Question: pure math courses that are relevant to machine learning?

I am thinking about doing research on machine learning in the [very distant] future, and would like to know more about what math courses are relevant to the field.

I've just taken a course on Probability and Stochastic Processes (covered Markov Chains, but not Hidden Markov Model), and a intro course on Real Analysis, but I'm trying to plan out the rest of my classes. I have more analysis courses lined up (Fourier Analysis, Complex Analysis, Real Analysis), as well as Algebra, Graph Theory and hopefully Probability Theory. Which math courses are important or essential in studying machine learning, and which are less important?

Also, I will be taking a course on Artificial Intelligence next fall.

I know next to nothing about machine learning, and am trying to plan ahead while learning as much as I can in preparation. Thanks!