While Discrete Math was mentioned, I would like to add more of CS Theory. In particular, at least Data Structures and Graph Theory, to start with.

While in many cases, theory only allows you to do the same thing faster, and so is not that necessary, in many other cases the result of good theory can

1. make an impossibly slow computation, into a possible solution.
2. give you a simple way to look at an unusual problem by reducing it to a well known one.