I am currently going to be a senior undergraduate with a double major in Math and Computer Science. In the past I have worked on Data Mining projects, and Mathematical Modeling. I have had a recent interest in Mathematical Finance. What Math and Computer Science theory are heavily used in Mathematical Finance? For Computer Science it would seem intuitive that Machine Learning/Data Mining theory would be useful. For Mathematics, probability and statistics are definitely essential. What I am looking for is what subfields, specializations and theories in Math/CS are heavily used in Mathematical Finance?