Wednesday, August 19, 2009

First Day(s) of School

This semester, I have two 4-credit-hour classes, and they take place on different nights. My schedule is

M/W7:00-8:50pmAdvanced Calculus I
T/R7:00-8:50pmLinear Algebra
It's inconvenient to have to travel to campus four times a week, but nice to only have two hours of class when I go (thus no temptation to skip the second class). And I initially thought the late hours would suck, but I've changed my work schedule so that I work 9:30-6:30 and just shifted my whole day later.

This also means I get up after Ed has left for work, and get home around his bedtime, so most of my time at home during the week will be alone. It's only been two days, but I've basically enjoyed it so far. I'm sure I'll enjoy seeing him on the weekends.

Anyway, I have been to both classes, so here are my thoughts so far.

Linear Algebra

The professor was friendly, very casually dressed, and just slightly spacy. I feel a little concerned that she won't make the class theoretical/"proofy" enough, but by the end of class I thought that she would. At some point, I wrote, on the edge of my paper that I save for comments, "Please go into the algebra of this," because one of the errors I made last time I did this was to focus too much on the algorithms of manipulating matrices and not enough on the underlying algebra. Immediately once I had written it she went into a long bit about the algebra of what we were doing. Nice.

This class is in the building right next to where I usually park, so that's convenient, but it's in an uncomfortable classroom - crowded, noisy, and with the one-piece desks that I don't like. So it is not a very desirable place to be for two hours.

We'll have two tests, a final, homework, quizzes, and class participation. She takes attendance and apparently cares if you show up. She also said there would be a lot of working together in groups, which I utterly dread, because (a) yuck, groups, ugh, but also (b) trying to move desks around in a totally packed classroom of one-piece desks sucks.

So I guess I'm giving this class mixed reviews so far. We have homework due next week that is almost all from the high-numbered problems in the textbook, so that's good.

Advanced Calculus I

If you're wondering what this class is, it is sometimes also called "Real Analysis" (which is to say, analysis of the real numbers, not real as in genuine). You could also say it is the "continuous math" to go along with my "discrete math" from a few semesters ago.

The professor is a slight, unassuming Brit with the obligatory charming accent. He told us that this is the hardest class in undergrad, but also the best, and assured us that it does not exist solely in order to keep you from getting into graduate school.

He also said the class is about three things:
  • The nature of the reals and their relationship to the rationals
  • ε's and δ's and proofs of everything in calculus
  • 19th century mathematics
Apparently the calculus we've already learned is 17th and 18th century mathematics, and now it's time to move into the 19th century, when various unresolved issues (like Fourier series) pushed the mathematicians of the day towards an axiomization of calculus.

I'm enjoying this class so far. I spent an hour last night working on our first homework, which was reasonably challenging and fun. One of the problems we had was several statements that we had to negate - math equivalents of things like
For every cat, there is at least one dog over the age of 7 who has chased that cat.
and more complicated ones like
There is some baby such that every woman in this household who is over 30 and of sound mind has diapered that baby.
I had fun writing the negations of them, though I also felt doubt as to whether I chose the most elegant or direct methods of doing so.

The class is also held in a classroom with long tables and regular rolling-type desk chairs, so it's very comfortable to be in for two hours.

We'll be having three exams plus a final, homework counts as 30% of the grade, and there is no paper, project, or threat of group work.

So that's how my semester looks so far.


Edward said...

Pardon a small amount of silliness:

EXISTS cat EVERY dog ( NOT overAge7(dog) OR NOT chased(dog, cat))

EVERY baby EXISTS woman ( inHousehold(woman) AND overThirty(woman) AND soundMind(woman) and NOT Changed(woman, baby))

Yes, I know he didn't want notation. He wanted English. Hence the silliness.

Tam said...

He did encourage us to do it in notation.

I think your second negation is wrong, though. Couldn't there simply not be any woman? (When I posted the original sentence I wondered that some of my negations might have been wrong, but it would be silly to think there is no number x at all, for instance.)

Tam said...

Oh, never mind. I withdraw my objection.

Sally said...

I have no comment on the notation silliness, but will confess that I never really got the episilon delta proofs in calculus. sigh It's sort of one of my guiding stars - I only plan to get advanced degrees in subjects that do not require me to take real analysis. I just can't bring myself to care about these issues, despite having been exposed to them. This stuff is obviously important but ... meh.

rvman said...

I liked analysis when I took it (part of my 'minor' in math at UNT - a graduate class in Real Analysis, and an undergraduate class in Topology).