<p>I just had a quick question regarding the weight of a study of higher math versus performance on competitions for applying for college. I am a junior in high school and I am taking introductory graduate math classes at a local university. Furthermore, this year I was introduced to Math competitions such as the AMC, and found them to be much different from the math that I was familiar with. As a result, I scored poorly on the competitions (I was one away from making AIME. Ugggh.) </p>
<p>My question is this: for admission to colleges such as Harvard, Princeton, Chicago, MIT, and Caltech, what matters more, competitions, or higher math classes? I know that MIT and Caltech have fields in their applications for AMC/AIME scores. How much of a disadvantage am I at for not having good competition scores under my belt?</p>
<p>I can’t speak for the other universities, but there are plenty of people at Caltech who never did math competitions. I don’t know many who took graduate math classes their junior year, so you may have something there :)</p>
<p>I think the general consensus seems to be that math competitions are more important than advanced math courses in college admissions. I think this is somewhat unfortunate although I understand the difficulty admissions officers might have in assessing the difficulty of advanced math courses. This is compounded that advanced math classes are presumably taken at a very large number of colleges and are of vastly varying difficulty depending on where taken. Admissions officers might also be unfamiliar with exactly what advanced fields of math cover. In conclusion, you won’t necessarily be at a disadvantage because of not having done well in math competitions because most students haven’t but your application is unlikely to receive any significant boost because of your mathematical abilities either.</p>
<p>It seems like the obvious solution to this would be to forward the applications or parts of the applications to the math department and let them chose which math majors to admit but that sadly isn’t how things work.</p>
<p>On the other hand, taking graduate level math courses (and presumably a decent number of upper division undergraduate math courses as prerequisites) while in high school will look unusual compared to the more common situation of taking the college sophomore level math courses at a college after completing calculus BC as a high school junior or earlier.</p>
<p>It probably depends a lot on exactly what classes where taken and where. It’s very likely that even graduate math classes at Podunk U are not nearly as hard as some undergraduate math classes at schools like MIT, Caltech, Harvard. It’s also not entirely clear in some cases what is a graduate class and what is an advanced undergraduate class because different universities number their courses in very different ways and in some cases it’s not even apparent from the course number whether the class is undergraduate or graduate. An example is that at University of Minnesota officially 4xxx classes are mainly undergraduate but in some cases will carry graduate classes, 5xxx classes are mainly graduate but also for advanced undergraduates, and 8xxx classes are primarily graduate. Yet in some departments such as math 5xxx classes are actually mainly for undergraduates with some having a number of graduate students and others having virtually none. In other departments such as physics 5xxx classes will be like 90% graduate students with a couple undergraduates similar to 8xxx math classes. MIT mixes undergraduate and graduate classes in their catalog so it’s impossible to tell by looking at the name and number. In any case because I imagine most admissions officers are unfamiliar with advanced math and the policies of every college in the country they won’t really know how rigorous your classes are. In contrast, USAMO means USAMO throughout the country. I think the better solution would be to require syllabuses to be sent in with the application and have someone affiliated with the math department evaluate them because whether something carries the moniker graduate seems less important than what the class actually covered.</p>
<p>The AMC is a way of measuring a student’s aptitude and natural ability in math. </p>
<p>I would say you are at a considerable disadvantage because there are many many more applicants than the number MIT and Caltech each accept that have very high SAT scores and are at or towards the top of their class. Academic competitions are one way of distinguishing those applicants (AMC, USNCO, USABO, etc). If you haven’t done well in such competitions, it is still definitely possible you can get accepted however you better have some other pretty damning credentials to back you up such as very high achievements in other fields, excellent essays/recommendations, and/or a hook.</p>
<p>But taking graduate level math courses can definitely help you out.</p>
<p>It seems unlikely to me that success in math competitions correlates more with success as a math major at elite colleges than success in rigorous college math classes. While doing well in plug-and-chug multivariable calculus classes or joke advanced college math classes [abstract algebra classes that don’t cover Lagrange’s Theorem or real analysis classes that don’t do any topology] isn’t particularly impressive, I would imagine that students who do well in rigorous college math classes while in high school [Rudin or similar for real analysis, Artin or similar for Algebra, Munkres or similar for topology etc] correlates very well with success in math classes even at elite college. Unfortunately, admissions departments don’t seem very interested in distinguishing between non-rigorous and rigorous college math classes.</p>
