Seriously, I'm looking for some community feedback on the kinds of things they want to learn about in physics/applied math. I'm bored and want to teach people some stuff. Here's your chance to get detailed knowledge of something fun you can't learn in school!
Possible topics off the top of my head are below. The idea would be that I would pick an aspect of one of these disciplines and do a few nice sets that explain that aspect and give serious practice. So, rank your top five topics in comments on this note, and if there is a large enough feedback I can do a series of sets with notes/problems over the next few weeks that will illuminate the most popular topic. Other topic ideas are also welcome.
Quantum information theory
2-d materials like graphene
More mathy topics:
Topology and geometry in physics
Principle of least action
Mathematical methods in physics
Group theory in physics
The role of symmetry
Why do we care about complex numbers? (life would be harder if we had to use quaternions all the time)