The first two weeks of school have come and gone, and I am officially one-eighth closer to the end of the semester, which is oftentimes more of a terrifying thought than anything else. But, I have to admit, it's been a very good semester so far.
A lot of people ask, "What exactly do you do in math grad school?" This is a very legitimate question, one which I am only now beginning to be able to answer clearly myself. Obviously, I study a lot and teach a little. I study two main branches of mathematics (algebra and analysis) and then I take some electives as well (like calculus-based statistics, a couple education courses, etc.).
Algebra is what we've all done in high school, but in grad school, we look at it in a much more general setting. As a basic example, in high school--or I guess even much earlier than that--we knew 2x3=3x2 because they both equal 6. But why is this the case for the real numbers; and, furthermore, in general, does axb always equal bxa? The answer is no, actually--it depends entirely on the set of elements (or numbers) with which you're working. So, algebra looks at questions like this and seeks to answer when things like 2x3=3x2 are true statements, and when such statements fall flat on their face.
Analysis looks at the structure of numbers. Like algebra, it goes back to the basics that we learned early on and seeks to prove propositions we take for granted. However, analysis looks more at the calculus side of things and seeks to answer why calculus works as beautifully as it does. Both algebra and analysis require a great deal of proof writing--proofs which often don't come until you've done a lot of outside research and a lot of thinking.
(Ok, math teachers out there, how did I do in my explanations?)
So that's the "boring" part of what I do, which obviously I don't find very boring at all or I wouldn't have devoted the past few years of my life to it. But the more "exciting" part of being a math grad student is the teaching. I get to teach College Algebra every semester to kids who just want get those three credits and get out of there. But I love it. I love the challenge of trying to make some of my enthusiasm for the subject rub off--even just a little--on my students. I get to know students who are scared to death of algebra when they walk in those doors, but who feel rather accomplished when it's all said and done (provided they put a little effort into it). And that's pretty cool, you gotta admit. I've also really enjoyed working at a secular university, where I can be a little glimpse of hope and light to some kids who feel rather hopeless. And, of course, there's always the humorous side of teaching mostly freshmen, who can be rather clueless about school and life in general. Some days I'm convinced it must be akin to teaching kindergardeners.
And that's school for me right now. Some days I love it. Some days I hate it. Most days I love it though--despite my complaints.
No, not the most exciting blog you've ever read, I'm sure. But, remember, we warned you in the beginning: we don't promise to be entertaining 100% of the time.