I'm currently a sophomore in college double majoring in math and physics and I've been wondering what would be a good grad school for mathematical physics. I have a pretty good math background (calc 1-3, diff-eq, linear algebra, topology, real analysis, functional analysis, abstract algebra, and number theory so far). My background in physics is weaker I think (physics 1 and 2, modern physics, modern physics lab, statistical physics, classical mechanics, electricity and magnetism, some quantum computation, and I'm taking quantum mechanics and particle physics next year). I like pretty much all of my math classes except abstract algebra. I also find my physics classes interesting but more challenging. I've gotten all A's in my math classes and A's and B's in my physics classes. Would my background be good enough to even get me into a good grad school? I was also wondering what would be a good area to look into for the future study that would do more with functional analysis. What other classes would you recommend for good grad school prep? Is there anything that uses topology in physics?