Study Signal Processing
i remember this question being asked on USENET at comp.dsp, but i don't remember all of my answer.

there are several mathematic disciplines that inform signal processing and formalize some of the concepts.

let's assume you have calculus of one and many variables and differential equations (any scientist or engineer should have those).

well, Complex Variables and Analysis of Complex functions to start with.

Linear Algebra: Matrices and Determinants

Fourier Series and Transforms

Probability, Random Variables, and Random Processes

Numerical Techniques

Metric Spaces and Functional Analysis

all those are useful math topics, sufficiently useful that i would recommend taking math classes in these if you end up in grad school in EE.  there are many signal processing topics that make reference to one or more of the above math topics.