Schools College Admissions and Math: What Are Schools Looking For?

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When applying to competitive schools like Harvey Mudd and Caltech, demonstrating strong math skills is crucial. Admissions committees typically look for achievements such as participation in math competitions, with specific emphasis on scores from events like the AMC and AIME. Advanced coursework, particularly in calculus (Calc III and beyond), is also favorable. While research experience is uncommon for high school students, involvement in summer math camps can enhance an application. For those seeking excellent math programs that are less competitive than top-tier institutions, schools such as the University of Chicago and University of California, Santa Barbara are noted options. Overall, standing out in math requires a combination of competition participation, advanced coursework, and relevant extracurricular activities.
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If you say math is your strongest area on your college application, what kind of math achievement do they generally look for (schools like Harvey Mudd and Caltech), besides competition math (and given you want to have a "good" chance, however ambiguous that is)? Summer camps? Research? Advanced math (how advanced)? On that note, what are some excellent schools for pure math that are relatively much less competitive (compared to Caltech, Harvard, and the others in that acceptance range)? I know of Harvey Mudd. Others?

Thanks.
 
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College's typically look for anything that makes you stand out, not just in math but in any subject. Math competitions looks good (in fact I think some schools actually ask for AMC/AIME scores on their appliaction), advanced math does (I'd say Calc III and higher). I doubt you'd have any research from high school.
 
Thank you! Anyone else?
 
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I have a specialization in condensed matter physics and materials physics, and off-late, I have been seeing a lot of research directions moving towards quantum computing (AMO and non-linear optics) and the huge chunk of quantum materials research (and funding) is dedicated towards QIS and QC research. I am wondering (sort of in a dilemma), if I should consider switching my field? I am currently at the stage of a postdoc.

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