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<p>Umm… Lets see… Harvard, Princeton, MIT, Berkeley, Chicago, Stanford…</p>
<p>My fingers say that’s 6, not 5 :D</p>
<p>Those are the six that show up in the top listings, though. From the stuff I’ve read, they are all considered pretty much as equals in terms of ranking.</p>
<p>For a student heading into Real Analysis as a freshman, it would be wise to consider the depth of the department and grad offerings. S was advised by the math profs at one LAC not to apply – they couldn’t keep him busy for four years, and at another one, they told him he’d be doing independent study the last two years. That convinced him to apply to mid-size research universities, but not necessarily or exclusively those six. (He applied to three of those top six, was accepted at two and rejected at one. He didn’t apply to Princeton, even after a guided tour from a math major friend there.)</p>
<p>ihs, the Core was why S picked Chicago > MIT. I think he has had second thoughts about that periodically, as he loves the Core courses, but he never does as well as he’d like. OTOH, he has spent two summers at MIT, so he found a way to get his cake and eat it, too.</p>
<p>OP- The bottom line- look beyond the one school you perceive as “best” and consider the over all fit of the school in academics and other aspects of your life. Have a list including more than the very top schools. You are competing with all majors for a spot in the college. While you may be far above almost everyone in math they may best you in other areas and get the spot you thought was yours. It isn’t until grad school that only math ability counts. There are plenty of students with high, even perfect, SAT scores and grades. So many that no one school can take everyone they feel will do well at their school.</p>
<p>So if you are female, here is the list of top 10 undergraduate producers of math and computer science PH.D.</p>
<p>[Where</a> Female Mathematics and Computer Science PhDs Received Their Undergraduate Degrees | InsideCollege.com](<a href=“The Best College Rankings and Lists | Inside College | CollegeXpress”>The Best College Rankings and Lists | Inside College | CollegeXpress)</p>
<p>You’ll notice that neither Harvard nor Princeton nor ANY Ivy school is even on the list. Nor Berkeley nor Stanford. St. Olaf’s is fourth.</p>
<p>Here is the overall list:</p>
<p><a href=“The Best College Rankings and Lists | Inside College | CollegeXpress”>The Best College Rankings and Lists | Inside College | CollegeXpress;
<p>As you can see, Princeton is on it. Neither Harvard nor Stanford nor Berkeley nor any other Ivy is. Both St. John’s colleges are.</p>
<p>So what we can learn from that, perhaps, is that IF you are male, Princeton might be among the top places to do undergraduate math (if you plan to pursue a math Ph.D.)</p>
<p>Like CountingDown’s S, mine was also cautioned against applying to LACs; he took Real Analysis as a freshman and was taking grad level courses his junior year. </p>
<p>mini, why do you suppose there are so few women coming out of the top ranked undergrad programs?</p>
<p>Well, if representatives of 50% of the population are not coming out of the so-called “top ranked” programs, maybe there is something very wrong with the rankings? Maybe they are driving females away? Maybe they aren’t providing the necessary nurturing to female students to become top scholars? And remember, on the basis of future math Ph.Ds., Stanford, Harvard, Yale (or any Ivy except Princeton), and Berkeley don’t even make the top 10 - even when male students are included. </p>
<p>This would be very different from ranking programs on the basis of how “demanding” they might be. That might be ONE basis for ranking, but certainly not the only one, especially if they are driving those who would otherwise be top students away.</p>
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<p>Maybe graduates from those schools (the ones on the top-10 lists) were unable to find employment and had to turn to grad school. Maybe the other similar departments were comparatively very weak and they had to turn to math over physics or whatever they really wanted to study. You can spin it either way.</p>
<p>The ranking given was done by percentage of students going into PhD programs. Of course schools like CalTech, Harvey Mudd, and MIT are going to be at the top, they have very few humanities and social studies majors. Also, I get the impression that the cultures at places like Harvard, Princeton and Stanford emphasize careers in consulting and finance, rather than going into academia (though I could be completely wrong about this).</p>
<p>I highly doubt that young women with CS degrees are having trouble finding employment out of UG and have to “resort” to grad school. Certainly is not the case among the many female math/CS majors S knows, across a variety of colleges and universities. </p>
<p>He also knows several young women who started out as math majors who moved to Econ, CS, and other mathematically-related majors where they could use other skills in their tool belt, and have greater career flexibility in the long run (and this economy, that willingness to reinvent oneself over time is an important skill to have, male or female).</p>
<p>mini, S has several female friends in math PhD programs and he got a lot of useful info about which programs to avoid, both for UG and for grad. Networking can be a useful skill. :)</p>
<p>I would be loath to pick a college <em>purely</em> on the perceived strength of the undergrad major one wants to pursue at age 17. There is a whole lotta growth that takes place in college, and a whole lot of other factors that figure into one’s personal happiness and development.</p>
<p>Warbrain, I agree–math grads with a B.S. coming from H, P, & Y are recruited well by finance, banking and consuting firms, with great salaries. Many may end up at business school with MBAs, rather than PhD.s.</p>
<p>Princeton is great for math, and has a broad range of other concentrations if the 17 year old changes his/her mind.</p>
<p>Some of S’s classmates were making over $50K as summer interns; it is easy to understand why they might choose to work a few years before going to grad school (if they went at all). One of his close friends ended up as a math concentrator after starting in an unrelated field; I have to wonder if she would take offense at the suggestion that she needed a different kind of nurturing than her male classmates.</p>
<p>The question was “where is the best place to study mathematics as an undergraduate”, not “which has the most demanding program or courses”, or “which has the most geniuses”, or “which has the most geniuses among the faculty”, etc. Or which has the most students going into finance?</p>
