Hello, I plan on continuing to study physics, mathematics and earth science. (independently) What are the mathematical pre-requisites for learning relativistic quantum field theory as smoothly as possible. On MIT's opencourseware, it indicates that a class on advanced ODEs is enough, but we all know that they usually teach the rest of the stuff in the physics class itself. I'm more comfortable with learning the mathematical theories independently of the class. So far, I have utmost confidence in my knowledge of Newtonian physics, (getting there with Lagrangian and Hamiltonian), electromagnetism, real analysis, calculus (single and multivariable), and linear algebra. I'm still getting there with ODEs but after those, I'm moving onto Fourier analysis, PDEs, topology and differental geometry. (needed for geodesy, seismology, quantum theory and general relativity) The plan is to start at basic Quantum Physics I and end at Relativistic Quantum Field Theory III. (see the opencourseware listings at http://ocw.mit.edu/OcwWeb/Physics/index.htm) Am I leaving out any mathematical course that would allow for this to go as smoothly as possible? Appropriate books are no problem for me to get my hands on so don't feel the need to leave anything out. Here's the link to MIT's math section. Can you guys help me to pick out the appropriate mathematical pre-requisites?