<p>Right. The thing, though, which I may not have made clear is the following – </p>
<p>Will one significantly sway your chances enough that you shouldn’t just pick whichever one you’d rather do? I was under the impression that given both are good options, and given MIT has its pick of people with the highest level of math competition awards, it almost doesn’t matter which one you do (i.e. same chance of getting rejected) as long as you’re pursuing out of sincere interest?</p>
<p>I did not say that studying higher math classes is not a good option. The issue is students want to study more to challenge themselves and to satisfy curiosity and interest, and for the benefits of studying it, not to please college admission office. If studying higher math classes by course title or course number but the classes are not challenging then it does not serve any good.</p>
<p>Fair enough. All I really wanted to clarify was that if one route is more interesting, it probably is better to take it, even if the other is somewhat more challenging and immediately impressive on paper, because neither seems likely to really sway the final decision for admission.</p>
<p>You’re certainly correct that classes that pose no intellectual challenge are probably not the best way to spend time.</p>
<p>MIT classifies differently students who take part in high level math/science competitions and those who take advanced courses. A high AIME scorer or USAMO qualifier, Intel Finalist, etc. is classified as an academic star, with significantly higher chances of admission that somebody who takes advanced math classes, who would not automatically be considered an academic star. Academic stars are still rejected but at a much lower rate and constitute about a third of the admitted class. This still means two thirds are not academic stars but have other factors in their favor. Transcripts in general, just like test scores will only bring you so much. At some point, the marginal advantage of a small increase in test scores, or strength of curriculum becomes irrelevant. In the end, MIT cares much more about what you may accomplish while at MIT and beyond that what you did in the past.</p>
<p>It doesn’t make sense to me why making USAMO would make someone an academic star but doing well in very advanced [rigorous third or fourth year college classes or even graduate level ones] wouldn’t.</p>
<p>The math for each one is quite different, but perhaps people don’t view them as equally challenging? </p>
<p>Most of my son’s friends at the local math circle have not gone as deeply into college level math as he has (dif. equations, upper division dif equ., dynamical systems, real analysis); yet, he does not spend time studying math competition math (combinatorics, number theory, stats and probability, etc) and consequently some of them have been to USAMO whereas my son has only gotten AIME 3X. He’s capable of being at their level (given the fact that in 7th grade, he was one of the top 8 students in Mathcounts in our large city along with some of these kids who have been USAMO participants), but he’s chosen a different route in math. We didn’t know about AMCs back then. He dropped out of math competitions for several years and only picked them up again in 10th.</p>
<p>Math competition math is wonderful because it’s a way for exceptionally gifted (or exceptionally disciplined and hard working) students to stay in high school with their peers while being challenged in math. </p>
<p>Math competitions aren’t for every kid, though. Not every kid is competitive like that. One of the most math gifted kids I know never did competitions but researched a particular math topic in a new way while still in middle school.</p>
<p>What has been discussed here are basic intro level college math classes for non-majors, such as multi-variable calculus, differential equations, linear algebra, essentially pretty basic stuff. Even calculus with proofs is considered basic as it is taught in many high school across the world. USAMO qualification is much more rare and IMO selection even more so. </p>
<p>A student doing advanced mathematical research on topological field theory under supervision of a well-known professor (I have interviewed such students) would clearly be considered an academic superstar. We are talking about a world of difference.</p>
<p>I think there’s a middle ground between low-level linear algebra, differential equations, or multivariable calc at a local university and doing topological field theory research under a well-known professor. </p>
<p>I curious how taking upper division [real analysis, abstract algebra, etc.] math classes at a respected but not elite university compares to say USAMO qualification. There are a number of people I know like sbjdorlo’s kid who don’t focus on math competitions but take quite advanced math classes. At least in my opinion, taking the upper division math classes seems like a better use of time than learning whatever exotic inequalities and esoteric Euclidean geometry theorems that help on the AIME and USAMO.</p>
<p>
</p>
<p>It probably depends on the college. For HYP, they care about the contests a lot more. For Caltech, doing well in abstract algebra will really help your application. For MIT, I’m really not sure, might be a toss-up.</p>
<p>
</p>
<p>AFAIK, that would still not qualify for academic superstar status. There are such stellar math applicants that such level of math achievement is simply not that impressive. Not to say you have to be an academic superstar to get admitted. The majority are not. </p>
<p>MIT is actually very big on math contests as it increasingy wipes the field at the Putnam and it aggressively recruits IMO medalists.</p>
<p>There’s also the question of opportunity. Taking upper-level courses can cost (a lot) of money. Competitions such as the AMC and AIME may be easier to do for a good number of applicants.</p>
<p>I took Calc 3 first semester my sophomore year and could have gone a lot further had my parents been able to afford the cost of the local university (the local community college later offered Differential Equations my junior year, at a much lower cost, and I took Linear Algebra online after that).</p>
