Hi PF, asking for course advice again. Currently I am finishing up undergraduate level series in: Abstract Algebra Real Analysis Particle Physics Topology. Next fall I will be registering for: Stat Mech/Thermodynamics (required for physics majors) Statistics and Probability (required for math majors) - - I can choose from: Math: Graduate level Real Analysis Graduate level Topology Graduate level Differential Topology (First course in series covering differential geometry) Physics: Graduate level Mathematical Methods in Physics Graduate level Mechanics/EM Graduate level General Relativity (I have taken the undergrad version) Which course (or pair of courses) will be most helpful in graduate school for quantum gravity/mathematical physics/high energy theory? Will I have enough time to take all of these courses in graduate school? (I'm interested in math enough to honestly take all these courses if I had enough time!) Options: Take 2 Grad Physics courses Perceived Pros: Looks better for graduate school/I will be prepared for graduate school Perceived Cons: Risk of never taking a formal class in graduate level math Take 2 Grad Math courses Perceived Pros: Good chance at being able to take even higher level mathematics in grad school Perceived Cons: Will being going to physics grad school without having taken any grad courses. Take 1 of each: Perceived Pros: Good Balance Perceived Cons: Lack of depth My perspective is that I want to be able to tackle theoretical/mathematical physics with a sophisticated mathematics tool belt (and because the math is interesting in itself and I can't see myself leaving it behind outright). What should I do? Thanks!