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..