Guidance in Mathematical Physics

[Kindayr]

Hey all, in need of some advice.

I'm currently at UWO going into second year. I'm enrolled in an Astrophysics and Pure Mathematics program, and need to choose which courses I need to take, specifically math courses, for my future.

I have a 4.0 and am strong in math. I'm wondering which math's and which topics in math will help me later on. Like which topics are best for someone aiming for graduate studies in mathematical/theoretical physics?

I emailed a renowned theoretical physicist (to remain unnamed) and he told me to basically focus on Fourier analysis, differential equations, integration methods, functions in the complex plane, special functions and their properties, etc.

Should I just focus on those?
The senior courses right now I'm looking at are:
Ordinary Differential Equations
Real Analysis
Intermediate Linear Algebra
Discrete Structures
Abstract Algebra
Group Theory
Metric Space Topology
Complex Analysis
General Topology
Field Theory
Lebesgue Integrals and Fourier Series
Rings and Modules
Algebraic Topology
Algebraic Geometry
4th-year Multivariable Calculus

A lot of these are intertwined. Which ones should I focus on, which should I drop, what courses would be wise to add? In my physics, I'm taking the obvious EM, Quantum, Classical Mechanics, Classical Field Theory, General Relativity etc.

I enjoy math very much and just need some guidance on my future academics. I have limited space to fit in 4 years (I may consider a 5th year, as the master's program I'm looking at is a 1 year intensive program). I want the best amount of tools I can get. Should I take a fifth year?

 

[R.Mesri]

Any advice would be appreciated!It sounds like you have a good understanding of the math courses you should be focusing on for your future in mathematical/theoretical physics. Since it seems you already have a basic understanding of the topics recommended to you by the theoretical physicist, I would suggest taking all the courses you listed that are related to those topics. Taking a fifth year is always an option if you feel like you need more coursework in the areas you want to specialize in, but I would recommend trying to take as much as you can during your first four years so you can get a head start in graduate studies.