Hi all, I have a B.Sc. and M.Eng. in Mechanical Engineering and I decided to switch to Astrophysics for my Ph.D. (for no reason other than following my passion). I still have a year or so before beginning the Ph.D program and I am willing to use this period to do some self study in Math to compensate my lack of mathematical background comparing to someone who did his undergrad in physics. what are the most important mathematical topics in astrophysics (or in theoretical physics in general) ? I understand that ALL fields of mathematics are important in theoretical physics, but I am hoping for some prioritization. Any info is most appreciated. To elaborate more on my background, I had a fairly good introduction to various fields of mathematics in my undergrad but the emphasis was all about calculus. Also my Master thesis was in Computational Fluid Dynamics which is all about numerical techniques for PDE's. Sometimes I even forget that there is more to Math than just Calculus.