Courses Can Graduate Students Enroll in Courses Outside Their PhD Subject?

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Graduate students often have the opportunity to enroll in courses outside their primary field of study, such as a math PhD student taking physics graduate courses. However, enrollment policies vary by department and may require students to consult with their advisors. Prerequisites for courses, like a formal undergraduate background in quantum mechanics, can be a barrier. Students who have self-studied may still face challenges in enrolling without meeting formal prerequisites. Options may include seeking permission from the instructor or auditing the course if enrollment is not possible. Ultimately, decisions are typically at the discretion of the department and the student's advisor.
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In graduate school, is it possible to enroll in courses even though one is not doing their phd in that subject ? So can a math phd student take physics graduate courses ? Also, does the math phd student have to formally satisfy the prerequisites for that physics course. Let's say he/she wants to take a course on graduate quantum mechanics, but that student has never formally taken an undergraduate quantum mechanics but has self-studied it extensively. Would there be any way for that student to get enrolled in that course or will they have to audit it ?
 
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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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