I am majoring in Physics and Math at Purdue University. For the physics requirements, I need to take two Mathematical Methods of Physics courses. Below are the catalog entries for the two courses. Mathematical Methods of Physics I Discussion of wide-ranging physics problems from mechanics, E&M, thermal, and modern physics with emphasis on reviews and introductions of mathematical methods and techniques that are essential in such discussion. Relevant mathematical methods include one-and multi-variable calculus, complex numbers and functions of a complex variable, and vector calculus. Mathematical Methods of Physics II Discussion of wide-ranging physics problems from mechanics, E&M, thermal, and modern physics with emphasis on reviews and introductions of mathematical methods and techniques that are essential in such discussion. Relevant mathematical methods include vectors, matrices and normal modes as well as ordinary and partial differential equations. Now for the math major, I need to choose three selective courses. I can choose from the following: Vector Calculus Abstract Algebra Partial Differential Equations Functions of a Complex Variable I (Complex Analysis) Galois Theory Probability Numerical Analysis Functional Analysis I have to take the Mathematical Methods courses my sophomore year and I need to take the selective courses my junior and senior year. Knowing this, are there some selective courses listed above that contain material already covered in the methods courses? For example, since vector calculus would be covered in the method courses, will I know enough of vector calculus to not need to take its respective selective course? Or do I need to know more of it to be successful? How about the other subjects? I plan on pursuing a PhD and focusing on General Relativity and QFT (differential geometry and topology is required, that's why it's not listed above). What has been your past experiences with your mathematical methods course? I'm curious to know.