Undergraduate Research in Mathematics

AI Thread Summary
Graduate school aspirations in Math or Physics can be supported by undergraduate research experiences, including Research Experiences for Undergraduates (REUs) in mathematics. REUs are accessible, but the level of mathematical coursework completed can influence eligibility and the variety of research topics available. Engaging in research on topics like continued fractions requires less background, while more complex areas such as linear algebra, modern algebra, or number theory typically necessitate completion of sophomore or junior-level courses for a deeper understanding. Overall, advancing through math classes enhances research opportunities and topic selection.
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I plan on one day going to graduate school for Math or Physics, depending on what graduate programs I get into and where my interest finally ends up falling. I am already doing some undergraduate research in physics and I began to wonder about if REU's in math were common and if so, what level do you typically have to be at in order to get involved in them?
 
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Sure they are. The question I would have for you is, how many math classes have you had so far? You could honestly do research in anything math-related, but obviously the higher up you are, the more options you will have as far as choosing an interesting topic. I just looked online and found someone that did a project on continued fractions:

http://archives.math.utk.edu/articles/atuyl/confrac/

As far as I know, you really don't need that much background to do this and it seems like an interesting topic. However, if you want to do something on linear algebra, modern algebra, number theory, etc.. you might want to get some sophomore/junior classes knocked out and you'll have a better understanding of what to do.
 
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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