New Quarter

I've got a shiny new quarter! We are on the quarter system, so this is kind of a pun.

So, what is on tap for the next few months? Class #1 is Complex Analysis, which is not just normal analysis but harder, but specifically analysis (think calculus) in the field of complex numbers. I don't know why but it seems like complex numbers are a thing that everybody who's had at least Algebra II should know about, but nobody seems to know by name. They're just numbers of the form a + bi, where a and b are real, and i is the familiar square root of -1. There are bunches of ways to think about them, but usually people think about the real numbers as being a line and the complex numbers being a plane where the real numbers are one axis and the imaginary numbers are the other axis. Other times people think of the complex numbers, with a "point at infinity" attached, as a sphere. Then the real numbers would form a great circle on the sphere, as would the imaginary numbers, or any other line, for that matter. The most important thing, though, is that this is the last of my "required" courses.

Class #2 is part two of Applied Functional Analysis, which I am taking just to fill out my credits and because the first quarter was almost laughably easy, so I'm assuming we'll continue on in that fashion for the next ten weeks.

Class #3, which I haven't gotten officially recognized as a class yet, but only because I haven't talked to the secretary over break, is a reading class with the professor who taught my Topology I & II courses over fall and winter terms. He asked me if I would want to finish (the relevant parts of) the book we had been using and then read some stuff about model categories and other nonsense, probably because I was the only one who liked all this abstract nonsense and diagram chasing and wasn't busy doing research about numbers in boxes or some such. So, I'm keeping busy reading and re-reading stuff until I can't think any more.

As far as teaching goes, I was expecting to be doing a recitation section or two for what I call "math for dummies," but the first years don't have any teaching experience yet, so they got all those, which means I am relegated to the tutoring center for nine hours/week. Until now, the most I've had in there is six hours/week, so I am trying to get my hours scheduled to days that aren't before large exams. Those are the worst days because all these people who have never gone to class and can't do basic algebra come in and ask you to basically teach them everything in a few hours, and it is frowned on to just tell them that that is stupid and they are stupid and should just drop their class because they will assuredly fail, even if it is true.

I should specify: there are a few types of students who come for help.

1. Students who come in periodically for help with specific problems/concepts that they don't understand - Most of these students are good and nice to work with because you can't do problems for them and then let them do similar problems, or just guide them through the problems step by step, or sometimes just casually watch over them as they work. Usually these students come from one of the many calculus classes or linear algebra, which is understandable, since linear is the first time that most people have to think abstractly at all, and sometimes calculus problems just involve seeing some clever transformation that isn't obvious the first time, but also sometimes they come from lower classes, trying to figure out when to apply what formula.

2. Hopeless students - These students are usually continuing education students or sometimes low-level people trying (often for the 2nd or 3rd time) to get the math requirements for their major done. These students are a huge pain to work with because while they try, they will never succeed, and you can't just dismiss them, because at least they are trying and aren't putting it off till the last minute. I don't know whether it speaks to the absolutely horrendous state of math education K-12 in the U.S., or if there is just a segment of the population that is completely incapable of reasoning or the use of symbols to further that reasoning. One of the biggest hurdles is people that, as I mentioned earlier, can't do even basic algebra. I really think that if you graduated high school without the ability to do everything in a typical Algebra I (I am talking h.s. or junior high level) class without any real thought or effort, you are basically on the same level as someone who is still sounding words out when they read and your school completely failed you.

The reason I can't figure out whether it is the fault of the educational system or of just some people is that people seem to lack a fundamental understanding of what they're doing, rather than the specifics of how to do it. For example, you are probably familiar with the quadratic formula, and most people that come in have at least that formula drilled into their heads. But if I give you the equation of a parabola and tell you to find x-intercepts, would you know to use that formula? People don't make the connection between an equation and a graph, that the graph is a set of points with coordinates (x,y) that satisfy a given equation. They don't seem to even understand what that means, i.e., that an equation is a statement which is either true or not. They can't distinguish between an equation and an expression, and instead just memorize how to solve equations and are baffled by what an equation, or any mathematical expression, for that matter, is saying. I don't know whether this is something that most people can be taught or if it is just something you have to work out for yourself.

3. Awful students - These are the previously mentioned students who don't care enough to do anything but care about getting passing grades. Another thing they love to do is try to make you do their take home quizzes/homework for them. Some of them realize that we won't just do their problems for them, but will do similar problems, so they "cleverly" copy their problems to another sheet of paper and then ask us to do those problems. I don't know why people think this will work. It is insultingly dumb and really annoying.

So that does it for my rant, and since this is already a basically impenetrable wall of text, I'll just end the update here.