So Im in my senior year of a Computer Engineering degree. I've always been interested in physics but never really thought to study it in depth. I've always read a lot of popular physics books, the kind for the lay person and all they do is leave me asking "why". They explain all of these marvelous ideas from different fields of physics but never give the details, which of course is not their intention. However Im not content anymore without knowing those details. I want to learn more physics, at least to the point where I can start to read physics papers and journals and actually understand them. The dilemma I'm at now is that I do not have the mathematical knowledge required to pursue this to much effect. I'm looking to fill the gaps of my Mathematical ignorance so that I can begin to really study some physics. From the math courses I have had and the books I already own I feel I still need more maths to be successful. I want to be able to get through a rigorous self study of modern Physics, with Quantum Mechanics, Relativity, Particle Physics and the like. I've taken three levels of Calculus, covering topics from basic differentiation and integrations, to multiple integration, surface and line integrals, basic Vector calculus (Stokes theorem, Divergence theorem, and Green's Theorem mostly) and have also had one course in Differential Equations, which admittedly was not my strong suit. So I guess mostly what I'm asking is, given this mathematical background and the goals I have in mind, where do you recommend I begin my mathematical studies? What topics would be most vital for me to cover, and what books would you recommend I purchase to begin my studies?