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&gt;&lt;br>
<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>PROMYS is an offshoot of Ross, and the two programs are extremely similar. I took AP Calc BC in tenth grade and was accepted to PROMYS, but there were also students who had just finished ore calculus. Admissions is based primarily on the admissions exam, which is difficult, but it’s totally worth it. You will learn a ton about number theory. Both camps focus on a series of daily psets, and some of them take 12+ hours to complete. I’ll never forget the time I fell asleep in BU’s elevator the day after an extra-challenging pset.</p>

<p>If you get accepted, spend a couple of days looking at proofs and spend the rest of your summer away from number theory. The psets are designed to guide you, rather than supplement learning, and you’ll start with extreme basics.</p>

<p>Sample proof, first week at PROMYS:</p>

<p>Proposition: 0*x = 0 for all x in Z.</p>

<p>Proof: 0<em>x = (0+0)</em>x by the additive identity.
0<em>x=0</em>x+0<em>x by the distributive property.
0</em>x±0<em>x = (0</em>x+0<em>x)±0</em>x
0<em>x±0</em>x = 0<em>x + (0</em>x±0<em>x) by associative
0 = 0</em>x + 0 by additive inverse
0 = 0<em>x by additive identity
0</em>x = 0 by symmetry
Q.E.D.</p>

<p>Yeah, it’s extremely rigorous, and it gets into quadratic reciprocity in the last three weeks. Don’t go unless you are prepared to suffer, but it is 100% worth it.</p>

<p>@DiscipulusBonus Were there ever kids at PROMYS that just finished their senior year? I didn’t apply because I was just in Algebra 2/Trig as a Junior (I didn’t like Math freshman year which took me out of the honors track, but Physics made me really love Math) and wanted to take a Summer course at my school to get into AP Calculus AB for Senior year, but should I have applied? Even though I may not be in the most advanced math class, I tend to enjoy creatively solving number theory and geometry problems. If I ended up going to PROMYS and no taking my summer Math class, I would be in regular calculus.</p>

<p>@Cosomological: Yes, there were a few. Personally, I think PROMYS is a more valuable experience than AP Calculus. In six weeks, I learned more than I did in two years of calculus and linear algebra. If you want to do something math-related after your senior year, I’d definitely recommend applying to PROMYS. (That said, I’m not sure if they regularly accept incoming college freshman or if the students I met were exceptions, so you might want to check their website and/or contact them about that.)</p>

<p>FYI, PROMYS does not require high-level math. You’ll learn a little bit, but their motto is “to think deeply of simple things,” and it really rings true in the psets.</p>

<p>@DiscipulusBonus Yeah, I think what I’m going to do is probably get a job somewhere like Barnes and Noble to save up for PROMYS. My Math class in Precalculus was $600, and PROMYS is $3,300 but I doubt that we would qualify for financial aid. I really hope I can attend at some point, even though it won’t count for college apps. Also, out of all of the schools on my list, I will probably not end up at any of my reach schools and instead Boston University. Maybe the fact that I’ll probably be going there might make it easier to deal with PROMYS schedule-wise.</p>

<p>I know of [HCSSiM[/url</a>] and [url=<a href=“https://math.stanford.edu/sumac/]SUMaC[/url”>https://math.stanford.edu/sumac/]SUMaC[/url</a>]. There’s also [url=<a href=“404 - Page Not Found”>http://www.uwyo.edu/epscor/fellowships-and-student-programs/srap/index.html]SRAP[/url</a>] and [url=<a href=“http://www.depts.ttu.edu/honors/clark_scholars/home.htm]Clark”>http://www.depts.ttu.edu/honors/clark_scholars/home.htm]Clark</a> Scholars](<a href=“http://www.hcssim.org/]HCSSiM[/url”>http://www.hcssim.org/), which are free research programs where you can specialize in math. I’m not sure you’d be eligible for all of these right now, but for future reference.

Just so you know, this is like considering being the president. Have a backup plan.
As far as colleges to apply to, I’d recommend looking into the University of Michigan as a match or a low reach, because it’s not as insanely difficult to get into as other places and they have a really good math program.

We did something like this in Abstract Algebra, except for rings in general. You could watch abstract algebra, number theory, or “intro to proofs” type videos on YouTube. </p>

<p>Check out Canada/USA MathCamp. Great program, with lots of emphasis on higher level math. It’s five weeks long and has great financial aid (non-profit program). </p>