<p>One (but only one) possible measure is the percentage that goes on to Ph.D.s in the subject. Another measure might be the number or percentage of graduating math majors. Another measure might be the number of future high school math teachers (that would seem like a very good measure to me, if math majors love the subject so much they are willing to forgo more lucrative careers.) There are likely other measures as well.</p>
<p>But the one place we do have clear data is the percentage of student body completing math and computer science Ph.Ds. In this case, overall, only one Ivy school (Princeton), and neither Stanford nor Berkeley, place in the top 10. </p>
<p>1moremom - I wasn’t trying to suggest AT ALL that female students require a different kind of nurturing than their male classmates. Rather, I was suggesting that perhaps they weren’t getting the SAME nurturing as their male classmates. </p>
<p>And, yes, I imagine Princeton is great for math, as are several dozens other schools (many of which likely rank higher on some of the possible measures I’ve listed.)</p>
<p>(The question is also NOT where students with 800 math SAT scores would best study math - the vast, overwhelming majority of math majors going to college don’t have 800 math SAT scores.)</p>
<p>This is an interesting thread. My S has BS in math from Princeton and is now in a top 6 pure math PhD program. My S also went to a public high school in a school district that is ranked 190 out of 200 in the state.</p>
<p>Princeton is great for students that have a very high level of ability and passion for studying math. These are students that were doing calculus in junior high. Mathematics is considered the most difficult major at Princeton and it is true that a lot of would be math majors end up majoring in something else. The physics and economic departments in particular try to lure the top mathematical talent into their departments. At graduation Wall Street firms are relentless in their pursuit of the math talent as well.</p>
<p>Up until the class of 2009 the average number of math majors per class was about 15. That number doubled when the department began to offer applied math classes which attracted students who might otherwise major in physics or engineering. It is true that the classes are daunting. Many of my S’s classes would start out with 15- 20 students and quickly drop to 10-12 after the first week.</p>
<p>As for the Putnam competition, it is not that highly regarded by mathematicians. The content itself is high school level math for those who intend to pursue PhD’s after graduation. My S told me that most Princeton undergrads post their highest scores their freshman year, because they quickly move beyond the material in the competition.</p>
<p>If you look at where the students in the top math PhD programs went to undergrad you get the same list as the top PhD programs - Harvard, MIT , Princeton, Stanford, Berkeley, Chicago along with other excellent programs such as Michigan. However most of the successful applicants to these programs are international students whose mathematics education is superior. The bottom line is that if you want to get into a top PhD program you have to have access to graduate level math education as an undergrad. </p>
<p>The beauty of Princeton as an undergraduate program is that they offer a lot of graduate level material in undergraduate classes. Their top faculty also teach undergraduates. My S’s first professor as a freshman was a Field’s Medalist. He was very well prepared for the program he is now in as are his classmates that went to Harvard.</p>
<p>If I may change the subject a little, what does it take to be a pure math major? What would a rigorous math curriculum look like?</p>
<p>At a minimum, I think a rigorous pure math curriculum would include Analysis at the level of baby Rudin, and Algebra at the level of Artin. I would also include point-set Topology, but it seems like many people get by fine without having taken it. After that, I think there can be a lot of discretion based on interest, but Analysis and Algebra should not be the most advanced classes for a schedule to be considered rigorous, I think.</p>
<p>Well a million years ago when I was in college (Harvard) I had a (female) friend who was a math major. One of her professors despite the fact that she was the only female in a class of five students was unable to remember her name the entire semester. She decided to go to law school rather than pursue a PhD. in math.</p>
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<p>What is “baby Rudin”? Isn’t [Rudin’s</a> book](<a href=“http://www.amazon.com/Principles-Mathematical-Analysis-Third-Walter/dp/007054235X]Rudin’s”>http://www.amazon.com/Principles-Mathematical-Analysis-Third-Walter/dp/007054235X) one of the usual books used in such a course?</p>
<p>Re: #76</p>
<p>Here is the pure math major at Berkeley as an example:
<a href=“http://math.berkeley.edu/programs/undergraduate/major/pure[/url]”>http://math.berkeley.edu/programs/undergraduate/major/pure</a>
However, it did not seem unusual for some of the most advanced math majors at Berkeley to take graduate level courses as undergraduates.</p>
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<p>This is also true at other schools and an important consideration for gifted math students who are considering some of the top LACs. (My son started taking grad courses his junior year.) I don’t know precisely what a rigorous math curriculum would look like but at Harvard a pure math major might start with Math 55 freshman year (honors abstract algebra and honors real and complex analysis) followed by more analysis and topology classes. Beyond that a lot depends on a student’s interests. [Harvard</a> Mathematics Department : Mathematics Courses](<a href=“http://www.math.harvard.edu/courses/index.html]Harvard”>Harvard Mathematics Department Administration and Finance)</p>
<p>Harvard’s math concentration is described here:
[Harvard</a> Mathematics Department :](<a href=“http://www.math.harvard.edu/pamphlets/prepair.html]Harvard”>http://www.math.harvard.edu/pamphlets/prepair.html)
[Harvard</a> Mathematics Department :](<a href=“http://www.math.harvard.edu/pamphlets/concentration.html]Harvard”>http://www.math.harvard.edu/pamphlets/concentration.html)</p>
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<p>(Half-courses are semester-long courses. Math 21 is regular sophomore level math including multivariable calculus, linear algebra, and differential equations. 100-level courses are junior and senior level courses.)</p>
<p>Harvard’s Math 55 is the most rigorous option of the following that math concentrators can take, though the others are accepted:
[Harvard</a> Mathematics Department : 21, 23, 25, or 55?](<a href=“http://www.math.harvard.edu/pamphlets/freshmenguide.html]Harvard”>http://www.math.harvard.edu/pamphlets/freshmenguide.html)</p>