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So I finished my undergrad last year in applied math and physics. I'm currently applying to applied math phD programs (but they are separate depts from the pure math depts). I don't exactly what I want to focus on, but I was thinking something in mathematical physics, PDEs, functional analysis, and operator theory. Perhaps the program I go to will let me work with a pure math prof doing stuff in string theory

The applied math courses I've taken include proof-based fourier analysis, linear algebra, and analysis. Also, courses in prob/stats, complex analysis, ODEs, PDEs, dynamical systems, and numerical analysis. So what should I self-study in the meantime? I was thinking topology or the second half of real analysis (integration, metric spaces. Lebesgue, etc).

The applied math courses I've taken include proof-based fourier analysis, linear algebra, and analysis. Also, courses in prob/stats, complex analysis, ODEs, PDEs, dynamical systems, and numerical analysis. So what should I self-study in the meantime? I was thinking topology or the second half of real analysis (integration, metric spaces. Lebesgue, etc).

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