You know how dogs tilt their head to the side, almost like they're trying to understand what people are saying around them, even though they have no hope or capability of doing so? I just reflexively did that, reading through REDACTED. I couldn't parse what was being said in the slightest, and those little comparative symbols were all Greek to me.
Hahaha >_> So, first of all, there's something you may not understand about mathematical texts and why they take 50 hours. The reason why is that it's generally expected that you'll spend an hour or more on each page. You don't understand it, and that's fine. Typically, you want to sit down with a pencil and paper and draw pictures, think about definitions, think about examples. You get a little notebook and write down definitions, then little bullet points underneath about things you get from that definition. Things you're curious about, and so on.
For example, let's say I'm thinking about the definition of a partial ordering (the first one). Well, first off, what in the hell is a binary relation? I'd better go look that up on Wikipedia or Mathworld. Okay, then what's a relation? What are some examples of a relation? Can I think of some things that aren't relations? What about ternary and unary relations? Can I think up examples of a partially ordered set? And so on, and so forth. It takes a long time, but it's something you should do for relaxation, rather than to stress out. Explore a concept and then move on, but don't move on until you understand what you were supposed to know before.
Second of all, EVERYONE has that experience the first time they have a run-in with pure mathematics. I can't tell you how many times I've ragequit, spent 8 hours dicking around with the same problem to no avail, or got caught up on something completely trivial. The main thing separating people who understand mathematics from people who don't seems to be patience (often a side effect of obsession, but whatever). If you don't get it, then walk away for a little while, do other stuff, and clear your mind. When you're ready, come back.
The other thing you may not know is that when they say something is "obvious," that means you're supposed to put aside the text and prove the statement yourself. It's not
really obvious unless you've gotten extremely accustomed to one-trick proofs and observations, which tends to take a damned long time. So, if you can't see something, don't feel bad. Just think about it for a while.
In brief, my head asplode. I haven't had a background enough in mathematics to transition from the comfortable, sensible processing of "X+Y=Z" into the (no doubt magnificently elegant and universally significant) fundamentals of math... it's like walking up to someone who's just learning how Water and Ice are the same thing, and trying to explain what a quark is. For starters, what the heck do they mean by a "set", and why all the nested definitions? It's like the subset concept applies not only to the math being depicted, but also to the descriptions themselves! Aaauauuuuugh! *brain melts and begins to drip out of one ear*
A set is a collection of mathematical objects. For a better definition and more information, see the
Wikipedia page. The reason why we use nested definitions is because otherwise, we'd end up with proofs that were so long no one could ever read them...
Yeah, it's brain-melting ;_; But ultimately, it's extremely rewarding once you've gotten your foothold.
I get the feeling that learning more of the rules behind mathematics would be interesting and revelatory, but I have huge hangups about math, due to certain... dark events in my educational history. Mathemelodrama aside, I'm still interested enough to poke my head in briefly, if I can summon the gumption. I may take another shot at the algebra text first, if simply because the name anchors it in the world I know and comprehend. If something sticks, maybe I'll delve a bit more... but it seems like this is looking at math in a theoretical light, while I don't have the vocabulary to process what's being said.
Nah, I completely understand. It's a difficult subject, and it's always been pretty hard for me (well, until a couple of months ago >_>). If you're interested and need some help with some definitions or anything, though, just let me know--it really is tough, and the only way to get the vocabulary is to spend a little while swimming around without a flotation device until things become clear and natural (which is around when you start building a ship of the line with laser cannon). I love the subject and am always happy to introduce someone else to it :3
As far as books, I'll give it a think. Something will probably come to me.
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Topic: Things that made you sad today thread. (Read 9476148 times)