How much math do you need to understand machine learning algorithms?

How much math do you need to understand common ML algorithms? Not just being able to apply the algorithms...but being able to fully explain why and how they work. And which specific topics?

My background is computer science so I'm only used to dealing with the discrete and am feeling rusty when encountering stuff like gradients and partial derivatives. I thought I'd just make a list of stuff to review and get it over at once.