Prerequisites for Tensor Analysis

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To prepare for studying General Relativity as a Physics major, it is essential to have a solid understanding of tensors, which requires specific math courses. Differential geometry is highlighted as a crucial prerequisite, as it provides the necessary foundation for understanding the geometric concepts in General Relativity. Additionally, Group Theory may also be beneficial, though its necessity is debated. Resources like Penrose's "Road to Reality" are recommended for self-study on tensors and manifolds. Consulting with an academic advisor for tailored course recommendations is also advised.
Judas503
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Hey there,

I am a Physics major and currently in my freshmen year. I would love to study General Relativity in the senior year of college. One of the requirements of General Relativity is the knowledge of tensors. But, which math courses should I take? I read in some blogs that Group Theory is necessary. Any answer would be helpful.

Thank you.
 
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Any class that teaches differential geometry I think. Ask your advisor.
 
Yeah, differential geometry is a very useful prerequisite. Penrose's Road to Reality has some stuff on tensors and manifolds and it's available at a relatively cheap price ($0 if you know how to use Google).
 
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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