What topics should I be comfortable in to do serious AI/ML research?

Question

I am talking about grad school or industry R&D lab level research in AI/ML.Apart from being a good programmer, what other fundamental topics should one be well versed in to become a good researcher in this domain?I am in undergrad and I would love to apply to grad school after I finish. What topics should I study and from where? Books, courses, anything? I want to prepare ahead.

optbuild · Accepted Answer

I see many people dive into ML research by tinkering along the way. Although I have no objection to particular tastes, two courses that made modern ML easy for me were:
1. Linear Dynamical Systems by Stephen Boyd [https://ee263.stanford.edu/archive/]
2. Convex Optimisation by Stephen Boyd. [https://see.stanford.edu/Course/EE364A]
Both lecture series and course notes are availabe from the official page of the instructor.