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Fri, Mar. 4th, 2005, 11:47 pm
thecontrolfreak: YES!! A Set Theory Community!

I'm glad you created this community. So's I can get my Geek On.

I've been studying a book thats started me at basic T-F logic and works its way through modal, quantificational, definitions, a small section on the Peano Postulates and recursion, and then ending at Set Theory. I'm fascinated by what I've learned so far, which is a very basic understanding of mathematical logic and some amazing definitions pertaining to functions in a Category Theory book I read as far as I could, which was thinking (from what I understood) that the differences lie in defining Unordered Objects and their Relations vs. Ordered Objects and their Relations. Category theory gave me a little more insight into the concept of a "function" as I kept finding no satisfying and thorough definitions.

Anyone know how exactly these theories app's might differ, and how much farther I have to study (Current Level: College Algebra, sadly) to do some Topology? The concept of Hausdorff Spaces (from what I understand so far) seems really exciting..

Sat, Apr. 2nd, 2005 07:11 pm (UTC)
dreamgoat

The standard way to do things is to go through the calculus sequence, then take some real analysis, then go after topology.

The reason for this is that people like to use the 'grounded' ideas in real analysis as a jumping off point for more abstract topology.

I don't think it _has_ to be done this way, but I've never heard of anyone doing it differently. You might try checking some books out of the library and seeing if any of them are readable. I mean, who knows?

I will give one piece of advice, though: if you find yourself beating your head against the wall continually, your energies will probably be better spent learning calculus, where the books are aimed at someone in your position. Once you get comfy with those ideas, and the ins and outs of mathematical writing, you'll probably find those topology books make a lot more sense.

One more thing: you definitely don't want to get into analysis without working through calculus, at least at concurrently.

Fear not, though, calculus is one of the most important/profound human advancements of all time. It's got all sorts of magic of it's own in store for you.

Good luck, and think about joining the 'mathematics' community on Livejournal--there's more posting action there.

Sun, Apr. 3rd, 2005 01:20 am (UTC)
tldz

The other thing you will probably want is some background in abstract algebra. You might also find some undergraduate geometry helpful, depending on what sort of topology you end up being interested in. In addition to mathematical maturity, which is part of what the previous commenter is getting at, topology was invented to solve certain kinds of problems that arise in other areas of math, so to do topology, you need to know about other things. (This is fairly common in all branches of math, though.)

Good luck.