<p>My kid took BC calculus early on too. She has many close friends who took Math55 as a freshman at Harvard. Some friends found that they were beyond math55 curriculum as freshman. So they registered in higher math classes. Some of these freidns never competed in math competitions, but others friends did very well in IMO.</p>
<p>Do the graduates of RSI (Research Science Institute) have better luck entering the doors of heaven than IMO? That is my impression.</p>
<p>RSI kids generally do very well in Harvard. If you look the RSI data from previous years, still it is around 70-75% admit rate (I have not seen data in so many years). There are still many RSI kids who do not get into harvard. But they do very well in placement to other equally selective colleges.</p>
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<p>Doing well in Math 25 is SO SO SO much easier than making gold at the IMO. The fact that you think the two are comparable at all in terms of the level of achievement that they respectively demonstrate implies that you have no idea what you’re talking about. The difference between the two is like the difference between learning a cookbook’s worth of recipes and becoming one of the best chefs in the world.</p>
<p>Harvard is a private institution and can do whatever it wants, but excelling on the IMO is probably the single highest academic hurdle that a high schooler can reasonably clear, and rejecting a high-scoring IMOer who isn’t a sociopath is straight-up ■■■■■■■■.</p>
<p>The point of my post is that this young man had done math at a much more advanced level than what is required to do well on the IMO. He chose not to participate in the IMO. There is nothing to show that, had he chosen to participate, he would not have done extremely well. It is not an either/or proposition. I am not asserting, contrary to what you think, that doing well in Math 25 as a high schooler is necessarily better than doing well on the IMO. My sole point is that the IMO is not the only possible pool of math talent.
Dismissing Math 25 will not endear you to some top mathematicians who took it and are now on the faculty of some top departments.</p>
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<p>Math 25 is not “advanced”, not for the type of students we are discussing, and certainly not for people who top the national olympiad and take the IMO. Most of them cover it on their own in high school, without the fanfare of taking it at Harvard. </p>
<p>Nor is math 25 advanced material compared to what one learns for the IMO, or a license to take graduate courses. It is a compressed introduction to standard undergrad material, nothing more. In some countries the same material is taught in high school to the equivalent population of students (those mathematically capable and interested), starting as early as the first or second year. However, in no country has anyone been able to teach more than a handful of students to master the IMO. There is just no comparison, especially when you refer to gold/silver IMO medalists from one of the strongest countries.</p>
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<p>There is one other small step that you’re forgetting. To participate in the IMO you don’t just brandish a Math 25 transcript from the Harvard registrar and ask where to get on the airplane. </p>
<p>Speaking of registrars, I guarantee you that for a high school student, taking Math 25 at Harvard is purely an ego trip. It is easy for the same student to read and master the same material (and much more) from books, and there is no advantage to taking it at a university, in fact there are substantial disadvantages to being kept on the homework and exam schedule that the Harvard course would impose. The student or his parents thought this would be an impressive big deal. It’s nice, but ultimately meaningless, whereas an IMO medal on his resume would have an impact for the rest of his life. </p>
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<p>Cases of amazing problem solvers who avoided olympiads, or participated and didn’t do well, are relatively rare. Certainly there are theoreticians who are less talented in problem solving, and there is (limited) room for them in academia. But the overwhelming likelihood is that someone who “opted out” of participation in the olympiads would never have made it to the IMO even if trying. The reverse is much less true; olympiad champions tend to also be good at theory, though some more so than others and they are not the only superstars.</p>
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<p>Uh, tell any top math faculty that you took math 25 in high school and the response will be “that’s nice”, or a rolling of the eyes that this information is being volunteered at all. Tell them that you qualified for a top IMO team and have a gold or silver medal and they will know instantly that you are (at least in cognitive and mathematical ability, if not academic accomplishment) a peer. People decades into the profession still remember who among their colleagues won the Putnam competition as students, whereas pretty much everyone was advanced in high school.</p>
<p>Is this really so hard to believe? I know a kid who was IMO medalist who didn’t get into Harvard and ended up going to MIT, and is pretty happy there. Harvard looks for well rounded people who will contribute to the school in multiple ways - being a math genius doesn’t guarantee acceptance more than anything else.</p>
<p>“Nor is math 25 advanced material compared to what one learns for the IMO.”</p>
<p>This is so wrong as to defy belief. IMO questions involve neither real analysis nor calculus on manifolds nor linear algebra.</p>
<p>That said, getting a gold in the IMO is definitely an accomplishment to be proud of.</p>
<p>I believe that the student who took Math 25 would have been quite capable of handling Math 55. In fact, I marvel that his high school schedule could accommodate coming to Harvard in order to take Math 25. As a sophomore, he began taking grad level classes, as did veterans of Math 55. I believe that his taking Math 25 had more to do with his high school schedule than his math abilities. That said, Math 25 is not just a compressed introduction to undergraduate math. Most of those who take it have taken MVCalc and LA and possibly some other college math classes, none of which is necessary to do well in the IMO.
