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As with all self-taught students, I am sure I have holes and gaps in my education. I have gone through the first chapter of Goldstein, and have done most of the problems for that chapter. I have not yet tackled Jackson, however, because I have heard that it is a difficult text to self-study. I also have Merzbacher's text on QM, but I'm holding off on that until I've mastered mechanics and EM (or is this a bad idea, and I should start with it instead of EM?).

Anyway, I have a thorough understanding of variational calculus (at least, I have mastered the content in the Arfken chapter on the subject). So you can deduce from that my current level of math - I don't know where I'm standing. I also have absolutely no background in linear algebra, matrices, tensors - that sort of thing.

My question is, what topics in mathematics do I need to master before I can confidently tackle these graduate physics books (especially Jackson)? I have a copy of Arfken's Mathematical Methods for Physicists (2nd edition), and Hildebrant's Methods of Applied Mathematics (both of the books I have taken from people who were throwing them away, so selection was limited), so anyone who has had experience with those books can help me more easily.

I realize how open-ended this question is, but if someone could give me the mathematical path to graduate physics, I would be extremely thankful. It would focus my pathless study of mathematics.