<p>So I really enjoy Calculus, and I'm somewhat good at it, and I want to use it to my advantage, like maybe doing some research or getting an internship to help my chances with colleges. I'm not really sure where to start. Any advice? What exactly do colleges look for?</p>
<p>Hmm… I am not sure a high school student is going to easily get into math research with just calculus behind you. And there aren’t really math internships. People who are good at math are often good at computer stuff, so that is an option (learn some languages, see if you can get some kind of programming part time job or something). Doing more STEM type activities can be good for college applications – does your high school have a FIRST robotics team you can join? Or start one… it was new at my high school last year.</p>
<p>I think colleges are generally looking for a consistent and deep interest in a given type of activity (eg, join math league or math club, or become a math tutor if math is really your thing). It sort of depends on what type of college you want to go to… The tippy top ones (Ivies, Stanford, MIT, etc.) are looking for people who have done something impressive well beyond their school community, in addition to great grades and test scores. But if your sights are a little lower, then the stuff I have suggested here will be good.</p>
<p>Another option is to take some more advanced math classes at your community college and do well. That isn’t research or an internship, but gets you closer to being ready for research because you need more math than Calc to do math research.</p>
<p>One other thing I can think of is that there are some math problems that haven’t been cracked that people have been working on for years. Maybe take a run at a couple of those, more for fun and learning than anything else. You probably won’t solve them, but I could see how a good college essay might come out of the experience of giving it a try. I am sure you could find some by searching the web. I remember a boyfriend of mine who was a math major in college would work on these (he was into game theory) for fun, and sometimes we would do it together. Even though I wasn’t a math major, I could understand most of what he was doing.</p>
<p>In addition to intparents’ good suggestions, consider tutoring kids in math who don’t have your aptitude. Assist one of your teachers with their match class.</p>