Programs Is it possible to take grad math courses in a PhD physics program?

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Australian students considering graduate studies in the U.S. can take advanced mathematics courses such as algebraic topology, complex analysis, and functional analysis, among others. Once the standard coursework for a PhD program is completed, students generally have the flexibility to enroll in additional courses, subject to qualifications, approval from their supervisory committee, and scheduling availability. While it is common for students to take courses outside their primary department, obtaining permission may be necessary. However, enrolling in a large number of courses, as suggested, could be challenging unless the student is financing their education independently.
Pendulum Swing
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Program?

I am an Australian student, may think about studying in America (saw video of Andrew Dottson mentioning it), in the future. Is it possible to take grad maths courses, e.g. algebraic topology/geometry, complex analysis, representation-theory/lie-groups, PDEs, Measure Theory, Functional Analysis, algebra courses, more geometry/topology courses, ..., etc

Thanks,

Pendulum Swing
 
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Pendulum Swing said:
Program?

I am an Australian student, may think about studying in America (saw video of Andrew Dottson mentioning it), in the future. Is it possible to take grad maths courses, e.g. algebraic topology/geometry, complex analysis, representation-theory/lie-groups, PDEs, Measure Theory, Functional Analysis, algebra courses, more geometry/topology courses, ..., etc

Thanks,

Pendulum Swing
That WOULD BE the point.
 
I did just that. Then I switched to applied math.
 
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Once you meet the standard coursework requirements of your PhD program, you more-or-less have the freedom to take any additional courses you want, provided (i) you're qualified to take them, (ii) your supervisor/supervisory committee is okay with it, and (iii) you have time to fit them in. For courses outside your department you will likely have to get permission to take them, but in my experience it's rare for interested and well-motivated students to be denied.
 
When I was a grad student in physics about 40 years ago at the U of Michigan, we were required to take at least two "cognate courses" outside the physics department. Most of us (including me) chose math courses. In my case they were complex analysis and intermediate differential equations.
 
Usually a class or two is not a problem, although it depends on the department's policies (which usually depend on who and how tuition in these classes is paid for). But your list contains at least eleven classes. That is going to be a harder sell, unless you are paying for everything out of pocket.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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