Economics major and math minor

b_r_um
Tue, 06 Jan 2009 01:14:51 +0000

A slight overview of subjects: linear and abstract algebra both deal with the structure of certain objects with familiar binary operations. Linear algebra deals with vector spaces, which you can view as a generalization of vectors as you learned about them in precalculus. The thing is, when you generalize, you end up finding that quite a few things you see (e.g. polynomials) in math have a structure that involves taking finite linear combinations of some basic elements. Abstract algebra just deals with many structures of this nature. And you see a lot of problems in mathematics as special cases of the theory of these structures. The idea is to pinpoint why familiar objects have the properties they do.

Real analysis deals with questions that have a calculus-like flavor – how continuous functions behave on different subsets of the reals, how they behave on convergent sequences, and eventually you generalize what continuity means. You also develop abstract versions of integration, where you integrate over things other than your favorite Euclidean space. Doing calculus on different objects is imaginably a powerful thing.

If I didn’t already appreciate abstract math, those two paragraphs would have scared the hell out of me!