Overload

If mathematics could kill, I would certainly have been vaporized by now. I have been attending about 7 hours daily of lectures in a hodgepodge of mathematics, most of which I do not understand. I think it's good in the long run though. I recently realized that practically all of my formal mathematical knowledge, with the exception of the linear algebra I learned "on the street", is analysis in one form or another. Calculus, real analysis, harmonic analysis, differential equations, some rudiments of functional analysis... it's all analysis. Naturally, this is a problem since most of math is not analysis, and I am pretty clueless about everything else. While I'm fairly bad at it, I have been consequently trying to focus intensely on the lectures involving algebra and category theory. If I can succeed in grasping it, then I should be able to understand the later lectures on topological quantum field theories. Not only are TQFTs interesting mathematical entities in their own right, but I believe they are of some importance in condensed matter physics.

My most recent efforts have mostly centered around category theory, which is absolutely bizarre. Category theory is an even higher abstraction of set theory: categories are arguably the most fundamental constructs of mathematics. A category consists of objects with arrows, or morphisms. There are also a few axioms that the morphisms must satisfy. The level of abstraction is simply ridiculous. The subject often seems more like hand-waving, magic, or philosophy than mathematics.