<p>EllenF,</p>
<p>I would echo what Marite said about LACs. They often offer a sufficient number of advanced math classes but to take the ones you want may require planning because they are offered in alternating years. If they are interested in a large number of them they may be able to advance themselves though AP and other classess to load up on them starting as a Freshman.</p>
<p>Sac:</p>
<p>You raise very good points. As it turns out, S's math class is not only full of math whizzes (very humbling!) but it is also very supportive. He is part of a study group that seems to work very well and whose members do not sound like they are trying to outdo one another.
I don't think it is at all a bad thing for a student who was very good in math in high school to discover in college that there are other fields of study that are more attractive (and, should I say, potentially more lucractive? I understand that the demand for pure math Ph.D. to be at about zero). And it is just as well to discover it early on. It does not mean foreclosing the option of taking more math courses, though they may be different ones.
S has taken some math courses in the company of economics majors.<br>
Larry Summers once said that he'd started out as a math major but realized that he could not compete with the math stars so switched to economics. Your S would be in good company!</p>
<p>Marite -- It's wonderful to hear you son is in his element. I think my son's interest in econ has more to do with some wonderful lecturers than anything in terms of career planning. Anyway, he has not yet made the full leap into a major. He's still taking the third course in the physics sequence for physics majors (quantum mechanics), an upper division math class in number theory and cryptography because it sounded like fun, a senior-level statistics class in an engineering department, the core class that is basically philosophy, and macro economics, as well as a jazz ensemble. All bases are covered.</p>
<p>Is your son straddling physics and math?</p>
<p>EllenF -- Marite's description of her son's experience also raises the issue of whether it's important for there to be a critical mass of other other "math kids." Again, I see the argument going both ways. There was a student on here who chose Vanderbilt over Yale and who stood out so much in his math class that his professor asked him to work with him. On the other hand, being at a place where you can be part of study groups that are a form of community could also be important.</p>
<p>
[quote]
Is your son straddling physics and math?
[/quote]
</p>
<p>That's the current plan. I'm told that combo is small and very supportive, so if he follows through, he would be in great company.</p>
<p>Your S does seem to have all bases covered; many of of his courses can work in different disciplines. I suspect that many students are influenced by charismatic profs into previously unthought of paths. the current FAS dean at Harvard started out as a German historian but fell under the sway of John Fairbank. His Ph.D. was in Chinese history. Still history, but not quite the same...</p>
<p>One of my concerns about econ is that it's a mob scene at just about every research university. Physics is more welcoming, I think -- but harder. I'm not sure that Lawrence Summers is the role model I had in mind for my S. My S is not a genius, but I'd like to think he has a little more social intelligence...</p>
<p>SAC, LOL! It would not be hard.</p>
<p>I'm afraid you are right about econ being a mob scene, and not just at research universities. If your S continues to like it, however, and has a congenial prof, that is really important.</p>
<p>
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Marite's description of her son's experience also raises the issue of whether it's important for there to be a critical mass of other other "math kids."
[/quote]
</p>
<p>I think that it is essential for all kids to find a critical mass of others who are like them, wherever their interests and talents lie. The overwelming majority of kids who are interested in majoring in math can find plenty of others who are like them at any good LAC or honors program at a state u. The number of superstar kids who are so exceptional at math (like Marite's son) that they need to be at someplace like Harvard or MIT to find a critical mass of kindred spirits is very small --- probably less than 20 kids per year in the entire country.</p>
<p>
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The number of superstar kids who are so exceptional at math (like Marite's son) that they need to be at someplace like Harvard or MIT to find a critical mass of kindred spirits is very small --- probably less than 20 kids per year in the entire country.
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</p>
<p>Ugh! say it ain't so, Texas! :) S's class alone has 26 kids, and they are all terrific. MIT, Caltech, Princeton, Yale, Chicago and some other schools have equally strong math students. I would put the number far higher than 20.</p>
<p>Less than twenty??? I agree they are few but AIME+USAMO alone would despel that they are <20. Try to remember that there are many math contests who identify kids and at Exeter alone there are more than 20 such kids.</p>
<p>Of course there are more than 20 kids who are great at math! But the number who are truly so unusual that they need to be at a top-flight research institution to find peers is very small. That group would not include all 100 or so seniors who qualify for USAMO, for instance. The majority of those kids would be fine at an LAC. I'm talking about the kids who arrive at college ready for grad classes and/or serious research.</p>
<p>And, there are kids who never enter math contests.
