Disclaimer: I write this as a computer-scientist that uses math a lot in his work (I’m a research assistant at a university).
Introduction:
There are three (overlapping) aspects of math in computer science:
Math that is actually useful.
Math that you can run into, and is generally good to know.
Math that lets you build more awesome math.
First is essential, because the students need to be able to do stuff. Second is important, because you cannot teach students everything, and at the same time trying to get into a new field all by yourself is quite hard (i.e. it’s good to know the barest basics of everything). The third are these which aren’t directly useful, but present meta-concepts that happen all the time (a bit like design patterns in programming); you can live without them, but intuition you gain there makes life much easier.The list was sorted by (subjectively defined) importance.