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I will be writing my bechelors thesis on the application of renormalization groups and p-adic analysis on stock markets. The problem is that I don't understand it yet. I need advice on the best path how to learn it.

What I know already:

- I've read most of Mac Lanes Algebra, so I know finite-dimensional linear algebra pretty well, some category theory and some group and ring and field etc. theory.

- Basic real analysis, this includes stuff like implicit function theorem, total derivatives and the like.

- Point set topology and some very beginning stuff in algebraic topology

- Smooth manifolds, as in Lee. This does not include more advanced stuff like Riemannian things.

- ODEs but not PDEs

- I'm beginning with Lie theory

What is the optimal path for me next? I guess I will need analytical mechanics, but as I don't know any physics the book from Spivak seems best for me, although the price is bloody.

Also I don't mind learning some physics in the process, like QM and QFT. Unfortunately I don't know any functional or complex analysis. Can you guys comment on this?

Thanks

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# Need advice with learning renormalization groups

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