I agree there is some dividing line between good at math and exceptionally gifted. But I wonder how you come up with a number.</p>
<p>And, back to the original question, given that at many universities there will be mathematicians who got PhDs at places like Harvard and MIT, is close contact with such faculty enough? Or do students need to be where there is that cluster of fellow undergrads?</p>
<p>Looks as if we cross-posted. You're talking about students who, as first years, are ready for grad classes and to do research?</p>
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Looks as if we cross-posted. You're talking about students who, as first years, are ready for grad classes and to do research?
[/quote]
</p>
<p>Yes. If you define "superstar" in a way that includes the top 20 kids at Exeter, and 26 kids in Math 55 at Harvard, and 20 each at places like Chicago, Princeton, Stanford, Caltech, etc, etc you might end up with a few hundred kids per year. But the mere fact that there are a few hundred of them means that they do not "need" to be at Harvard or MIT to find peers. Any top 30 or so college will have at least a few of them to hang out together. The kids who truly "need" to be at one of the top 3-4 math programs in the country, in the sense that they cannot find peers anywhere else, are the int'l math olympiad gold medalist types, the kids who win USAMO, the Davidson Scholars, Clay Research Scholars, and the national winners of Seimens-Westinghouse and Intel. There are similar kids who do not enter competitions, but who do research or take very advanced courses (like calculus in middle school or grad courses in high school) who would also be included. That number is very small. Everyone else who ends up at Harvard, MIT, etc with a plan to major in math could probably have chosen a less selective school and ended up with a perfectly fine educational experience, including peers.</p>
<p>Of course, this totally skirts the issue of whether kids need intellectual peers among their fellow-students in college, or if it is enough to have intellectual peers among the faculty.</p>
<p>
[quote]
The kids who truly "need" to be at one of the top 3-4 math programs in the country, in the sense that they cannot find peers anywhere else, are the int'l math olympiad gold medalist types, the kids who win USAMO, the Davidson Scholars, Clay Research Scholars, and the national winners of Seimens-Westinghouse and Intel.
[/quote]
</p>
<p>If a these 20 or so students Texas137 is talking about all formed a single "bargaining unit" to negotiate with a college to take them all, they wouldn't have to go to a Harvard or an MIT to find peers, they could find a congenial university (with nice weather and other amenities and reasonable tuition--bearing in mind that pure math is one of those "chalk & talk" majors that doesn't need expensive specialized labs) where they would all have one another as peers.</p>
<p>I can see it now. College admissions turned on its head. Instead of committees of adcoms composing their entering classes, you could have groups of students ("unions" of kindred spirits, as it were) soliciting proposals from colleges to take the entire group. Once a cohort landed at a particular college, the college could probably attract some pretty terrific math faculty (at least as "visiting professors" for a few years.)</p>
<p>Labor unions sprang up because there was an asymmetry in power vis-a-vis large industrial employers. One side of the market (the large employer side) was highly organized and had a good deal of power, the other side (the mass of individual employees) was highly decentralized. As a result, labor unions grew up to address the imbalance. Of course, they weren't a perfect mechanism...and introduced problems of their own, and reasonable people may disagree about whether, on balance, they were a good thing.</p>
<p>But it's hard not to think--whimsically--about the parallels here. Maybe these students need an agent, LOL.</p>
<p>Certainly, there are schools that have made a practice of trying to lure the kind of students Texas137 is discussing with extremely generous merit scholarships. (Both Duke and Chicago have tried this strategy, but even though Chicago has an incredibly strong graduate math program, in a number of years Duke seems to have been more successful in attracting top math undergrads with their offers, perhaps because of their good weather, their campus culture, or some other mysterious factor.)</p>
<p>More seriously, it should be noted that not all the students Texas137 speaks of actually wind up going into pure mathematics or even majoring in math. So there may be other important criteria to consider in selecting a college besides math peers.</p>
<p>One recent IMO gold medalist majored in social studies in college and is now a social worker. Another recent IMO gold winner majored in music at Duke couple years ago. Another Duke grad and former IMO goal medalist is planning grad school in computional biology. </p>
<p>Some of these students in the category Texas137 mentions have strong double interests--one recent grad double-majored in math & music at MIT; another double-majored in math & theater at Duke. Another recent IMO gold medalist (and top Intel Finalist) graduated with honors in math & linguistics in college, is currently teaching English in China and considering grad school in economics or statistics. Still others have gone to work at investment banks after graduation.</p>
<p>The following link has some interesting interviews with some of the students who scored high on last years Putnam college math contest at different colleges, with reflections on their educational paths, past, current, and future.</p>
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Any top 30 or so college will have at least a few of them to hang out together.
