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How to teach yourself cutting-edge mathematics and physics
First of all, no matter what you study, I think the following knowledge is necessary for you.

1. Four major mechanics, including classical mechanics, thermodynamics, electrodynamics and quantum mechanics. The order of study can be in the order I listed.

2. The basic requirements of mathematics are calculus and linear algebra. I think you should already have this foundation. A slightly advanced application requires basic variational methods and complex variable functions.

I will probably list the prerequisites for other advanced courses.

1. differential geometry->; Theory of relativity

2. atomic physics->; Elementary particles (nuclear physics)->; String theory

3. quantum mechanics+electrodynamics->; quantum field theory

Gravity field is something you will encounter in string theory and general relativity.