It is truly surprising to me that some posters are trying to make me knock IMO. I do not. I am–to repeat myself–suggesting that there are different ways to show that one is capable of excelling at math in college. Being an IMO medalist surely is one. But it is not the only one. That is all I am arguing. And with that, let me bow out of this extremely repetitious discussion.</p>
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<p>Do bother to solve some IMO problems before talking nonsense. Quite a few of the questions fairly directly involve analysis, linear algebra, abstract algebra, finite fields, error-correcting codes, combinatorial set theory, group theory, projective geometry, Markov chains, multivariable constrained optimization, probabilistic methods, graph theory — the list can be continued. Often the competition problems are elementary rephrasings of statements from the more advanced subjects. Let me know if you want specific examples.</p>
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<p>The statement being contested was that taking Math 25 in the last year of high school “enabled him to begin take graduate courses in the freshman year”. Now you’re saying that he may have had additional background and didn’t take the grad courses until another year (and presumably, more courses) had passed. Either way, Math 25 is not a grand tour of the undergrad curriculum, is not a surrogate for it, and is not a particularly advanced or non-standard course. </p>
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<p>So it was an ego trip after all?</p>
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<p>Math 25 is a compressed introduction to a fraction of undergraduate math, and as such it avoids many of the pieces that are most essential for taking graduate courses. This is why people generally don’t take grad courses as the next step. </p>
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<p>I get the feeling you don’t speak from experience. Do you have any idea how shallow the MV / LA background is for some of these students? The math 25/55 sequence to some extent exists because the students are smart but need a consolidation of their background without doing it at the pace of the slower students. </p>
<p>With respect to the IMO, the idea that “you don’t need advanced math to do the IMO” is true only in the most irrelevant, technical sense. In reality most serious competitors need and use the advanced knowledge in learning and mastering the IMO material.</p>
<p>One thing that I don’t think has been mentioned is that although a student may have something extraordinarily good on his application, he may also have one or more things that are not very good at all. Even a math genius may have poor grades in other subjects, recommendations that indicate that he is difficult or arrogant, a disciplinary record, who knows what. I don’t mean to suggest, necessarily, that this is the case for this particular kid, but you can’t really know without having all the facts.</p>
<p>I read on one of the CC threads that lots of people choose to attend RSI over IMO. I, as a math challenged human, must ask… is math research (graduate and above level) at MIT/Harvard seen as more prestigious for a high school student than scoring a medal at an international competition?</p>
<p>But then again, does it really matter? Either way, RSI or IMO, these people are geniuses!</p>
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Maybe RSI over MOSP, but if one were invited to IMO, I would be shocked if they turned it down for RSI. Once again, I don’t think there exists a higher high school accolade than being part of the IMO.</p>
<p>Damn, that DataBox fool seems like a genius, where does he go to college (or is he still a high school student)?</p>
<p>And yes, I admit I was misled thanks for clarifying Wharton.</p>
<p>Okay, one more go.
The young man I am writing about attended a suburban school. From my son’s own experience, I know how complicated it was to set up a schedule that would allow him to attend daytime classes at Harvard (not HES evening classes). As a result, a number of classes he would have liked to take were not available to him. I do not know exactly why his friend took Math 25 instead of Math 55; but I would guess that scheduling played a part in it.
No, I do not have direct experience of Math 25, 55 or any other math class at Harvard. I am a parent, not a student. But my S was a CA and was able to describe the difference between the different types of freshman math courses in terms of coverage and emphasis on proof. To return to the friend, it is entirely possible that he began taking grad level courses in his freshman year. He certainly took grad level math classes with the 55ers. Anyway, I am not claiming he is better than an IMO medalist. But I certainly think that he is every bit as good. And his career at Harvard confirms this. He won one of the highest prizes.</p>
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You seem to suffer from the preconception that covering more material faster is automatically superior to acquiring a deep understanding of less material in a more rigorous way.</p>
<p>That isn’t to knock the many extremely smart people who take an accelerated curriculum, but that’s just as much about availability as talent. Most public school math classes are at such a low level that even a definitely-not-brilliant person such as myself could go at twice the pace if such a curriculum were offered.</p>
<p>Those who take rigorous college math as high schoolers are obviously standouts (and would probably do quite well on the IMO), but simply being able to stick xyz community college classes on one’s resume and jump into more advanced material doesn’t mean a lot.</p>
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<p>The IMO is (mostly) rigorous but it is not less material. It ranges over a lot of topics that when covered in courses runs from high-school to graduate level. It simply cuts across a different curriculum in a different order than the usual sequence, which is more aligned with the needs of engineering and science. The conventional ordering of subjects is relatively arbitrary and there is no sense in which, say, hard combinatorics is “less advanced” than real analysis. The answer to which one you need in the olympiad is the same as when asking which one you need for research: YES.</p>
<p>^ I was speaking generally, but that sounds right to me.</p>