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I want to do a PhD in theoretical or mathematical physics. I have excellent grades in classical mechanics, electromagnetism, quantum mechanics, thermodynamics ans statistical physics while I'm average on all the other courses. I study on my own topology, analysis, linear algebra (from Roman's book) and group theory (from Rotman's book). I also have excellent recommendations letters from professors of the physics department and from the math department.

It would be a shame if I couldn't go to grad school. So I'm asking: is it possible to go to grad school without a degree from a university? Thanks in advance :)