UCSD Classes posted under Home by George on 2008-03-29 11:42:44.0
The spring quarter is coming up, and classes start in two days. Currently Analysis B, First Order Logic, and Analytic Number Theory look appealing (assuming I can do the last one, as it is a graduate course and I am yet unsure as to the difficulty). Interestingly, the number theory class will be taught by Harold Stark, world-renowned number theoretician who did extensive work on the Gauss class number problem. It should be a fun quarter.
Interesting ideas from classes to come in many more blog posts!
SDMO posted under Home by George on 2008-03-29 11:39:59.0
The San Diego Math Circle held the SDMO today, a few of the problems were interesting. In particular, the last one, dealing with intervals. Let I, I1, I2, ..., In be intervals such that I contains I1 through In. Show the the union of the left halves of intervals I1 through In contains at least half of I. On first looking at this problem, it seemed to shout measure theory at me, and I was almost tempted to start thinking about it in terms of more general metric spaces and using Lebesgue measure. I don't think this should be too hard... some algebra should do the trick I think. Perhaps the intervals could also be generalized to be any desired set. A follow up may come if I get some time to work on this.
Math Team Heuristics Lesson posted under Home by George on 2007-11-27 20:13:34.0
I recently created a heuristics lesson which I taught to CCA's math team. It includes three basic principles: invariance, extremity, and pigeonhole, with explanations, examples, and problems for them. Additionally, there's a history section on pigeonhole and applications section on invariants. For the more advanced reader, there are more difficult things to think about which are included as sidenotes or extensions to problems.
Economics posted under Home by George on 2007-11-15 18:26:39.0
My current economics class just covered comparative advantage optimization problems, and naturally I was inclined to generalize the solution to the problem. I wrote an algorithm in javascript which allows for as many people/goods as one could want. Linkage.
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