REU program for math+physics freshmen

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The discussion centers on a first-year student at the University of Kansas seeking advice on their qualifications for Research Experiences for Undergraduates (REU) programs in math and physics. The student outlines their coursework, which includes substantial classes in real analysis, abstract algebra, and various physics subjects, alongside some research experience in optics and participation in a summer science program at MIT. They express uncertainty about whether to switch from complex analysis to additional courses in abstract algebra or real analysis, seeking guidance on how to enhance their competitiveness for REU applications. The conversation emphasizes the importance of both coursework and research experience in strengthening applications, with suggestions likely focusing on the value of advanced math courses and gaining more substantial research involvement.
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Hey everyone, I am a 1st year student with junior year standing in math and physics at univ. of Kansas and I just wanted to see if I have enough qualifications to have good chances at REU progrmas in math/physics for next summer.

In math, by the end of this year, Ill have had 2 semesters of real analysis, 1 of complex analysis, 2 semesters of abstract algebra, 1 semester in probability theory, and 1 in statistical theory. Also, I have no prior research experience in math.
A few notes on math: I have the option to switch out complex analysis for a 3rd semester in abstract algebra on commutative rings, or I could switch out complex analysis for a 3rd semester in real analysis on measure theory.

In physics, by the end of this year, I'll have had 2 semesters of advanced mechanics, no semesters of advanced E&M, 1 semester in QM, 1 in mathemtical physics(basically applied math), and 1 in particle physics. As for research, a year ago I was involved in optics research that got published in physical review B(but I made minimal contributions, so I am like a 50th author), I was participant in MIT's summer science Program during high school, and next semester I am getting inovolved in research on dark matter, but Idk if I'll make significant progress within one semester.

Do you think I have enough background to be a competitive applicant for the REU programs? If not, what is it that I'm missing? Should I stay with my current arrangement in math courses or do you think one of the other arrangements will make me a better candidate for REU programs?

Thanks for your opinions:)
 
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Also, Idk if this really matters, but in physics ill also have had a laboratory in modern physics and an advanced laboratory in digital/analog circuit design.
 
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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