<p>I am interested in math, but I'm not sure how to express it. My counselor knows I'm interested, and I take very rigorous math courses (will finish them all by senior year). I also became an AIME qualifier. I've also joined the math club and did much to the club (too lazy to explain what at the moment). </p>
<p>Would these show my interest? </p>
<p>I told these to my friend, and he says its all rubbish. I said that you need at least 7 awards that have the word "national" are that are very presitgeous if I want to get into Stanford (eg: Presidential Award, Siemens AP award, etc).</p>
<p>Is what he said true? I don't have any such prestigeous award (I do have AP scholar and national merit). Will that really hurt me? Thanks.</p>
<p>If you're a junior, I highly recommend Stanford Math Camp. You get to learn cool math and it shows a passion for math. </p>
<p>I think taking advanced classes (especially anything beyond calculus, ideally more than a year beyond calculus) shows interest. The essays and recommendations are both great opportunities to express your interest in math. The favorite activity question or intellectual interests question would both be places where it would make sense to talk about your passion for math. </p>
<p>You don't need prestigious awards to get in to Stanford. I didn't have any, and I'll be a junior there in the fall.</p>
<p>You absolutely, positively do not need a national award (or even a regional award) to get in. I had a few awards, all of which were gained being a part of different clubs (they are not prestigious, but showed some effort).</p>
<p>I think you are thinking exactly what Stanford is thinking (parse that beauty of a sentence very carefully :) ) Stanford really takes into account leadership at your school. Tutor math students who don't understand some of the math concepts. Get a good recommendation from a math teacher. Go a year beyond calculus (like Linear Algebra for instance). And keep involved. Stanford is one of the few top schools who don't look exclusively for super-applicants, but people who have a passion and can benefit form Stanford's program.</p>
<p>The way I see it, you shouldn't have to find ways of expressing your different interests, ways of expressing your different interests should find you. If you're really, truly interested in math, do some programs over the summer. Someone above mentioned Stanford Math Camp, but there are plenty of others nationwide that would probably be similar in scope.</p>
<p>One word of caution, though, would be to be careful about how you express your interests on your application. Saying your very interested in math is like saying your very interested in science, or english. They're all very big subjects, so big that no one would are try to specialize in them without narrowing down their field a bit. I think admissions officers somewhat take kids with a grain of salt who say that they are merely interested in history, or science, because saying your interested in something so big really shows that you haven't spent all that much time dealing with it because you haven't narrowed it down at all. I remember when I was applying to schools I though about writing about how much I loved political science at the time. Thankfully someone dissuaded me from doing that, because now that I've been in college I've realized that by saying something like that all I would have shown is that I knew nothing at all about political science.</p>
<p>So, what all that means for you I would say is that you should look for ways in which you can specialize your interest in math. Take programs that expose you to specific fields/types of math, so that you can say your interest is not only broad, but focused in some areas as well.</p>
<p>A great way to find a focus area for your math would be to try and find a job or volunteering opportunity this summer with a group that uses practical applications of relatively advanced mathematical concepts. I don't think there are places like this on just every street corner, and I don't think they'll be actively searching out high school students, but I'd bet you that if you seek some place like this out, express your interest and desire and show some pre-existing knowledge in their field along with a willingless to learn more, that they'd be glad to at least look into hiring you. A good place to start looking for a group that would match this description might be to go onto the Math Department's website and see what, if any, corporate affiliations they have. You could also do this same thing with any local universities in your area. Or you could see if a prof. would be willing to work with you directly, maybe not at Stanford, but at a local college you might be able to find a spot.</p>
<p>Docketgold makes a good point: specificity is a great asset. When I wanted to describe my love of Political Science, I discussed the war in the Congo and the resulting conflagration in the surrounding countries. I then made connections between that and some of my own work, and why I want to learn more about IR, etc.</p>
<p>Far too often, looking at the up-and-coming class essays that I have read, people make huge generalizations that are rather parochial. This is what was described above and is something that you should be aware of.</p>
<p>As for finding your interests, I think it is much more powerful to do something individual and unique than another summer program. Find a professor that is doing something interesting at a local university. Learn a whole new subject. Do some investigative work in an area of math that sounds interesting. All of this shows that you have a passion - whereas submitting an application to a summer program is a little bit easier.</p>
<p>That's not to say summer programs are bad. But don't use them as resume filler because you don't know what you want. The admissions counselors will see right through that.</p>
<p>The problem is that you can't really do much in math research until towards the end of your undergraduate experience usually. Most high school students don't have the opportunity to really explore different branches of math. Summer programs might allow you to get a taste of one or two different areas of math and learn a bit about them. </p>
<p>Those activities you listed should all show interest.</p>
<p>I'll be the first to admit that college admissions place high school students in a pretty nasty catch-22 with things like research because on the one hand they want to see that you've done significant research and projects by the time you've applied, but on the other hand the vast majority of people are applying in the first place to a school like Stanford because of the research opportunities it provides.</p>
<p>But I definitely think you should go about engaging your budding interests in ways that will be meaningful both to you and and any potential readers of your college application. Although a "math program" might look boring and cliched, I would estimate that it carries more weight than someone trying to describe their "personal exploration of mathematics", barring someone doing something truly extraordinary.</p>
<p>If you do decide to look for summer programs, don't just limit yourself to ones that are math only or highly centered around math. Don't be afraid to do ones that might only have one course offering in math, but also has a large selection of courses in a wide variety of subjects - you never know what you'll stumble on to.</p>
<p>You could take further classes through EPGY online in the upcoming years. I highly recommend Stanford Math Camp. There are only two classes: Number Theory and Topology. The program is great. It has about 40 students, and you all become pretty close by the end of the four weeks. Both topics are very interesting, and you get a chance to do a research project on one of the two topics and present it at the end of the week. It seems that a strong recommendation from your prof at SUMaC makes a pretty big difference in admissions. About 25% of the students in my program are now students at Stanford. Several chose to go to Harvard, MIT, Brown, Princeton, or Yale instead. (I'm not sure how many are at one of those schools, but I'm sure it's at least another 30% of the students) It's great if you find a particular branch of math that you love, but I don't think admissions officers expect you to have a strong enough math background that you'd really know enough to pick your favorite branch. My friends who are math geniuses wrote about their experience on math team if I remember correctly.</p>
<p>"The problem is that you can't really do much in math research until towards the end of your undergraduate experience usually."</p>
<p>Depending on your specific interests, this can be very inaccurate.</p>
<p>In any event, if you really love mathematics for its own sake, consider looking at the Hampshire College Summer Studies in Mathematics (HCSSiM).</p>