Awesome class, and an introduction to math that isn't just plug-and-chug formulas (Calculus, Differential equations). It teaches you actual mathematical thinking and how certain conclusions are reached via proofs.

Basic set theory, logic, combinatorics, and graph theory.

He has a tendency to make offhand political comments and to be annoyed by questions, but he's good otherwise.

Do yourself a favor and read ahead.

No idea.