a total of 29 problems) before the end of the semester. This is the second set of problems that I am attempting. In the first set I was able to solve six problems on my own, I needed help on four, and have incomplete proofs for one. The source of the problems is the first compilation of 100 Mathematical Problems by Yang Wang, a professor at Georgia Tech., so I am working on the first fifty-one problems, and find it very rewarding even if I have to ask others for help. Asking for help and learning something new is better than being clueless for eternity. Obviously I only ask for help after I have put in a considerable amount of effort (normally a weeks worth at least).

Well I need to sleep now, early class tomorrow, so I shall leave you with a parting quote.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of a sculpture.
-Bertrand Russell

1 comment:

Laura said...

You don't by any chance know symbolic logic, do you?