Today in class we learned to differentiate inverse trigonometric functions… which isn’t that difficult or interesting, really. Then we spent a long time talking about complex numbers, and how many things had been “hidden” from us throughout our lives learning mathematics.
I can’t decide if I think my professor is a really smart guy, or a bit of an ass. Probably every day he brings up some point or intricacy or method that he claims no one else will tell us, and is absent from every textbook out there — despite being totally legitimate. Probably every day he says that this or that teacher or author didn’t/doesn’t truly understand a given concept. He talks about the high failure rate of Calculus 1 all across the country, and how much lower the failure rate is in his classes. He brings up things we’ve already learned, and tells us we’ve been lied to or given half the truth. He goes on about how “some of you think there’s a worldwide shortage of parentheses,” and not only the fact that many of the students make notation errors (especially ≈ versus ≡ versus = versus another one I don’t know how to type in here), but the fact that many textbooks “get it wrong.”
I dunno. I believe what he says. I understand that being lazy about notation causes ambiguity. I appreciate application problems and in depth explanations and images of the concepts. I’ve definitely had teachers who totally mechanized math. Made it a series of boring steps. I just… I don’t know. I wish my professor would be a little more positive, I guess? I mean, maybe the guy who wrote our textbook was really a terrible mathematician. So why do we keep revisiting that point? I’d rather Prof. would say, “Oh, and so-and-so invented this stuff we’re looking at right now. What a genius, right?” I know I’m not the most positive person in the world, but I do try not to criticize people all the time.
So… complex numbers. Very cool stuff. I remember when I was a kid, wondering why during the first week or every math class, it seemed like they’d define the different sets of numbers. We never really got to understand the differences, and were never tested on what was what. I think I only knew some of the sets because I heard them repeated so many times. But today we went over that a little bit again, and I realized that it’s like I’m only starting to do math. Algebra is like the language. Geometry is like drawing (visualizing, writing). Trigonometry I can’t come up with some simile for, but is really pretty cool (largely because I find it easiest). And calculus? Calculus I don’t know, of course, but I get this feeling I’m on the brink of something. On the brink of some real, abstract, beautiful mathematics.