<p>Please rank these schools based on the strength of their undergraduate math departments. To be more specific, I'd especially like to know which of them offers the best preparation for a further research career in mathematics(rather pure than applied). The more details you can provide, the better.</p>
<p>Cornell University
Duke University
University of Chicago
University of Pennsylvania
Williams College</p>
<p>First of all, there’s no such thing as an “undergraduate math department,” except perhaps at Williams where there are no graduate students. The other four are all comprehensive research universities with major-league math departments, and from the standpoint of an undergraduate, any of them can teach you what you need to get to the next level, and you aren’t going to come anywhere near exhausting what they offer in four years. I have a general sense that Chicago is half a notch above the other three, especially as far as pure math is concerned (and probably a full notch below them for applied math, which when it happens at Chicago tends to get called “economics” or “biology” or “statistics”. Chicago is a very math-y place, and math is an extremely popular major or second major. Penn, Cornell, and Duke all have really good departments, too. But each of them only has about half the number of math majors that Chicago has, and many more of them are doing applied math. (Plus, at Penn, there are 400 or so finance majors at Wharton, and that kind of shifts the atmosphere some.) The undergraduate pure math community at Chicago is pretty special.</p>
<p>Honestly, however, unless you are an absolute prodigy (in which case Chicago is one of the places where you are more likely to find some peers), you should probably make your decision among those schools based on factors other than the strength of the math program, because the strength of the math program will be one of the things that is least different among the four, and there are lots of other things that are really different.</p>
<p>Williams is in some ways a totally different model of how to get an education. I don’t know as much about the math department there, but I can say categorically that it is also probably great, in a somewhat different way. Chicago probably has 30 or so active professors, 10 emeriti, and maybe 20 lecturers at any time, plus 100 or so grad students, and maybe 350-400 undergraduates majoring in math or statistics. That’s a huge community, with lots of people with very focused interests. Williams has about 18 active professors (some of whom may be on leave at any point, which is also true everywhere else), which is in fact pretty impressive, and based on its website maybe 150 majors, which is also really impressive given the size of the college. (But it only graduated 21 people whose primary major was math last year, so lots of those are second majors). The ratio of faculty to majors is better at Williams than at Chicago, and there are no graduate students to compete for attention.</p>
<p>Williams doesn’t have the breadth of courses or volume of cutting-edge research that any of the research universities has, although what it has is probably pretty good. But what Williams has that Chicago doesn’t have is faculty whose main job is teaching undergraduates, and who precisely because they don’t necessarily have a world-class expert in everything are willing to take responsibility for making certain you learn what you need to learn to provide the base for what you want to do next. At a research university, you can absolutely get a world-class education, but you can also have important gaps in what you have learned because no one will really be checking to make certain you have a solid base. That will be your responsibility (although I’m sure it is easy to get advice if you ask). At Williams, especially given their tutorial structure, people will actually make certain that you are super-prepared for graduate school, if that’s where you want to go.</p>
<p>Basically, at Williams, you will probably wind up attaching yourself to two or three faculty members, and letting them guide you in lots of ways. You would do exactly the same thing at Penn, Cornell, Duke, or Chicago. You would have more people to choose from at those schools, and they would have more on their plates to keep them from totally focusing on what you need. You will also be a smaller fish in a much bigger pond.</p>
<p>If you look at the Williams Math Department web page, you will see that seven of last year’s graduates went directly into PhD programs. None of them are in pure math; all are some applied field – Computer Science, Computational Biology, Earth and Atmospherics, Cognitive Psych. All are at great, great programs, by the way. Most of the majors are working in financial industry jobs and management consulting, which will be true of all of the schools you are looking at. In other words, it’s clear that Williams turns out successful math majors; it’s a little less clear that it turns out successful pure math PhD students.</p>
<p>^I second everything said above. There’s no ranking of undergraduate math departments (or really, undergraduate anything besides perhaps business and engineering), so you should select your college based on other factors. ANY of these schools can be a platform for acceptance into graduate school. Chicago, Cornell, and Penn are obviously large research universities with tons of professors on the cutting edge of pure math research. There’s no doubt that the math professors there are excellent researchers from top departments; if you join their working groups/work with them you’ll learn a lot about research and what’s new in the field. Your intro math classes will probably be quite large, but once you get into upper-level classes they’ll be smaller seminars.</p>
<p>One thing I know about the pace of the math classes at these elite institutions (my husband’s a math major at an Ivy League, a top 5 department) is that they go very quickly. It’s an intense experience. It’s also a little bit sink-or-swim, a condition my husband has expressed frustration with. But there’s support - advanced undergrads and grad students run the math help room, where you can seek tutoring help with your work. Plus, if you really want a fast-paced and intense experience, one of those departments can be good for you.</p>
