here's a link i found looking into the subject: http://datascience.ibm.com/blog/the-mathematics-of-machine-l...
and here's some recommendations for math/ml texts i got in another thread that may be of use: https://news.ycombinator.com/item?id=13275031
the blog article was useful, thank you! A problem with most of the recommendations is that they are targeted at software engineers wanting to learn some ML. They mostly don't need to understand back propagation fully and don't have that complex of a problem. So the requirements are the absolut basics (what are vectors/matrices and how to multiply them). Also their math-background is either non-existent or a long time ago. I am a student and constantly learning math, so i am in a different position. I am also interested in really understanding NN, including recent papers. They vary, some being not very math-heavy (the dropout paper) and some being the opposite (bayes neural network, only skimmed some papers). Many paper introduce a new idea borrowed from other branches of math, so you can't specialise too much. A broad understanding is important. Also we still lack a unifying theory, so we definitely don't know what math will become really important in the future.
While the courses i listed are required for most CS majors, i think they are more important for ML than many other fields of CS (of course there are exceptions). I think a deeper understanding of LA, Calculus and Numeric compared to normal CS-majors is beneficial (but if you majored in math you probably had to take these in more depth than most CS-majors). Also i would double down on Probability (so a course on Probability-Theory, Markov-Chains etc.). Optimisation Theory is also important, but often already somewhat covered in the other courses. I don't think one can point to a specific course that will be really important for NN in the future, nobody really knows whats coming. Just learn as much math as possible, so that you are prepared to learn and understand all the future theory and techniques that are not yet discovered. Maybe we will all be solving stochastic differential equations in the future, because they accurately predict the performance of various NNs?
Edit: I forgot tensor-mathematics, i haven't taken a course yet, but it seems pretty straightforward.