Classes to take for Theoretical Physics

[Broccoli21]

Hey guys, i'll be a sophomore next year, and I was wondering about what classes you could recommend me taking then, as well as advice for future coursework.

Which 4 of the following would be (the most) useful for theoretical physics?
-Differential Geometry
-PDEs
-Fourier analysis
-Complex Analysis
-Combinatorics
-Real analysis II (finish off baby rudin and more)
-Abstract algebra (all of dummit and foote)
-Dynamical systems
-Data structures (would CS be useful for a physicist?)
note: I will be taking statistical mechanics and classical mechanics II anyways

Thanks in advance!

If you are curious: I have taken (including this semester):
Calc and Vector Calc
mechanics and EnM
Differential Equations (ODEs and systems of them)
Linear algebra (went all through Axler)
difference equations
Real Analysis I (about 2/3 of baby rudin)
intro to quantum mechanics
probability theory
classical mechanics I

 

[Jorriss]

-Fourier Analysis and Complex Analysis would be the safe bets in terms of being useful.

Real Analysis II will likely not be useful for physics unless you do some very advanced QFT, string theory, etc. That being said, it's one of those classes that'll just make you smarter, so it would be a good idea, imo.

PDE's depends. If the course goes far enough to cover greens functions, it'd be a great addition.

Are there no numerical analysis courses?

Well, there's my input.

 

[micromass]

To add to what Jorriss said:

Differential geometry is quite useful in general relativity. I suggest you take this course sooner or later. No pressure though as you'll probably not see GR until you're in grad school.

Data structures is a programming course. This is a very useful skill to have as a scientist. The chances are very large that you will have to program at some time in your carreer.

Fourier Analysis, Complex analysis and PDE's are no-brainers: YES, they will be very useful to you.

 

[Broccoli21]

Fourier and Complex are obviously useful, but what about discrete stuff like abstract and combinatorics? Is that ever useful, or should I not bother taking pure maths such as those?
Also, I have to choose between Fourier and PDEs, as they both give the same credit. PDEs is much more theoretical. Here is the descreiption of both classes:

Math 115: Fourier Series and Boundary Value Problems
Complex variables and residue calculus; Laplace transforms; Fourier series and the Fourier transform; Partial Differential Equations including the heat equation, wave equation, and Laplace's equation; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions.

Math 180: Introduction to Partial Differential Equations
Partial Differential Equations (PDEs) including the heat equation, wave equation, and Laplace's equation; existence and uniqueness of solutions to PDEs via the maximum principle and energy methods; method of characteristics; Fourier series; Fourier transforms and Green's functions; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions.

There is a numerical analysis, but not that semester unfortunately.

 

[FieldDuck]

http://en.wikipedia.org/wiki/Combinatorics_and_physics

I wouldn't say it's useless, I just doubt you'll learn enough in one class to really make it useful per se. Nevertheless, I personally find it interesting and it's really quite neat how you can apply a lot of ideas from Combinatorics to a lot of different kind of problems.

 

[micromass]

Fourier and Complex are obviously useful, but what about discrete stuff like abstract and combinatorics? Is that ever useful, or should I not bother taking pure maths such as those?

They might be useful, but I wouldn't take the course.

Also, I have to choose between Fourier and PDEs, as they both give the same credit. PDEs is much more theoretical. Here is the descreiption of both classes:

Math 115: Fourier Series and Boundary Value Problems
Complex variables and residue calculus; Laplace transforms; Fourier series and the Fourier transform; Partial Differential Equations including the heat equation, wave equation, and Laplace's equation; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions.

Math 180: Introduction to Partial Differential Equations
Partial Differential Equations (PDEs) including the heat equation, wave equation, and Laplace's equation; existence and uniqueness of solutions to PDEs via the maximum principle and energy methods; method of characteristics; Fourier series; Fourier transforms and Green's functions; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions.

They appear to have the same content. I would take the PDE course.

The difference is that 115 includes complex variables and laplace transforms. You'll learn more about this in a complex analysis class, and you can self-study Laplace things.

Furthermore, the PDE class features Green's function, which is quite neat.

 

[Broccoli21]

Thanks for the advice guys! I'll probably take PDEs instead of Fourier series. I guess I can wait for later to take stuff like abstract and combinatorics.