Wow. Heard this from Rob at tonight's game night. "Shortest math joke ever: Let ε<0."
Anyway, on to the entry's original opening sentence.
You may recall that philosophy class of Dr. Grieco's. After he died - well, Mrs. Todd had his class materials, so... we decided to just work off of that. Unfortunately Mrs. Todd was too busy to actually teach the thing, so the result has been that it's all just turned into discussion centered around whatever it was we were supposed to be doing now. Some of the time it's just seemed like we don't know what we're doing and we're going in the wrong order, but most of the time it seems to work.
Enough of that. On to the happenings of Tuesday and Friday. Tuesday was when we were supposed to begin the bit about mathematics. It was supposed to be led by me, being the only real math nerd in the class unless you count Emily, and Sara, who, well, knows the least math, or at least she says herself to be. However, Tuesday half the class (including Sara) was missing because they're all on debate team and they had some big debate somewhere. We started anyway, and started talking about why we study math, which led to the whole topic of why we go to school in general - and "experience of schooling" was something we were actually supposed to have done earlier, but never did. So that worked, sort of. Anyway, towards the end, I wanted to bring it back to math, because I wanted to explain the idea of structure in math - something which, most of these people only having seen high-school math, wouldn't have seen before - and, to a large extent, you can't really talk about math without it - and I'd certainly say it's philosophically important... but of course I had not nearly enough time to explain by this point, and we continued as before.
So someone, I forget who, suggests to me perhaps I should write it up and hand it out if it's going to take that long to explain. So I spend Tuesday and Wednesday TeXing up (rather badly, not having used TeX before) a thing on very basic group theory, as really, I can't think of any good way to explain it without giving examples, and groups are probably the simplest good example, so...[0][3]
Anyway I send it to Sara, as she's supposed to be presenting it with me, or something like that, and, knowing the least math, she's probably also the best one to check it and make sure it's clear. It really isn't. So I spend Thursday rewriting it and adding a glossary of math terms at the end for those who diddn't know the words I was using. The new version, she says, is good. Of course by now it's already Friday. It's 9 pages long because of the huge margins, so I don't want to take up printer time printing out a copy for everyone; I print out one copy and figure I'll make copies of it, but I don't have time, because I'm doing this right before IGS. It hardly matters. The point of writing it up was so that I wouldn't have to explain it in class; now I'm going to have to anyway.
So, I begin to do so. Whee. Groups. Some examples. Here are two groups. They look the same, don't they? How can we formalize this? Homomorphisms, isomorphisms. That's where I stop - I wrote up more in that thing, actually, explaining as far as the First Isomorphism Theorem, but of course in class we immediately started discussing the whole idea of isomorphism.
Here I should probably note that I'm not very good at explaining these things but thankfully Vlad could explain what I was saying to those who didn't understand.
Not everybody seemed to entirely get it, though everyone seemed to have some idea of the significance of it, and why it was more important than just in math. JT, though, violently objected to the whole thing. "I feel like I've been ripped off," he said. "What do you mean?" "I feel like I've just been conned into sitting through a math lesson." He seemed to be the only one, though, so I'd say my evil plot to subvert the philosophy class introduction of the idea of isomorphism and structure went pretty well. :) (Especially since Mrs. Cosgrove[4] says the whole mathematics part a lot of people generally didn't like, and that Dr. Grieco had thought about not doing it.)
Now I'm going to go send the thing I wrote to everyone, once Sara confirms that she can understand my latest revision of it. :P
-Sniffnoy
[0]Actually I should note here that I pretty much avoided anything that was entirely specific to groups; I wanted things that generalized. I used normal subgroups and not everything has an equivalent to that, but oh well. Rings have ideals, and, well, that's really the extent of my knowledge on such, but I'm sure there must be other sorts of systems with an equivalent... oh, and vector spaces and modules. OK. That's good enough generalization for me.
[3]Well, graphs are simpler than groups, but people think of graphs abstractly anyway, so had I introduced isomorphisms as graph isomorphisms, it wouldn't have seemed such a big deal. That's what I think, anyway.
[4]Since, apparently, some teacher has to be there during the class, and Mrs. Todd isn't, Mrs. Cosgrove is. Awful, I know.
--
"The vast majority of Iraqis want to live in a peaceful, free world.
And we will find these people and we will bring them to justice."
-George W. Bush
