/sci/ - Science & Math

>>11564863
There are really a few different areas of TCS. I would say the main one are recursion theory/traditional TCS, cryptography/applied math, and modeling.
In my opinion, recursion theory is pretty boring except for the entry level Godel/Tarski/Turing type stuff. If you don't already that stuff, it's where you should start, but like I said, I don't think it's actually the most interesting area of TCS. After you understand the basics about recursion, decidable sets, formal models of computation, etc., you can move on to the interesting stuff in cryptography and the theory of models ("theory of models" is a term I just made up and doesn't actually related to Model Theory) . Cryptography draws on a lot of tools from analysis, algebra, combinatorics, and number theory, and it's really interesting, but you need to know a lot or math. The "theory of models", as I have unconventionally termed it, is really interesting, especially if you aren't necessarily concerned with traditional math, but more so empirical science and philosophy and stuff. By "theory of models" I mean a catch-all terms for studying the models of natural and social phenomenon. Stuff like game theory, dynamic logic, epistemic logic, agent based modeling, replicator dynamics, evolutionary game theory, etc.
In the world of cryptography, I think an interesting place to start would be with the Theorem on Friends and Strangers.
With respect to theory of models, I would suggest looking into the Muddy Child Problem or the Hawk-Dove Game.