Which Math Courses Best Prepare for Graduate Physics?

[Jim Jam]

I've taken the typical undergraduate physics program required math: calculus series, linear algebra, Diff Eq (this fall, 2012), and an extra mathematical reasoning/proof writing class.

I need a few more maths to complete my physics degree and pick up a math minor, and to prepare for physics grad school. The plan was to take PDE and Graph Theory. I know Diff Eq and PDE are very useful so I'll definitely take them, but Graph Theory is just interesting and perhaps not so useful. Complex Variables is frequently mentioned as being good preparation...

Swap graph theory for something else? Take it, and take more math?
Possible upper level math choices: Complex Variables, Numerical Analysis, Graph Theory, Intro to Topology, Real Analysis 1, Intro to Mathematical Logic (pure math, symbolic logic, etc.).

 

[Lord_Sidious]

Complex Variables and Numerical Analysis would be the ones you would use out of what you listed, if you are not getting too much into the theoretical/mathematical side. I am a Physics major/math minor and have been looking up what I would need and I have decided to take upper level PDEs, complex variables, and applied linear algebra.

 

[deekin]

Complex variables, numerical analysis, and PDEs do seem to be the recommendations of choice, because I was told the same thing by a number of people, including the physics dept chair at my school.

 

[Jim Jam]

So not to bore everyone with my scheduling issues, but it looks like Complex Variables is out of the question. Numerical Analysis looks good, here's the description my school provides:

Introduction to Numerical Analysis
Accuracy and precision. Linear systems and matrices. Direct and iterative methods for solution of linear equations. Sparse matrices. Solution of nonlinear equations. Interpolation and approximate representation of functions, splines. Prerequisite: [Multivariable Calc]. [Introduction to Computing in Mathematics] and [Linear Algebra I] are recommended.

Would that qualify as

too much into the theoretical/mathematical side.

to be of any use?

 

[espen180]

If you want to do theoretical physics, you should at least know the following topics.
- Algebra (Groups, rings, modules, vector spaces, categories)
- Topology (general ,algebraic and differential topology are needed)
- Real and complex analysis
- Differential geometry and analysis on manifolds

Basically, a physicist can never know enough mathematics.

 

[Jim Jam]

If you want to do theoretical physics, you should at least know the following topics.
- Algebra (Groups, rings, modules, vector spaces, categories)
- Topology (general ,algebraic and differential topology are needed)
- Real and complex analysis
- Differential geometry and analysis on manifolds

And out of curiosity, on what basis are you selecting these topics?

 

[Lord_Sidious]

And out of curiosity, on what basis are you selecting these topics?

I would say because groups and abstract algebra for particle gauge theory, abstract vector spaces are used a lot, like in quantum mechanical hilbert space..."topology (general ,algebraic and differential), and differential geometry and analysis on manifolds" are used for general relativity but those not really used for basic graduate physics unless you take GR.
Numerical Analysis would be useful because you will have a better feeling for getting numerical solutions to linear and nonlinear equations.