Physics prerequisites for quantum mechanics and general relativity 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.)
 A: So concerning your first question, I believe that this really depends on the level at which you want to understand the topics you listed. I believe you can actually get quite far in both Quantum Mechanics and General relativity with little training in physics. However, to form a deeper understanding of what is actually going on some prerequisites will help a lot.
I guess my starting point would be classical mechanics for both subjects, which given your mathematics background should probably not be too difficult.
Depending on what you want to do, skipping Electromagnetism might be an idea, however, at least seeing the basic concepts should not take too long and will give you a broader overview of topics in physics, though you probably do not explicitly need it for either of the topics you want to study at the end of the day.  You will however probably need to study wave optics at some point as this is often taken as a starting point for Quantum Mechanics.
As you mentioned special relativity is a must (though again you can probably keep this quite short and just focus on the major ideas). Apart from these I'm not sure you'll actually need much else.
As far as references go I'd probably stick to works that are rather conceptual in comparison to mathematical if you want to progress quickly, however if you want to see how the mathematical ideas you've developed fit into these starting topics more mathematical works might be more interesting. (However this will probably take a bit longer).  One canonical reference for getting an overview over a broad number of ideas are ''Feynman Lectures on Physics" which are available online and are very much enjoyable to read as Feynman was an incredible scientific writer. These cover a range of topics including most of what you'd need but are more conceptual than mathematical in nature.
I can always recommend David Tong's notes on most topics which can be found here. He's got notes on all topics you will probably need. I haven't read the relevant ones, however, having read most of his graduate-level notes at least partially I am sure these are just as well written. They do include a good number of exercises as well and, as most were written for a course he taught, are not too long due to the requirement to fit into a single term.
If you want something more detailed, for Quantum mechanics both
"Modern Quantum Mechanics" by "JJ. Sakurai" and "Quantum mechanics" by "Claude, Cohen-Tannoudji et al." are standard works that you can never go wrong with. (Both contain ample exercise). Be warned however: These Books are really detailed (e.g. the second is a 1300 page two part work on Quantum mechanics) so you'll probably only ever need a few selected chapters and reading (and understanding) the whole work will take ages. However they of course also contain everything you'll probably ever need in terms of basic Quantum Mechanics.
For General relativity, there are a few canonical works you can never go wrong with (though I haven't read any of them to a high degree so I'll abstain from giving any details). One such book is ''General Relativity'' by ''R. Wald'' which is sure to contain everything you'll need.
I can however generally recommend starting with lecture notes on all topics as they'll give you a good broad start and often list great resources to dive deeper into the subject. This can be very helpful to not get lost in the finer details. For GR one such set is given by Harvey Real: GR. These notes are nice, however spend quite a lot of time on differential geometry basics so maybe they are not the ones for you. (They do however contain lovely exercises, great references and are well written in general). He also has notes on Electromagentism and Black holes (i.e. applied GR) which are probably just as nice.
Hope this helps.
