I’m a mathematician with a specialization involving differential equations and probability theory, and I’ve also spent a lot of time studying topics like differential geometry, algebraic topology, and Lie theory. My physics background is quite weak, however, and I’d very much like to see how some of these advanced mathematics subjects get used in applications. Specifically, I’d like to eventually learn the principles of both quantum mechanics and general relativity, and how advanced mathematics gets applied.

Question 1. What are the physics prerequisites to learning quantum mechanics and general relativity?

For quantum mechanics, I know I’d need to have classical mechanics down pat. Some physicists have told me that I’d need to learn electrodynamics as well. For general relativity, obviously I need to learn special relativity first. Is there anything I’m missing for either?

Question 2. Assuming a strong mathematics background, what are good textbooks or resources to learn these subjects from? (Preferably ones with lots of problems for me to practice from.)