<p>Oh - and ucb- just to add</p>
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<p>Pretty decent for a math department that doesn’t offer many high-level courses, huh? ;)</p>
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<p>Caltech specifies that freshman applicants have calculus in high school:
[Freshman</a> Applicants - Caltech Caltech Undergraduate Admissions](<a href=“http://admissions.caltech.edu/applying/freshman]Freshman”>http://admissions.caltech.edu/applying/freshman)</p>
<p>Caltech’s Ma1a course “will introduce the mathematical method through (One Variable) Calculus, with which the Caltech freshman has reasonable familiarity, at least for doing calculations”.
[[Ma1a</a> - Fall 10 - 11] - Calculus of One and Several Variables](<a href=“http://www.math.caltech.edu/~2012-13/1term/ma001a/#des][Ma1a”>http://www.math.caltech.edu/~2012-13/1term/ma001a/#des)
Note the use of the Apostol calculus book and the heavy dose of proofs and theory in the lecture notes for the course. Caltech’s Ma1a course does not appear to be a “typical” freshman calculus course.</p>
<p>Regarding MIT, its courses 18.01-18.02 does not appear to be laden with proofs and theory like the “introductory calculus” courses at Caltech and Harvey Mudd, but is accelerated (covers through multivariable calculus in two semesters instead of three). MIT students do have the option of choosing “with theory” versions of these courses.
<a href=“http://student.mit.edu/catalog/m18a.html[/url]”>http://student.mit.edu/catalog/m18a.html</a></p>
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<p>Great post. Could you share the link as I’d like to look at the numbers on others? Thanks!</p>
<p>I see that it’s US News grad school ratings, but I’d love the link for getting the numbers on various programs, or maybe that’s just something you put together.</p>
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<p>However, if the student is focused on a particular subset of STEM fields, then consideration of a school that is strong in those STEM fields, even though it may be relatively weaker in the ones that the student is less interested in, would also be appropriate.</p>
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<p>That is exactly the point I was about to make. In am in a STEM field and my school, while ranked top 25 overall for STEM majors is number 1 in my field. The rest of the top 5 in my field are either not on the top 25 list, or “only top” 25. </p>
<p>Then there is the example of my coworker whose kid got into MIT but chose Ga. Tech for his engineering specialty because it was just as highly ranked.</p>
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While this makes sense–how frequently do STEM kids change their areas of interest after getting to college?</p>
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<p>Doing some quick mental addition of the numbers in [nsf.gov</a> - NCSES Baccalaureate Origins of S&E Doctorate Recipients - US National Science Foundation (NSF)](<a href=“http://www.nsf.gov/statistics/infbrief/nsf08311/?govDel=USNSF_178http://www.nsf.gov/statistics/infbrief/nsf08311/?govDel=USNSF_178]nsf.gov”>404 Page Not Found | NCSES | NSF), I note that of future S&E PhD’s hailing from the top 50 undergraduate institutions, Berkeley accounts for almost 10%.</p>
<p>I wonder how the numbers would change if one included the next 50 undergraduate institutions, which surely include other large publics. Their percentages might be lower, but given their huge numbers of students, I bet they contributed a large fraction of the overall future PhDs.</p>
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<p>The figures I quoted are all from the US News online edition which you can find at</p>
<p>[Best</a> College Rankings, Best Graduate School Rankings, Best Hospitals, and Best Health Insurance Companies - US News Rankings](<a href=“http://www.usnews.com/rankings]Best”>http://www.usnews.com/rankings)</p>
<p>But you’ll need to buy a subscription to their College Compass service to get access to all the data.</p>
<p>I should add that you should take all these ranking with a grain of salt The grad program ranking are based entirely on reputational surveys. My experience with the academic fields I’m most familiar with tells me the rankings bear some relationship to how academics in those fields judge various graduate programs; whether that means you’d get a better undergraduate education in that field is another question entirely. And as other have noted upthread, graduate program rankings don’t help at all in assessing LACs; there, the information tends to be even more spotty and anecdotal.</p>
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<p>However, if the student is likely to change major, would it necessarily be to a different STEM major? If there is high likelihood of changing majors, attending a school with good non-STEM departments of interest as well as the initial target STEM departments would make sense (so Caltech might not be suitable unless the student’s primary non-STEM interests were English literature, history, and/or history and philosophy of science).</p>
<p>Biology majors seem to be especially unlikely to switch to other STEM majors, since they often take biology-major-specific versions of chemistry, physics, and math, so they would not be able to switch without retaking those courses.</p>