<p>Additionally, while math competitions may measure “problem solving ability” more if you define problem solving ability as the ability to solve problems through clever solutions without much machinery that isn’t how most college math classes operate. While cleverness is still important when you use lots of machinery it’s much more important to understand the machinery than to be very clever with elementary mathematics.</p>
<p>@noimagination - In specific, I am taking classes such as Topics in Lie Theory, and Representation Theory. </p>
<p>And as far as the rigor of the courses I have taken… we didn’t use Rudin’s text in my Analysis course, but we did use Artin’s text in my Algebra course. Furthermore, for Linear Algebra, we used Hoffman and Kunze. Does that qualify as rigorous?</p>
<p>Also, would success in research competitions such as Siemens make up for my failure in math competitions?</p>
<p>Those classes seem pretty rigorous. However, I doubt most admissions officers have the slightest idea of what Lie Theory or Representation Theory are so I’m not sure how much they will help you in admissions although presumably admissions officers at schools like Caltech and MIT are more likely to know what those things are. Doing well in research competitions will definitely help you as admissions officers are likely to be familiar with those.</p>
<p>The admissions people at the schools you are considering take lots of students who participated in math competitions…and a lot who didn’t. </p>
<p>Not all students go to schools that participate in competition math, or encourage students to participate in competition math…and not all students who have the opportunity to compete enjoy competition math.</p>
<p>The schools you are considering look for interesting students who will be able to handle the curriculum. They expect you to be able to handle the regular freshman curriculum that they offer…they do not necessarily give brownie points to your application just because you are so “advanced”. Obviously being far advanced shows you can handle the math curriculum…but what else will you bring to the campus?</p>
<p>The fact that you have pursued graduate level math classes shows that you are far advanced, too, and that you are mature enough to seek out additional opportunities that are not necessarily offered to you on a platter at your high school.</p>
<p>Participating in math competitions is not a sure golden ticket. Not participating in math competitions is not the kiss of death to your application.</p>
<p>Yes if you are a Siemens regional finalist that is a boost and an even bigger boost of you are a regional winner and most if you are national winner. Same with intel.</p>
<p>Caltech values performance in college classes highly (beyond multivariable calculus and differential eqns.) MIT does somewhat as well. </p>
<p>For Harvard and Princeton, if you are applying as a math major you are unlikely to get in without at least USAMO qualification, and MOSP qualification may in fact be required. </p>
<p>Doing real research in math will help, especially with MIT and Caltech but maybe even for Harvard and Princeton. Usually the people who can do math research in high school also make MOSP, so it’s hard for me to tell how valuable math research would be alone. </p>
<p>I feel you will be competitive at U. of Chicago with what you have because it is somewhat less selective than your other schools and because they are looking for intellectuals first.</p>
<p>I am doing pretty well in those courses, thanks for asking. The course on Lie Theory isn’t as in depth as I would have liked though (not to sound arrogant or anything). We have mainly focused on Lie Algebras as opposed to Lie Groups themselves. But then again, I don’t really have the necessary background in differential geometry to really study Lie Groups in depth…</p>
<p>You can definitely get into Harvard or Princeton as a math major without USAMO qualification and you certainly don’t need MOSP. I’m also pretty sure that most people who do math research in high school don’t make MOSP either.</p>
<p>I do agree though that MIT values these kind of classes of math classes more highly than Harvard those. Although this is only anecdotal it is suggestive of larger trends, I know seven people (including myself) in the high school classes of 2011 and 2012 who will completed at least one 5xxx math class at the University of Minnesota by the time they finished high school. One only applied to the University of Minnesota and another had a low gpa. The other five got into MIT. Only two of those five got into Harvard.</p>
<p>I forgot another person who got into MIT but not Harvard. Of the six who got into MIT (also I’m grouping waitlists with rejections)
4x USAMO + Red MOP ==> Harvard
4x USAMO ==> rejected at Harvard
(me) 4x AIME + USAMO senior year so after college decisions ==> rejected at Harvard
2x AIME ==> rejected at Harvard
I’m not 100% sure about the other two but the one that got into Harvard made AIME once or twice and the other one who didn’t get into Harvard made AIME a couple of times.</p>