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id the sloth

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I have plenty of math major friends and they tell me all the time about how they keep running into physics majors in their classes. I was wondering what mathematics courses would be useful for someone planning to head in the direction I am heading in?

I have completed calculus up to mulitvariable, lower division linear algebra and differential equations (They are lumped together in one semester at my school), and a year of math methods for physical scientists (First semester was things like complex numbers, applications of taylor series, and Fourier series and transform. Second semester was basic PDE's: variational calculus, basic attempts at symmetry solutions, forbenius series, eigenvalue problems and the like).

My math major friends tell me I should take upper division linear algebra and real analysis. One even suggests abstract algebra because his professor says it is crucial to quantum field theory. I personally feel very comfortable with not needing linear algebra after taking Quantum Mechanics but I'm not sure about the others.

Just for the sake of being thorough, the classes that I am currently considering are:

-Real Analysis (It is mandatory for the ODE course and I hear it is necessary for graduate PDE. Also a prereq for differential geometry and complex)

-Linear Algebra (People say it is very hard to get by in the more rigorous upper division math classes without this class)

-Numerical Analysis

-Complex Analysis

-Metric Differential Geometry (I don't know much about it but from what I can gather it is more or less an advanced geometry course which seems useful)

-Optimization (Like I said I'm doing applied physics, and this seems useful for applied majors)

-PDE (Basic PDE course, it studies PDE a little more rigorously than the mathematical physics course I've already taken)

I definitely do not plan on taking all of these!

If you had actually read all that, I feel like I should give you a prize but I'm afraid I can only offer my sincerest thank you.