Math Summer Programs

<p>I know this is way early, but I was looking into some math summer programs for next summer. I just came back from a science one this year and realized that science wasn't my thing. Math was. I searched some up and found out that many of the people who go to these programs compete in many math competitions. I have done several in middle school and usually placed in the top 10. I will be a sophomore next year and will be starting competitions.
Math classes: I took AS level math this year (I'm pretty sure I got a perfect score on the Cambridge exam), and I finished the class with 100+ averages all 4 quarters. Next year, I will be taking AP Calc BC.</p>

<p>Anyway, onto the summer programs. I found these so far with these explanations as the way most people view it:
RSI (MIT): very selective, 75 selected out of 3,000 applicants (data from one of the years) <a href="https://math.mit.edu/news/summer/rsi.html"&gt;https://math.mit.edu/news/summer/rsi.html&lt;/a&gt;&lt;/p>

<p>HSMC (Texas State): more laid back, not as competitive, easy to get in <a href="http://www.txstate.edu/mathworks/camps/hsmc.html"&gt;http://www.txstate.edu/mathworks/camps/hsmc.html&lt;/a>
<a href="http://talk.collegeconfidential.com/summer-programs/835472-my-experience-with-the-texas-state-honors-summer-math-camp-p1.html"&gt;http://talk.collegeconfidential.com/summer-programs/835472-my-experience-with-the-texas-state-honors-summer-math-camp-p1.html&lt;/a&gt;&lt;/p>

<p>PROMYS (Boston University): rolling decisions (sooner you apply, the more likely you'll get in), around 10% acceptance</p>

<p>ROSS (Ohio State): VERY competitive, very difficult to get in, brutal
<a href="http://talk.collegeconfidential.com/summer-programs/867050-why-you-should-consider-the-ross-mathematics-a-letter-program.html#latest"&gt;http://talk.collegeconfidential.com/summer-programs/867050-why-you-should-consider-the-ross-mathematics-a-letter-program.html#latest&lt;/a&gt;&lt;/p>

<p>So...
What are some other things to note about these programs?
What are some other good programs?
Realistically speaking, which one would I be able to get in (given my lack of experience with math competitions but also my math classes)?
What factors do they look at during admission processes?
What should I do to increase my likelihood of getting into the programs and actually surviving?
Which programs look good/not as good for college?
What are some competitions I should sign up/apply for?
Whenever I'm bored, I like to watch math videos (Numberphile, ViHart, etc.) on YouTube, but are there any channels that will aid my thinking for higher level math concepts that I may learn in these programs?</p>

<p>I really enjoy math, and despite the fact that I fall asleep doing homework all the time, I never fall asleep during math homework, no matter how tired I am or how late it is. I am certainly considering a career in this field (considering math professor), and I would like to prepare myself as much as I can.</p>

<p>SUMaC is another math camp that is worth considering. It carries high prestige and some say it can get you into Stanford. Admission is primarily based on an exam that tests abstract math capabilities.</p>