Hey animboy and welcome to the forums.
In terms of useful knowledge I would recommend calculus, discrete math, a good solid statistics pathway, a good solid computer science pathway, and on top of these, any AI specific courses.
In terms of learning algorithms in AI, many are based on probability measures and information, and the goal is to produce a model of some phenomenon that converges to the actual model represented by the data. There are formal definitions for what convergence is mathematically, but that is the basic idea.
From this you will need to draw on a variety of fields to do this and this has a bit of variation depending on what kind of model you are dealing with, and what kinds of patterns you are trying to codify.
For example if you are trying to use these applications in the area of signals intelligence, then you will probably be incorporating things like Fourier transforms in your work. In other areas you might need to use different techniques to get the information you want because the transform required is the one that decomposes your data into the stuff that you actually need.
In addition to the above, it's important to know domain specific information in the same way that any other field has very narrow and specific domain knowledge.