REU vs. Research at my school & taking classes

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The discussion centers on the decision between pursuing a Research Experience for Undergraduates (REU) or staying at the current institution to conduct research and potentially complete a double major in physics and math. The individual enjoys their current research in plasma physics but is uncertain if it aligns with their long-term goals. They face a choice: an REU may offer diverse experiences, while staying could lead to a double major, enhancing their academic credentials. However, the math classes that would be most beneficial for their physics career are electives that do not contribute significantly to a math major. The consensus suggests that research experience is more valuable for graduate school applications than additional math credentials, emphasizing the importance of sustained research projects that could lead to publications or conference presentations. Additionally, self-learning math or auditing classes is proposed as a viable alternative to formal coursework. Overall, the emphasis is on prioritizing research experience to strengthen graduate school applications.
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Currently I am doing research with a professor in plasma physics, which I am enjoying, though it isn't what I would like to do in the long run. This summer I am going abroad, but next summer it looks like I will have the choice between applying for an REU (which, of course, I may not get anyway) or staying here, doing research, and taking classes. If I stay here over the summer and take classes, there is a chance that I may be able to complete a double major in physics and math (in addition to my other degree in philosophy), but if I don't stay, I will walk away with a two degrees, one in philosophy and one in physics with a minor in math. So, my question is, for grad school, which looks better and would be more beneficial to me - an REU, or summer research with the potential for getting a double major in physics and math? I feel like at an REU there is at least the potential for doing something different from what I am currently that may interest me more. The other issue to take into consideration is that the math classes I feel would be most beneficial for me as a physicist are math electives, and so do not contribute much to that degree. It seems like if I were to major in math, I would have to cut back on some of the classes I want to take (Elementary Partial Diff Eq or Vector Calculus or Compex Variables) for some classes I don't really want to take (Intro. to Advanced Math or Prob & Stats). So maybe the minor would actually be more advantageous? Although, if I stayed over the summer, even if I didn't go for the major in math, it would give me a chance to take a class like Numerical Analysis, which might be helpful... I'm rambling now, so I'll just stop here. Thanks in advance for your assistance.
 
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In my opinion I think Research would look much better on a application. After all research is a big part of graduate school, not so much undergraduate mathematics.
 
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Anyway, I think you should consider that the research you do with the plasma's professor will be somewhat sustained, and you may get more out of a project that you've worked on for longer (say a poster, or even a paper). You're the best judge of that. Also, not sure if you can do this, but if you can work with him through the year (while you're not abroad of course) then that would certainly produce good enough work to get you at a conference at the very least.

Also, why do you want a math degree? You could easily learn it on your own, or if you feel that you do need classes you could simply sit in on them as necessary (without having to jump through the requirements hoops, or worry about grades). Certainly certainly certainly research experience is seen as much more indicative of your potential to complete a Ph.D, and is therefore more beneficial to your graduate application.
 
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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