For context, I have a graduate level computer science background and after doing some research on agent-based modeling and systems science I am convinced there is potential to formalize emergence and evolution into its own theoretical discipline which can be a foundation for unified science -- bridging theoretical 'STEM' and practical 'non-STEM' schools.
At the end I want to go into an academic or research program doing exactly that but that might be at least some years for personal reasons. I am also concerned getting into a formal academic program without the background to pick who to be taught by might end up stunting me. A lot of the work in the field is downright esoteric and my fear is doing research and getting mentored too deep in the wrong rabbit hole can make it impossible to formulate anything with interdisciplinary value.
So I want to do some self-guided studying for the time being (2-4 years) to attain the kind of background in functional analysis that can help me formulate my own concepts, or at the very least know how to find and understand research others publish for what I mentioned above. What are some ways I can go about that after brushing up on real and complex analysis?
If you want to learn functional analysis you need to find a book on the subject and read it. Rudin Functional Analysis, for example. Hmm, maybe first you should study something like the chapters on Hilbert spaces and Banach spaces in for example Rudin Real and Complex Analysis or Folland Real Analysis.
(Yes, that seems like a pretty lame answer, being sort of obvious/trivial. But it is the answer. What other sort of answer might you expect?)