@0celo7 Depends. 4.0 GPA in a magnet school going into senior year, going into my third year of physics and my seventh of science (fourth at an AP level), varsity sports, 2300+ SAT superscore and still probably a failure compared to some of my clasmates.
Actually, definitely a failure in comparison. Some of the kids at my school are geniuses. I look like an idiot in comparison.
@FenderLesPaul Good in theory, but in practice the schedule most colleges offer is the one you have to take. You can add courses and take a grad course, but only if you want five or six courses in a quarter (or semester).
-sigh- my experiences are with studying Lagrangian mechanics beforehand and being made to take the courses again, doing every problem in ch 1-4 of griffiths electrodynamics beforehand and then being made to take a course using ch. 1-4 of the same book anyways, and same with real analysis. :(
Algebra will be useful since many examples come from it, but as for category theory itself, I think it actually hasn't got any prerequisites, but it's a vast field - e.g. if you want to look at things like topoi or Grothendieck topologies or whatnot, good understanding of topology and the notion of homotopy is useful.