Saturday, October 14, 2006

Come together, right now

With the latest journal entries (and a few informal meetings with some of the teams), I'm beginning to get a sense as to how far into their respective research projects the course's teams are. While there's a little discomfort here and there, it appears that most teams have been able to find at least enough resources to get a good start on the actual research.

The team of chemists is working on narrowing their focus within the topic of crystallography, having found a wealth of information on that subject.

The two teams working on traffic patterns seem to be taking their projects in very different directions, which is what I'd hoped would happen. Both are now considering models for traffic flow, beginning to understand how they work and how they might be used. One team is even looking towards finding real data to test and refine the models they come up with.

The team working on wastewater treatment has also looked into models involving differential equations, and into data to refine those models.

The Monopoly team has found a bundle of sources analyzing the game from a mathematical standpoint. One of these mentions those two magic words that drive a linear algebraist wild: "Markov process." I talked for a bit yesterday with a couple members of that team, and we came up with a plan of action for their research in the coming weeks. Dare they consider a multiplayer model for the game?

All in all, the research projects are coming along nicely.

There's no shortage of "extracurricular activities," either. Yesterday I showed the class how a 35 x 36 matrix naturally arose in my research during analysis of a problem from graph theory: one equation short of a fully determined system! And yesterday I received a paper from one of my atmospheric science folks, an article in a very recent atmos journal dealing with Markov processes as they arise in weather forecasting. I'm going to take that home with me today and flip through it...perhaps the student who brought this in might be interested in leading a class on this topic in a few weeks, once we've got eigenvalues under our belts?...

...Speaking of which: in the next couple of weeks we're going to be blazing through determinants, with the primary goal of understanding them well enough to approach eigenvalues/vectors, since these puppies are the COOLEST things since sliced bread, and will prove eminently useful in just about every research project.

Stay tuned!

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