Schools Math Programs Summer Before College

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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.
 

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