Friday, February 17, 2006

Spring 2006 courses

The semester is in its full swing now. I have dropped the class in which I considered two pitchers of Gatorade, and I am now taking two math classes and two psych classes. Gah. I'm such a typical junior double-major. Anyway, I shall now discuss the four courses in which I am enrolled.

This title makes the class sound like something Betty Friedan would have complained about, where women go to college merely to major in courses on how to manage a family budget, conflict resolution for spouses, and how to raise children properly. "Here's a course on how to make good decisions for your family, like how to decide whether to buy the name brand which may have more vitamins, or the store brand which is cheaper."

But that is not what the class is about, so when I tell people I'm taking it, I call it Decision Theory. That's what it is, really, so there you have it. Professor Kirby's research is all about decisions, so it's pretty cool to be taking a course with him on the subject. We've been talking a lot about economics, in terms of maximizing utility and using utility curves to understand why people make various decisions, and I have found the examples given in the readings to be quite interesting. It turns out that a lot of Nobel Prize-winners have worked on this sort of thing.

The only problem with psych classes is when they involve too much math. This is not because the math is too challenging for me; it is because I find it difficult to keep my eyes open. I had this trouble in psych stats when we went over for the twentieth time how to add, subtract, multiply and divide numbers. Now I have that trouble when we learn how it is, exactly, that the probability of A and B is the product of their individual probabilities. And we didn't even mention that the events were disjoint. Pity.

Psychotherapy: Theory and Research
This course makes me glad I didn't go to Wellesley. I was actually considering it for a time, and gosh, that would have been the most horrible decision ever. This class is composed of 12 females, and Professor Heatherington is also female. There is nothing particular about it that is bad, but the whole dynamic is just weird. Girls. Girls are weird all together with no boys around. It makes it feel like it's a special class for special people. And it's not.

Anyway, the class is all about psychotherapy, including psychoanalysis (Freud), behavior therapy, and anything else of that sort. We do the readings, and we come to class to discuss them. That is really all there is to it. The readings are long, and the class is all females. I am learning more about behavioral therapy, and the more I read, the more I believe it. I thought I didn't want to have kids, but now I'll probably have to have some just so that I can try out techniques of behavioral therapy on them. You know, to see if I can make them afraid of oranges and love apples, to see if a precisely planned-out schedule of reinforcement and punishment makes them achieve higher and higher until they are accepted to Harvard Graduate School at the age of 12. I am going to live vicariously through my children.

Tiling Theory tutorial
This is my second math tutorial, and an excellent second math tutorial it is. Tiling theory is about how you can tile the plane with shapes. For instance, you can tile the plane (i.e., the floor) with squares, triangles, hexagons, parallelograms, rectangles, and plus signs, among many other shapes. However, given an arbitrary planar shape, there is no finite algorithm for telling whether it can tile the plane. So we are investigating what is known and drawing lots and lots of pretty pictures.

The way the tutorial works is that we do some reading and a problem set over the weekend, and then my partner and I go to Professor Adams' office and one of us presents the material, and we all talk about it for an hour or so. Sometimes we ask questions and then try to prove the answers on the spot on the board. We always draw lots of pretty pictures.

Combinatorics is about arranging things, like how many ways there are to arrange the letters in Williams (1260). It's also about all the nifty little relationships you can get out of Pascal's Triangle.

Combinatorics involves some cleverness and a lot of multiplying. I haven't come to accept the fact that I am now taking a math class in which a calculator might be useful, so I haven't yet remembered to bring along a calculator when I do my math homework. Therefore, I have done all of the multiplication by hand. The largest numbers I have had to find so far have been 264 and 32x27x56, unless you count such things as 212 and 1012 which have more terms to multiply and come out as larger numbers, respectively, but are not very hard. I also multiplied .97 in decision theory class, but that was just to make sure that the author of the paper wasn't lying. The thing is, in combinatorics, most of the numbers cancel out. It would take me longer to type all of the exclamation points into my calculator than it does for me to write the expression on a piece of paper, cancel out everything, and multiply the very few numbers that remain.

I believe that calculators are useful mostly for the purpose of preventing this kind of needless work. When kids use calculators to add two-digit numbers "just to make sure it's right," that's useless. When kids have added numbers many times and are confident in their ability to do so, I think it's okay for them to use a calculator to add up three five-digit numbers. When they've plugged numbers into the quadratic equation a hundred times, they can use a calculator to find the solutions after that.

But for instance, once I loaned Ronit my calculator for an exam. The exam involved some sort of combinatorics problem, and Ronit didn't know where the factorial symbol was on the calculator, so he spent a long time typing out something like all the digits of 35!/(33!2!). When he got back from the exam, he complained that he had had to waste a lot of time typing out 35x34x33x... because I hadn't told him where the factorial button was. I got a piece of paper, multiplied 35x17, and told him he was a stupidhead. Which he was. This is why I say that students are too reliant on calculators and do not use their brains enough.

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