Schools Math Programs Summer Before College

AI Thread Summary
Prospective math majors seeking summer programs before college can find both cheap and free options for research and learning. While Research Experiences for Undergraduates (REUs) are competitive, they are not entirely out of reach for high school seniors, especially at smaller universities. Many participants in the discussion express interest in applying to various REUs despite their limited formal credentials, as they have independently studied advanced topics such as abstract algebra, linear algebra, real analysis, multivariable analysis, and complex analysis. Engaging with professors who run these programs can provide valuable insights and increase chances of acceptance. Overall, the emphasis is on the importance of proactive applications and leveraging self-taught knowledge in the pursuit of summer math opportunities.
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I'm a prospective math major going to college next fall. Are there any cheap or free math programs available for a graduating high school senior during the summer? Research sounds exciting but I'd be fine with just learning material.

By the end of the year I'll have learned basic abstract algebra (dummit and foote), linear algebra (axler and halmos), basic real analysis (baby rudin), multivariable analysis (baby spivak), and basic complex analysis. I don't have much in the way of formal credentials since I picked up most of that stuff from reading. I'm guessing that REUs are out of reach.

Thanks in advance for any suggestions!
 
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From talking to professors who are running them, REU's aren't out of reach for high school seniors, but it is competitive. I'm in a very similar same position, and I'm applying to lots of REU's to get a possible chance at a smaller university.
 

Thread 'Self Learning Math/Physics'

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"...
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Thread 'What should I do if I found a paper with same result as mine?'

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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