Fields that require both CS and pure math I'm mainly a CS major, but I also want to learn more advanced  mathematics. I see lot of cross over between CS and applied math, same can't be said about pure math.
Definition of 'advanced': Something a pure math major learns during and after late undergraduate years.
What are the fields that combines advanced mathematical topics with computer science? 
Theoretical computer science and computational group theory are good examples.

Cryptography is a field which requires lot of Number theory. Formal languages and automata theory requires some Graph theory, and these automata things can be connected to computer science as well.
