<p>The University of Chicago math department posts a graduate student directory
(<a href=“People | Department of Mathematics | The University of Chicago”>People | Department of Mathematics | The University of Chicago).
Many of the listed graduate students post CVs that show where they got their undergraduate degrees.
Represented colleges include:
Caltech
UIUC
UC Berkeley
Brown
ISI, India
MIT
Princeton
Haverford
University of Arizona
Stanford
NYU
Toronto
Bard
Reed
Duke
Barnard
McMaster University
Harvard
Morehouse
Queen’s University
Waterloo</p>
<p>This list is not exhaustive (since some students don’t post a CV).
However, it’s enough to indicate that Chicago’s rather large, distinguished math department gets students from a pretty broad cross-section of colleges (including Ivies and other elite private universities, LACs, state universities, and non-US institutions). Highly selective colleges (of various types) do seem to be over-represented.</p>
<p>The two outliers on that list seem to be Bard and Reed. The others graduate students all seem to come from major research universities or LACs next to major research universities.</p>
<p>^ Haverford isn’t really next to a major research university. It does have a consortium relationship with UPenn, but that relationship doesn’t seem to be as close as its “bi-colllege” relationship with nearby Bryn Mawr or its “tri-college” relationship with Bryn Mawr and Swarthmore. </p>
<p>Thank you to everyone for your suggestions and insight so far. Mudd, Williams, Bard, Haverford and Reed will definitely go on my list. I will also make sure to explore Chicago, Caltech and Harvard as options (Math 55 certainly seems quite interesting- thanks for the tip!). </p>
<p>If anyone else has any suggestions or can share some of their experience at any of these schools, I’d love to hear. </p>
<p>(I’d caution against placing too much emphasis on Ph.D production–brilliant mathematicians go on to work in many fields outside academic mathematics!)</p>
<p>^I was going to say the same thing as @marvin100 - PhD production can be used as a supplemental piece of information, but I wouldn’t put too much emphasis on it, especially if you don’t plan to get a PhD yourself. There are a lot of things that influence PhD production aside from the rigor of a mathematics program.</p>
<p>I know you’re looking for small liberal arts colleges but I would encourage you to consider Columbia, too; while I’m hesitant about the overgrown-LAC characterization in general (there are a lot of things that separate large research universities from small LACs, and the professional schools are not just “attached” but are integral parts of the university), I think it can roughly apply in this case. The intro classes are not that large - but you’ll skip over all of those and be in small seminars. Columbia’s math department is highly theoretical (one of the reasons my husband actually switched out of it, to statistics, lol) but there are classes you can take in a lot of math-related fields to explore what you can do with the degree - finance, engineering, operations research, some actuarial-sciences-related classes, statistics, etc. The student body is ~6,000 students which is more medium-sized, but it can feel smaller than it is.</p>
<p>No insult intended about Ivies being overgrown LACs, but I think you know where I’m coming from - Ivies grew out of the LAC tradition, whereas most large research-based universities grew out of the land-grant/A&M type schools. Yes, I know that’s not universal, but it a good generalization and explains how Ivies are not really like Big State U.</p>
<p>I would too … but what are some better objective measurements?
Of the schools near the top in PhD production, which ones are false positives?
By what measure?