<p>Williams - being an elite SLAC - recruits professors on the basis of being really excited and passionate about mentoring undergraduates in math AND being good solid researchers. If you check out the faculty profiles of the math department, you’ll see that they got their PhDs at top math departments (most in the top 20); many of them did research post-docs before beginning at Williams; they are all active in research; some of them even take research sabbaticals and bring their work back for their undergraduates to help them with. And since Williams gets their pick of the litter when hiring, they hire people who are both excellent researchers and great teachers, enthusiastic about working closely with undergraduates and mentoring them.</p>
<p>But consider other factors, too. Do you want the SLAC experience, a medium-sized university, or the large public/private hybrid that is Cornell? Chicago is known for being a quirky nerdy school, so you may feel at home there - or if that’s not you, you may feel alienated. Chicago and Penn are in the middle of large urban areas; Cornell and Williams are in more suburban and rural-ish areas with not much going on around but the school. That could be a GOOD thing, though, as it keeps people on campus on the weekends and often provides for a very vibrant campus life.</p>
<p>All the above is better advice than I can give. And I would lean toward Williams as a personal preference just because I like LACs, and you’ll undoubtedly get the university experience as a grad student, but YMMV. </p>
<p>However, the best math student I have ever known, and will likely ever know, chose Chicago over a whole bunch of other schools last year. He is so far beyond brilliant that you can’t comprehend how good he is at math. He could do his Calc III homework in the car on the way to school every morning. It’s a 15 minute ride and he was in 8th or 9th grade. No studying, to him math is like breathing. I imagine most of his undergrad work in math will be at the grad level, since he’s already mastered a lot of the undergrad level math. He’s also a little quirky, but has toned it down considerably in recent years. Sort of like a sane John Nash. That’s the calibre of the top talent at Chicago.</p>
<p>MrMom62, you will find students such as the one you describe at all 5 of these universities. These are all among the 15 most prestigious institutions to receive an undergraduate education in the United States. All 4 of the research universities have 20 Math Graduate programs as well if the OP is an incredibly advanced math student.</p>
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<p>Probably any school with a good math department has a few of those students who come in ready to go right into junior, senior, or graduate level math courses at frosh entry (I remember encountering a few when I was in college). If the OP is such a student, attending a school with a good graduate program in math is likely indicated, since graduate level course work and research opportunities as an undergraduate are likely needed to keep such a student interested.</p>
<p>^^That’s a good point.</p>
<p>FWIW, the accomplishments of the student I know are quite far beyond even the most accomplished HS math students. I don’t wish to identify him further, but let’s just say he was easily one of the top 15 math students in the country for his age group, and to lower the further would only identify him with a little detective work. I’ve never met a real prodigy before him, and his parents are super nice. They are the furthest thing you can imagine from Tiger Parents.</p>
<p>thank you, all. I learned so much from these posts.</p>
<p>UCLA seems to have gotten its share of math prodigies:
<a href=“Newsroom | UCLA”>http://newsroom.ucla.edu/portal/ucla/at-just-14-ucla-math-student-moshe-229359.aspx</a> (student)
<a href=“14-year-old math, chess prodigy enrolls at UCLA | UCLA”>http://newsroom.ucla.edu/portal/ucla/14-year-old-math-and-chess-prodigy-248334.aspx</a> (student)
<a href=“Terence Tao - Wikipedia”>http://en.wikipedia.org/wiki/Terence_Tao</a> (faculty)</p>
<p>I’d personally go with one of the research universities. Try going for a combination of department strength and fit. Unlike the liberal arts (e.g. majors with lots of writing,) I don’t think LACs are well suited for math students. One of my math professors in CC once said that math was one of those things like music where you either had the talent in it or you didn’t. I tend to agree. I don’t see a LAC conferring many advantages over an RU, but i do see it as conferring disadvantages (lack of advanced graduate classes for the student to take.) Universities also have larger faculty, exposing you to more classes, more subjects, and more leading researchers. If you’re really heavily interested in math and want to focus on research, i highly advise picking one of the universities you listed above.</p>
<p>Many of the Putnam competitors in mathematics overwhelmingly go to research universities too, as you can see here:</p>
<p><a href=“Putnam Competition Individual and Team Winners | Mathematical Association of America”>http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners</a></p>
<p>And since I’m most familiar with the institution, here’s a story about some recent UCLA students who did well in the Putnam competition and their experience with the professors and department. Here’s a quick excerpt from the students in the article:</p>
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<p><a href=“UCLA math students place third in prestigious North American competition | UCLA”>http://newsroom.ucla.edu/portal/ucla/ucla-s-student-math-team-is-3-246022.aspx</a></p>
<p>If you are already very advanced in math (i.e. completing college sophomore or higher level math while in high school), then your choice may want to include consideration of the graduate level subareas and how they may interest you. Both pure and applied math at that level have many subareas, so checking the faculty rosters, research areas, and graduate level course offerings (which are often seminars of faculty recruiting students into their research areas) at each school may be helpful in terms of finding the best fit math department for your and your interests. Start at the math department web sites; you may want to contact faculty members directly if you have more questions.</p>
<p>Of course, as an undergraduate, you will encounter general education requirements, so you may want to see how each school’s general education requirements fit your academic interests. If you are also interested in math-related fields like economics, computer science, statistics, physics, industrial engineering / operations research, etc. you may want to check each school’s offerings in those areas.</p>
<p><em>deleted</em> </p>
<p>I’ll respond to your PM instead.</p>
<p>So; disari, what did you decide, and why? Your decision-making process would be very useful to other students.</p>