Representation Theory, Part 1: Irreducibles and Maschke’s Theorem

Good luck to everyone taking the December TST tomorrow! The goal of this post is to give the reader a taste of representation theory, a la Math 55a. In theory, this post should be accessible to anyone with a knowledge of group actions and abstract vector spaces. Fix a ground field $latex {k}&fg=000000$ (for all… Continue reading Representation Theory, Part 1: Irreducibles and Maschke’s Theorem

Why do roots come in conjugate pairs?

This is an expanded version of an answer I gave to a question that came up while I was assisting the 2014-2015 WOOT class. It struck me as an unusually good way to motivate higher math using stuff that people notice in high school but for some reason decide to not think about. In high… Continue reading Why do roots come in conjugate pairs?