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rhotonsix

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- TL;DR Summary
- How relevant is it to study and work through problems in a book like Rudin's analysis to build a mathematical foundation for studying theoretical physics

I am recreationally self studying physics and math with the ultimate goal of understanding theoretical/mathematical framework of classical mechanics, general relativity, and quantum mechanics (in addition to the actual physics). The question I have is how deep in the realm of pure math does one need for such a goal. For example I am working my way through baby Rudin, and reading and working out his proofs in the text is not an issue, but a number of the end chapter problems are extremely challenging. How useful is it if my goal is to study theoretical aspects of physics to spend a lot of time solving the problems in a book like Rudin’s? Would my time be better spent on texts like Hubbard’s vector calculus/differential forms book which strike a balance between the pure (proves all the major theorems of multivariable analysis in text rigorously) and applied (treats computation as well)? I am in no rush and have no problem spending the time to tackle the Rudin level problems but just unsure if it is counterproductive to my goal, which is to build a decent mathematical foundation for studying theoretical physics. Thanks in advance.