TITLE: Mathematics for machine learning
QUESTION [21 upvotes]: I would like to know what mathematics topics are the most important to learn before actually studying the theory on neural networks.
I ask that because I will start to learn about neural networks and machine learning on my own to help in the analysis I am doing on my PhD about patterns of genome evolution. 
Thank you in advance.

REPLY [3 votes]: As a deep learning practitioner with mathematical background I was yearning to have some satisfying mathematical framework of what I do in my every day job. In my opinion, very well fitted mathematical foundations of deep learning principles are captured simply by Empirical risk minimization (ERM) concept. I encourage everyone to read just Chapter 1 from The Nature of Statistical Learning Theory of V. Vapnik. In my opinion it is an eye opener.