This can be a very weird question, but I haven't seen the same situation with mine in this forum, so I'd like to put this. Let me introudce my situation first.
I'm now a math student of master program in a university in Korea, and I was majored in economics and math as an undergrduate. As a freshman, though my first major was economics, I took a class of mathematical logic, and it was great to me. From that time, I decided to have double major in math and economics. And taking math courses like linear Algebra, Algebra, Analysis, Complex Analysis, Logic, Set theory, Statistics, Homological Algebra, Topology and so on.
But as time went on, I felt that the motivation of standard math courses are somewhat different from mine. Yes, mathematics has a culture of broad range, but, even if the core courses are very useful and beautiful, I think it has a slightly different motivation from mathematical logic. "What can be a good course to take if I liked logic class?" I asked to myself, and I decided to take "Formal languages and automata theory" in cs. It was fantastic. And at that time, I learnt there existes the area of theory of computation or theoretical computer science. But in Korea, culture of cs is more oriented in the way of engineering area, so I felt that it would be more helpful to train myself in math dep. than cs, so I chose to go to master program of math.
But now, in my university, there are more strong culture of concetrating on "classical" mathematical things, not computation or even combinatorics or logic. So, I realized that if I pursue this way, then I'll be just a "pure" mathematician. Considering interconnectedness of academia, it can be also a good way, but I don't like to do that. So I'd like to change a university to pursue tcs research.
However, I've just taken two courses in cs - Formal languages and automata theory, and c programming. And I have no research experiences in cs. I'd like to self study my own to have sufficient information of tcs area for a while, but it's just an individual thing. And I'm so confused because I don't know what courses to take from now on, and what resonable amount of knowldeges are needed to start reasearch in tcs(especially the knowledge in cs). Briefly, what should I do to switch from math department to cs to research tcs topics?
Recently, I have some interest in computational complexity theory and start to study "gems of theoretical computer science" and it's very interesting. But that's only plan that I have. I wish my plan would be more concrete. Any help? Please?