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Ramblings about Classes

January 16, 2011 at 11:51 pm
By Collin Hazlett

(In which I ramble about my classes and a bunch of math books I got.)

If you remember from two posts ago, the types of classes I'm taking this term are (1) math, (2) biology, and (3) psychology.

This is a bit of a change from my schedule last term, which I seem to recall was something like (1) math, (2) math, (3) math, and (4) math.

However, I have a strange feeling that the classes I'm taking this term actually have a lot to do with each other... even more than they did last term, when they were all in the same subject.

Here's why I'm getting that feeling:

In Ordinary Differential Equations (my math class), we predict the long-term behavior of different systems, such as populations of different animals which breed and eat each other. We do this by using... well, ordinary differential equations. We start with certain assumptions about the way the system works, we translate those assumptions into differential equations, and then we solve them (sometimes it turns out to actually be impossible to solve them precisely, but we can still often figure out enough about the shape of the solution curves to be able to tell what happens to the system in the long run).

In Energy Flow in Biological Systems, we talk about processes that go on in metabolism. These processes usually start with a large amount of chemical A and a small amount of chemical B. Then we add an enzyme that catalyzes a reaction that turns A into B, and the concentrations of the chemicals change and end up settling into an equilibrium with a small amount of A and a large amount of B. A whole chain of these processes can be coupled together to form a metabolic pathway. We don't model metabolism with differential equations, but I bet that biochemists in real life do.

In Social Behaviors and Interpersonal Processes, we talk about the ways that a person's thoughts and behaviors are affected by other people. This, as you can imagine, is a rather broad topic. It manages to be really interesting, though. Psychologists can come up with surprisingly good models of the way people behave in relation to other people. And then, once we have a model of the way individual people act when they are with others, we can try to see how this model gives rise to the behavior of groups and societies. We don't do this with differential equations, but, again, I bet somebody does. Or, if not differential equations, then something similar. I've heard of "computational sociology"- perhaps that's what computational sociologists do.

This is exciting to me. I've taken pretty "pure" math up until now, and I've loved it, a lot. But now my three classes are showing me a more applied side of things- and it turns out I love that too.

The green turtle Chelonia mydas has the strange property that its gender is heavily influenced by the temperature of the nest in which its egg develops. An egg raised in warm conditions will probably hatch into a female, and in cool conditions it will probably turn out male.

In a fit of mathematical excitement, I've found a few books on the subject of systems science and applied math. Some of them I checked out from the library, some of them I requested for my birthday, and one I got for free from the Free Math Book Bookshelf in the CMC. Here they are: Complexity by Melanie Mitchell, Sync and Nonlinear Dynamics and Chaos by Steven Strogatz, The Tipping Point by Malcolm Gladwell (that was the one I got for free), and Thinking in Systems by Donella Meadows. It's a lot of books, and it'll take me a while to get through them all. But hopefully this will give me a better idea of what kind of applied math is out there and whether I want to spend my life doing it. I'll also, you know, ask my math professors about it and all that. I am very excited.

You, on the other hand, really have no reason to be excited about a list of a bunch of math books that I bought. Sorry about that.

Thanks for sitting through it. I did give you a turtle fact, as promised. I hope you enjoyed it.

You know what? As an extra reward for enduring my rambling, here's a screenshot of something from an upcoming post, for you to speculate over:

Paint the Floor 

 

Comments

  • February 23 2011 at 11:00 am
    Robert

    As far as I know, all turtles develop gender through an egg-temperature difference during embryonic development. The male comes from the cooler egg, and the female from the warmer egg.

    When I was checking that on wikipedia, I was surprised to discover that crocodiles swap the gender/temperature relationship - males come from the warm eggs.