Best math classes for a physics major?

[ZeroZero2]

Best math classes for a physics major??

So I'm double majoring in physics and math, what are some beneficial math classes?

REQUIRED FOR A MATH MAJOR:
- Calculus I
- Calculus II
- Calculus III
- Linear Algebra
- Abstract Algebra
- Differential Equations
- Intermediate Analysis
- Vector Analysis (I could replace with either Complex Analysis or Advanced Multivariable Calculus, but Vector Analysis is required for a Physics major)
- Survey of Undergraduate Mathematics

ELECTIVES:
I need to take:
- Partial Differential Equations I & II (required for a Physics major)

So I need three more math classes, here are most of my options:

- Advanced Multivariable Calculus
- Discrete Mathematics
- Complex Analysis
- Intro to Higher Geometry
- Intro to Stochastic Processes
- Intro to Real Analysis I & II
- Graph Theory
- Advanced Abstract Algebra
- Topology
- Nonlinear Dynamics and Chaos
- Differential Geometry
- Mathematics of Signal Representation
- Integral Equations
- Theory of Ordinary Differential Equations
- Numeral Analysis
- Advanced Linear Algebra I & II
- Number Theory
- Mathematical Statistics I & II

I could also take a seminar or a "special topics" class

Any suggestions??

-

 

[Troponin]

My personal choices would be:
Differential Geometry
Complex Analysis
Linear Algebra

If I were to take any more, I'd probably do numerical analysis and Integral equations. I'm still an undergraduate though, so I don't have any personal insight on what will help in grad school.

 

[Fredrik]

How is "intermediate" analysis mandatory but "intro" analysis optional? You need to know the basics of linear algebra really well, but I can't tell if the introductory course is enough, because I don't know what it covers. If you intend to work with mathematical physics in the future, you're probably going to have to study real and complex analysis, differential geometry, integration theory, topology, functional analysis and the theory of representations of Lie groups and Lie algebras.

 

[ZeroZero2]

How is "intermediate" analysis mandatory but "intro" analysis optional? You need to know the basics of linear algebra really well, but I can't tell if the introductory course is enough, because I don't know what it covers. If you intend to work with mathematical physics in the future, you're probably going to have to study real and complex analysis, differential geometry, integration theory, topology, functional analysis and the theory of representations of Lie groups and Lie algebras.

Thanks!

The course description for Intermediate Analysis is "Properties of real number system, properties of continuous functions, and sequences of functions" and the only prereq is Calculus 3.

On the other hand, the description for Intro to Real Analysis is "Properties of continuous functions, partial differentiation, line integrals, improper integrals, infinite series, and Stieltjes integrals" and it's prereq is Advanced Multivariable Calculus (and a prerequisite for AMCalculus is Intermediate Analysis...)

The intro Linear Algebra course description is: "Solutions of systems of linear equations, matrices, vector spaces, linear transformations, similarity eigenvalues and eigenvectors."

and Advance Linear Algebra is: "Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors.
Similarity of matrices, diagonalization, Hermitian and positive definite matrices, normal matrices, and canonical forms, with applications."

 

[Klockan3]

How is "intermediate" analysis mandatory but "intro" analysis optional?

It is "intro to real analysis" which is definitely a higher level course than "intermediate analysis". When they just say analysis they basically mean calculus but when they say real analysis they mean something like Rudin.