[/quote]
</p>
<p>My S took a sohpomore/junior level math class at a top tier LAC while a senior in high school. His mid term score before scaling was 30 points higher than the next highest grade in the class. He just took his first mid term math exam at Princeton and he estimates that he got about a C+ before scaling. He said one of the problems was USAMO difficulty. My brother went to MIT and said when they'd pass out exams some of the kids would just start to cry.</p>
<p>There is a big difference bewteen the top math programs and good math programs, so I think kids really need to look at fit.</p>
<p>
</p>
<p>I know you have a closer acquaintance with more of those people than I do, so I will take this statement at face value. I suppose some of those young form their friendships as they work up to that high level of math achievement at summer programs, or as they meet in math competitions or at research fairs. </p>
<p>For onlookers, I'll note that it's easy to confuse, by misremembrance or slip of the keyboard, the </p>
<p>Davidson</a> Young Scholars program </p>
<p>and the </p>
<p>Davidson</a> Fellows awards, </p>
<p>which are both activities of the Davidson</a> Institute for Talent Development. </p>
<p>According to the 2004</a> Davidson Institute annual report, there are now hundreds of young people in the Davidson Young Scholars program, too many to constitute the select group that Texas137 was talking about, so I think her reference was to the Davidson Fellows program, which indeed has done very well at selecting just a few math superstars in the last few years. </p>
<p>To wisteria, I will say muchas gracias for the link to the interviews with Putnam award students. I had the privilege of meeting Paul Zeitz, an IMO medalist on the first ever team to the IMO, and a coach of the "dream team" that achieved a perfect score across the whole team at the Hong Kong IMO in 1994. He was a math competitor par excellence, but he majored in history at Harvard. After quite a few interesting career turns, he is now a professor of mathematics</a> at the University of San Francisco, and has some interesting colleagues there.</p>
<p>"My S took a sohpomore/junior level math class at a top tier LAC while a senior in high school. His mid term score before scaling was 30 points higher than the next highest grade in the class. He just took his first mid term math exam at Princeton and he estimates that he got about a C+ before scaling. He said one of the problems was USAMO difficulty. My brother went to MIT and said when they'd pass out exams some of the kids would just start to cry."</p>
<p>My D was the best student in her Calc BC class senior year. So, good, but not fabulous as a math student. Just took her multivariate midterm at Princeton. Even the kid she knew who had already TAKEN multivariate said the exam was impossible. These top math programs know who they are looking for. My D will be on of those who have a talent for numbers, but major in something that uses that skill in the service of a different discipline. And luckily, there are a lot of those fields in the world. For the kids who are way good at math but not beyond belief talented, this math talent is a great gift to make their way through the world. As they compete with the rest of us who have no clue....</p>
<p>At S's school, Core classes include 5 math and 5 physics. I'd expect that the lower half (in terms of grades)shift majors. At most other colleges, any of these students would be tops.</p>
<p>NYU's Courant Institute of Mathematical Sciences
<a href="http://cims.nyu.edu/%5B/url%5D">http://cims.nyu.edu/</a></p>
<p>
</p>
<p>This statement represents why I think kids should go to the highest ranked school that they can get into. For me, it's about continuing to stretch the limits of one's abilities. My son was one of the top students at a prep school which sends 99% of its graduates to 4 year schools. He worked hard and had the natural ability to stand out among his peers. Yet, he now finds himself in a situation where virtually all of his classmates were in that same HS pool, whatever their geographic location. I LOVE the fact that he is finding his classes to be pretty challenging -- that's what I'm willing to go into debt for, and postpone retirement, new cars, vacations etc. From what I understand about how the human brain develops, most people peak in their mid-20s, as far as raw brain power goes -- this is not the time to sit on his laurels, and coast. I would like to see him taken the hardest classes he can reasonably handle, and see where he ends up. </p>
<p>To peak in HS, and end up where one is easily at the top of the class limits any student's growth -- I think that's why it's even more important for the kids that texas37 is describing to be in a group of like-minded kids. During WWII, there was a reason that the government located the best minds in the country in Los Alamos -- it's about synergy.</p>