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<p>I agree with both comments. A STEM-oriented applicant who is quite certain she wants to do math or physics but not engineering might be better served at Harvard or Chicago than at a “tech” school, while one inclined toward engineering but not pure math or pure science might be better served at a Carnegie Mellon or Georgia Tech. But my sense is that MIT and Caltech attract a lot of applicants who could just as plausibly do pure math or pure physics as engineering. Some may think they know which way they want to go but change their minds once they get there; others may be undecided or wavering even before they enter. Get into MIT or Caltech and you’ll be among the best of the best whichever of those fields you end up in, with no penalty for switching midstream. Same is true, I’d say, for Stanford, UC Berkeley, and Princeton, and to a slightly lesser degree Cornell and Michigan; less true for most schools on this list.</p>
<p>There’s probably a similar pure v. applied science ambivalence between chemistry and chemical engineering, and no doubt others as well.</p>
<p>The standard claim is that most college students switch majors at least once (though I’ve never seen citation to an actual source for this). What is less clear is whether STEM majors switch with the same frequency as humanities and social science majors. I’ve always heard that at many schools it’s harder to transfer into engineering than out of it, because of the way courses are sequenced in engineering programs. As a result (and because engineering turns out to be more rigorous and demanding than many people expect), there tends to be a net outmigration from engineering to other majors. But I don’t know whether those students tend to repopulate other STEM fields, or become poets. Some of each, I’d imagine, but I’d love to see some facts and figures if anyone has them.</p>
<p>In general, though, because one’s college career will often include unanticipated twists and turns, it may be wise to seek out the school that offers the greatest all-around strength, if that option is available to you.</p>
<p>(On the other hand, it almost sounds like to cruel joke to suggest to those aspiring to MIT and/or Caltech that they should have Stanford and Princeton on their lists as back-ups, in case MIT/Caltech don’t make the offer).</p>
<p>My idea is something like this: “If you’re really sure you want to major in a STEM field, but aren’t completely sure which STEM field you’ll end up in, you should strongly consider the Tech Ten.” And then the list. I’ll try to make a draft list based on this thread, pretty soon.</p>
<p>UCBAlum: What exactly is the LAC Ceiling you mentioned upthread?</p>
<p>The “ceiling” refers to the absence or lesser availability of graduate-level courses and opportunities at an undergraduate-only school. This can be an issue for students who are already advanced going in (particularly in math, where some students are two or more years ahead of the normal sequence), since such students often want to take graduate-level courses and do graduate-level research as undergraduates.</p>
<p>An analogy at the high school level would be if a math-loving student who is ahead in math attends a high school that offers no math more advanced than precalculus, and options to take college math courses while in high school are not realistically feasable.</p>
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<p>But not Cornell or Michigan.</p>
<p>I don’t think, though, that Stanford, Princeton, Cornell, or Michigan will be in Hunt’s Tech Ten. Isn’t Hunt specifically looking for tech schools?</p>
<p>The worm went thru Caltech NEVER taking an engineering class. He shifted majors between CS and NS, and is in grad school doing both. Psychology courses were very popular. I attended one of the profs event days, when many of her students presented their research, and it was clear why she was a favorite prof. Econ courses were good. The worm had so much exposure to patent attorneys, he pondered that field. The success rate for students applying to dental school, med school, law school, is extremely high. To outsiders, the school is seen as narrow, but really it is not. Just saying.</p>
<p>Thanks for the explanation UCBalum. This begs the question, what is the standard math for incoming college freshman? I fear both kids may end up in this situation.</p>
<p>UCB, you describe our local HS to a T. In junior year, the worm took 4 or 5 classes each term at the local U. The physics teacher was a retired nurse. AP English teacher was a Xtian fundamentalist. History teachers (a mother and daughter) were quite good. I understood why the worm and GC thought he should leave early.</p>
<p>What a nightmare – poor wormy. Glad he got out of dodge when he could.</p>
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<p>Yes, that should be a consideration for some students. But the “ceiling” would be less of a factor at challenging undergrad-only STEM schools like Mudd where there is very little AP credit granted, intense academics for all.</p>
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<p>The expected college freshman math course at most colleges is single variable calculus. (Caltech and Harvey Mudd “freshman calculus” includes a lot of real analysis proofs and theory; MIT’s “freshman calculus” is accelerated, with an extra theory option available.)</p>
<p>Freshmen who have had AP calculus BC are a year ahead. Freshmen who have had math beyond that (e.g. college courses in multivariable calculus, linear algebra, and/or differential equations) are more than a year ahead. It is students in the latter situation who major in math that are most likely to want to take graduate level courses as undergraduates. Even if they do not, they may want a greater selection of upper division math courses than is available at more LACs.</p>
<p>Harvey Mudd does have a higher “ceiling” than most LACs in this respect, although its advanced math course selection is still a lot smaller than at a big research university like Berkeley.</p>