What are some notable false negatives? By what measure?</p>
<p>Certainly, many brilliant mathematicians choose not to get PhDs (and nevertheless have excellent career outcomes). This may be why a few schools with super duper math departments AND good undergraduate focus aren’t right at the top of the normalized rankings. So no, one shouldn’t necessarily conclude that Oberlin has a “better” math department than Harvard or Chicago. No ranking should be used to make final choices between closely ranked colleges. And by “closely ranked”, I’d include schools that may be 10 or 20 positions apart.</p>
<p>Nevertheless, in my opinion, PhD production is one of the better objective proxies we have for measuring undergraduate academic program quality. Whether you plan to get a PhD or not, if you care about academic quality, it should interest you to know that a program is (or isn’t) attracting, motivating, and preparing many students to succeed at that level. I think PhD production (like many other objective measurements) can be a good discovery tool for building an initial list of ~10-20 colleges to look at more closely before settling on your application choices.</p>
<p>Your list of possible LACs might (should?) depend on what you plan on doing for a career. </p>
<p>You said that you’re interested in schools where pursuing other non-math fields would be encouraged. Encouraged by whom? If you see yourself in a career at a research university, in mathematics, then the people who would eventually decide your future probably would not encourage you to explore fields outside of math in much depth. Generally, they want to see maximum depth and rigour in math, which is very hard to attain at a LAC. </p>
<p>What are your career goals? Private industry? What type of private industry? Teaching? Research?</p>
<p>How interested are you in the other fields you mentioned? Are you passionate enough about them that you could be steered away from math, as a career? </p>
<p>The other thing that makes me hesitant about using Ph.D production as a marker of undergraduate strength in a discpline is growing anecdotal evidence that this is also a marker for financial means. It’s pretty obvious to me that a lot of talented kids are either postponing graduate school or foregoing it altogether because they feel - for a variety of reasons that they can’t afford it. If you look at @tk21769 's rankings for the 2012-2013 period, they seem almost indirectly proportionate to the percentage of Pell Grant recipients on each campus:</p>
<p>31% Harvey Mudd
23% Caltech
19% Princeton
19% Reed
19% Oberlin
18% MIT
17% Cornell
15% Swarthmore
12% Harvard
10% Haverford
9% Chicago
9% Williams
9% Grinnell
9% Stanford
6% Columbia
5% Berkeley
4% Macalester
4% Bryn Mawr
4% Michigan
4% Amherst
3% Holy Cross
2% UCLA</p>
<p>However, the OP is a rather unusual student, who (from other postings) is taking an honors college sophomore level math sequence as a high school junior. As such, there may be many schools including LACs where the OP would run out of advanced math courses, even though such schools may be perfectly suitable for math majors who start college with having just completed AP calculus in high school.</p>
<p>PhD production is also influenced by the kind of students the school attracts. At many of the non-LAC schools, even those students choosing liberal arts majors (e.g. math, biology, political science, English, economics) often have pre-professional motivations (i.e. other than PhD as their goal). Also, the heavier employer recruiting at bigger schools may draw some students away from the PhD path.</p>
<p>You seem to be suggesting that schools near the bottom of the list above (UCLA, Michigan, Berkeley) may have undergraduate programs stronger than (or as strong as) schools near the top (Harvey Mudd, Caltech, Princeton). It’s just that fewer UCLA, Michigan, Berkeley students can afford to pursue PhDs. </p>
<p>That is one possible explanation. However, I would think the burden of proof is on you to show some other math-dependent outcome in which UCLA etc. out-perform (or perform equally well). PhD students generally are fully funded by their programs with full tuition scholarships and stipend money. This may not help enough if you leave college with heavy debts (although Berkeley and UCLA happen to have lower average debt at graduation than Harvey Mudd.)</p>
<p>An alternate explanation is this:
small colleges (private universities and LACs) tend to provide better student-faculty engagement, which tends to outweigh the benefits of wide course selection. So, even students who arrive well-prepared can find ample opportunities for advanced research with good faculty mentoring. </p>
<p>^I’m thinking specifically of the case of Swarthmore and Amherst, two schools widely considered comparable in just about every conceivable measure. Yet, inexplicably, they are separated by 11 ranked placess in your list. Is it a coincidence that Amherst has the highest percentage of Pell Grant recipients among selective LACS while Swarthmore has among the lowest? I think not.</p>
<p>That may be a factor.<br>
However, note that Amherst confers a relatively small percentage of degrees in STEM fields, compared to some other LACs (such as Carleton and, if memory serves, Swarthmore). Compare the mathematics staffing and course offerings of these two schools. You might conclude that Amherst’s department is relatively weak compared to some other LACs’.</p>
<p>If demographics accounted for Amherst’s relatively low position in my list above, why wouldn’t the same factors apply to its PhD production in the humanities? </p>
<p>So I think PhD production can be a useful metric not only for exposing relatively strong colleges (including colleges that aren’t otherwise very highly ranked), but also for exposing strong departments within colleges. I’m thinking for example of Colorado College, which has relatively high PhD production in geology, or Eckerd College, which has relatively high PhD production in oceanography. </p>