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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 im like a 50th author), I was participant in MIT's summer science Program during high school, and next semester Im 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:)