<p>At least in Minnesota high school students can take those advanced math classes for free at the University of Minnesota through PSEO.</p>
<p>Also somewhat off topic but cellardweller didn’t MIT do badly on the Putnam this year?</p>
<p>True, relatively speaking. Although they had more top 25 and top 100 placements than any other school, it is the first time in many years they failed to get a Putnam Fellow (top 5). They had averaged two per year in the past decade.</p>
<p>zrathustra,</p>
<p>You bring up a great point. We could not afford the univ route. My son did all the community college classes through Dif. Equ. and then worked with an online tutor who gave us a great rate. We also had financial help from an outside source. My son was also able to audit 19 units of college physics at two different univ. for free. We feel very fortunate for all the relatively inexpensive opportunities.</p>
<p>Art of Problem Solving, of course, has outstanding courses. They’re not cheap but they’re not as expensive as some online entities such as EPGY.</p>
<p>
</p>
<p>In a sense though, they are both kind of arbitrary things. What is to say that an introductory analysis course really will be more useful? In practice, most of the results in such a course are taken for granted anyway. </p>
<p>However, I do agree that for quite a few people, the first option might appeal more, and in that case, it makes sense to pursue it. I think either of these two candidates will learn whatever it takes for them to succeed. Just because someone takes some college math classes doesn’t mean he/she will eventually even have much interest in mathematics, in which case it was just a way to develop sharp reasoning skills and pursue a challenge.</p>
<p>I hope cellardweller is making a distinction between superstar and star, having used both words. I’m thinking a superstar has like an IMO gold medal, and a star might have almost made USAMO. I would say there is bias if someone making the USAMO is considered a superstar, while someone who shows interest and ability in handling challenging mathematics in a somewhat more standard setting is considered academically ordinary. Bias towards competition math, that is.</p>
<p>Academic star is a designation of the MIT admission’s office given to applicants with specific academic achievements. My understanding is that it is reserved for applicants who have won special awards or placed in highly selected competitions: Intel and Siemens semi-finalists and above, USAMO qualifiers and above, science olympiad medalists. State, school and local awards do not count as that would probably cover all qualified applicants. </p>
<p>I am not aware that MIT gives the academic star designation to applicants with superior credentials in terms of classes taken or even research accomplishements: that group would probably be too large and the designation may lose its meaning. By definition the star system involves a well-recognized academic award which needs to be rare and highly selective to be counted. There are at most 500 USAMO qualifers while there are potentially ten of thousands of students having taken advanced college math classes while in high school. </p>
<p>Probably well over half of academic star candidates are rejected so it is no guarantee of admission, just a higher chance of admission than candidates who are not academic stars. I have interviewed many successful candidates but none so far were classified as academic stars, even though their qualifications were excellent. </p>
<p>A superstar is not an offical MIT designation but would be Intel winners and IMO medalists and the like which are actively recruited by MIT through emails and letters. While not auto-admit candidates they would probably be offered admission unless there was a major flaw in the application.</p>
<p>Thanks, that is very clarifying. I guess the one sticky point in all this is that not everyone who takes some classes past calculus and basic college physics has the same interest, aptitude, etc in those things. I think unfortunately, this is a bit tough to gauge, especially if the candidate is not mature enough to express his or her interest in a distinguishing fashion. </p>
<p>I am interested in all this partially because I did not even know what the USAMO was until well into college, and I know a fair number of enthusiasts who are somewhat the same.</p>
<p>One interesting thing is there are tenured professors at the same (super top) places both with IMO gold medals and no track record whatsoever. Clearly, they have abilities beyond what many others with no IMO/etc track record do, so I imagine letters and other things are pretty crucial to getting the full picture.</p>
<p>I knew a lot of people in advanced classes (like abstract algebra) in high school, and it was generally easier to get an “A” in these classes than it was to make USAMO. In those days there were only 150 USAMO winners per year and no Art of Problem Solving Books existed yet…I don’t know if it is any easier today to make USAMO considering that the number of qualified entrants probably has increased.</p>
<p>Still, there are a lot of people who can get A’s in high level classes. </p>
<p>I can’t really tell you what it takes to make USAMO because I wasn’t able to do it myself, even though advanced math came easily to me. If it’s like it used to be, knowing some combinatorics and number theory should help. Some people easily picked the so-called “math tricks” necessary to solve these problems just from math team; later I found out much of these “tricks” were based on number theory. As a more verbal person, it was easier for me to learn mathematics when given the entire context. Of course, there are more than number tricks on the test, but the other problems could be typically solved if you had done well in algebra, geometry, and trig. Some of the number tricks problems were kind of, well, you can guess the three letters I’m thinking of–I had NO IDEA where someone could solve this from scratch other than Gauss himself.</p>
<p>I actually have no idea what three letters you’re thinking of. I’m immensely curious.</p>
<p>I’ll give you a hint. It’s an acronym for a phrase and I don’t think the phrase would get through CC’s filter.</p>