Mathematical Physics as a graduate program

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Atypical preparation for admission to a mathematical physics program often includes a strong foundation in rigorous mathematics, such as Real Analysis and Topology. While some programs may teach these subjects from the ground up, many expect students to have a solid understanding of basic mathematics, including analysis and algebra. Independent studies in advanced topics like differential geometry and special functions may also be required. A double major in mathematics can be beneficial, but the necessity varies by institution. Resources like "All the Mathematics You Missed But Need To Know For Graduate School" can help bridge knowledge gaps for incoming graduate students, covering essential topics and providing guidance for further study.
Convuler
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Hi guys,

I was wondering whether atypical preparation is needed for admission to a mathematical physics program? i.e. Do you need to take Real Analysis, Topology, and other "rigorous" mathematics even if you are only a physics undergrad, or will such mathematics be taught from the ground up in graduate school.

Thanks!
 
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There was a professor doing mathematical physics at my undergraduate uni. and he would make you take independent studies on topology, diff geometry, special functions, etc, during the summer terms, but you were expected to know the basics, i.e, analysis, algebra, etc. I guess the best you can do is double major in mathematics? But I guess that also depends on where you are applying to.

http://www.phys.vt.edu/~ersharpe/advising.html

I think you can send him an e-mail and he'll be more than happy to answer.
 
Garrity's All the Mathematics You Missed But Need To Know For Graduate School might be useful.

Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge. But few have such a background. This book, first published in 2002, will help students to see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential geometry, real analysis, point-set topology, probability, complex analysis, abstract algebra, and more. An annotated bibliography then offers a guide to further reading and to more rigorous foundations. This book will be an essential resource for advanced undergraduate and beginning graduate students in mathematics, the physical sciences, engineering, computer science, statistics, and economics who need to quickly learn some serious mathematics.
 
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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