Tuesday, February 02, 2010

A Math Class of the Second Kind

My third math class this semester is "Senior Mathematics Seminar," which is a 1-hour class that meets once a week and could be about anything. Our particular class is about wavelets, which are like functions with finite absolute area. (In other words, the area under the curve, whether above or below the x-axis, is finite over the reals.) That's my understanding so far, at least.

I realized after the first day of this class that I've experienced two types of math classes, and this is the rarer second type. Of course, this categorization is as suspect as all such attempts, but bear with me, if you please.

I used to think of math courses as going in a line, roughly from arithmetic up through algebra and then calculus. But that's really as far as that particular line seems to go. Beyond that, the field spreads out and you have classes like probability & statistics, linear algebra, etc., that do not go in a specific order. Of course, those classes then spawn their own chains.

But these days a different classification makes more sense to me. Now I see most classes as sort of "tool" classes, where you learn a lot of tools that are broadly applicable (like calculus, linear algebra, set theory, etc.). And then the other classes are more "application" classes (whether they are applied or theoretical) in which you use various kinds of tools to understand some new area. My second geometry course was one of these application-type classes, using a lot of linear and abstract algebra (and a touch of geometry, though not much), and this wavelets course is the same way (so far mainly with respect to calculus and analysis).

At any rate, the class has been all right so far. Our professor has roughly the style and personality of a very toned-down Steve Martin - like maybe Steve Martin playing a math professor in a serious movie. I was confused a lot this past week, and left class feeling like I'd been crying, though of course I did not actually cry, and I've realized that I really need to read the book before class rather than only looking at it afterwards (which is kind of obvious, but not my usual M.O. for math). It looks like we'll only have graded assignments and possibly some kind of small projects later on; there's been no talk of exams. So it should be all right, though it's hard for me to see how I have time for two classes (this one and Advanced Calc II) that require serious thought.

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