I am an electrical engineer 20 years from my last formal course in grad school. I wish to teach myself advanced optics, particularly diffraction theory, analysis of polarization using Jones calculus, aberrations, etc. I realize that my mathematics chops are sadly rusty through years of disuse, hence I am seeking advice on the best way to regain my facility in this crucial area before venturing into the physics. I had the following in mind: 1. Thorough review of calculus (working on Strang cover to cover and have Apostol has well). 2. Multi-variable and vector calculus (need good reference book here). 3. Linear algebra/ODE/PDE (haven't decided on the books) I am hoping that this should enable me to tackle something like Introduction to Fourier Optics by Joseph Goodman, as well as other more rigorous optics texts. I would greatly appreciate any advice on this. I would also like to tackle some grad level quantum mechanics, say Cohen-Tannoudji and I would like to know if I am missing something. Thanks!