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__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:

*(Complex Analysis)*

Vector Calculus

Abstract Algebra

Partial Differential Equations

Functions of a Complex Variable I

Vector Calculus

Abstract Algebra

Partial Differential Equations

Functions of a Complex Variable I

*Galois Theory*

Probability

Numerical Analysis

Functional Analysis

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.