Comments on Math Departments of Various Schools

College Search & Selection
1

<p>I'll almost certainly be majoring in mathematics, and it is very important to me to go to school with a strength in the field. I have a pretty good idea of the zeroth tier schools I'd like to apply to (MIT, Chicago, Princeton, Caltech), but now I'm trying to comb through the tier one candidates. Currently my list consists of:
- Rice
- Vanderbilt
- WUSTL
- Duke
- Notre Dame
- Carnegie Mellon
- Johns Hopkins
- Northwestern
- Tufts</p>

<p>Regarding these schools, I have a few questions. Most importantly, what is your opinion of their math departments? For which schools is math considered a strong point, and for which is the focus primarily elsewhere? Specifically, I'm interested in pure math, in case that has any influence.</p>

<p>Addionally, are their any similar caliper schools that I glaringly left out? I know there's a continuum of goodness and that you could suggest schools right below or above this list all day, but are there any that indisputably sit comfortably in the middle?</p>

<p>A criticism I hear a lot from people reviewing lists is that it appears people simply amalgamated all of the schools ranked highest by some criteria, without regard to the atmosphere the school offers. On that note, are any of these schools "odd ones out" in terms of the students that go there? Are they all totally different, or is it possible to construct some equivalence relation between groups of them sharing similar characteristics?</p>

<p>Before I get any harshly worded replies, I'd like to say that this is very early in my college list generation process, so I have only very vaguely taken into account the all-important fit criterion. Thank you in advance for any help you can provide.</p>

2

<p>have you considered at all the most-important affordability criterion (it’s good to find a student using the correct singular of this noun, even when s/he spells caliber incorrectly)? have you run the net price calculators and taken the results to your parents? what are they willing to provide you each year?</p>

<p>Any of these schools will give you as good an education in math, if not pure math, as anyone could want. Some might be better than others for YOU. Can you afford any of them?</p>

3

<p>that’s not harshly worded. wait til you see some of your first college grades.</p>

4

<p>@jkeil911‌
I can definitely pay for them. Between financial aid, scholarships, and a nice college fund, the net price calculators and my parents agree that cost will not be too much of an issue (if two schools truly are identical in other respects, then it will start to play a role).</p>

<p>Surely they must be different in some respects. If real merits are all actually quite similar, than I’m willing to take into account prestige, especially in the eyes of those looking at graduate school applications. I’ve seen statistics regarding PhD productivity of undergraduate schools, and only Rice made the top 10 (if memory serves). Is Rice actually considered the best of the group, or this some weird quirk of the way the statistic was collected?</p>

<p>How do you no I’m not in the market for measuring tools in addition to collages? I can’t get buy with a low caliber caliper!</p>

5

<p>you’re right, OP, it could be =D> but I thought we were talking about colleges and not the visual arts ;)) </p>

6

<p>Are these colleges really all equally regarded in their math departments? If so, does anyone have any feedback on more personal experiences regarding math or the college at large?</p>

<p>To come up with this list, I basically took all of the non-ivy private universities with average SATs greater than 2100, so I find it hard to believe they are really very similar at all.</p>

7

<p>Given the quality of these departments and the fact that were discussing undergraduate math education, any differentiation of one school from another would be as worthwhile as the ranking systems that are out there. That is to say, the rank is going to depend on whom you ask and the different criteria each differentiator is using. </p>

<p>You might find, however, a school in the group that isn’t as strong as the others in pure theory, but I’m not the person to make that differentiation. Maybe there’s someone here who can.</p>

8

<p>Take a look at the faculty rosters, course catalogs, and class schedules to see what subareas of math each school’s math department emphasizes. Even though you may be undecided on a subarea emphasis, you may be able to see how broad each department is, and how deep it is in particular subareas.</p>

9

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<p>It’s hard to give a straight answer, because several factors can have confounding effects on PhD production rates. Students at some schools may be less inclined than students at other schools to seek academic or other careers that require PhDs (for reasons that may have nothing to do with instruction and mentoring quality). It is sometimes suggested, for example, that a large number of engineering majors at some schools depresses their per capita PhD production rates (since it’s easy for engineering majors to get good jobs without graduate degrees). However, among these 9 schools, Rice and CMU have by far the highest percentage of engineering majors (tied at 23%, compared to percentages in the teens for the others). All these schools are about equally selective; they all have roughly the same entering 75th percentile SAT-M/ACT-math scores.</p>

<p>Below are the number of PhDs earned by alumni of each of these 9 schools in mathematics/statistics between 2006 and 2010, according to National Science Foundation data on webcaspar.com. The absolute number of earned doctorates is shown in column 2. The ~current number of undergraduates (according to Wikipedia) is shown in column 3. The number of math/stat doctorates earned per 1000 undergrads for the 5 year period (assuming a constant number of undergrads) is shown in column 4. The 5th column shows the percentage of math/stat undergraduate degrees conferred (according to recent Common Data Set, section J data). The last (6th) column is my crude estimate of the percentage of math majors who earned PhDs from 2006-10 (assuming the number of math majors has been fairly flat … which may not be the case).</p>

<p>School…PhDs…Undergrads…PhDs per 1000 alumni…percent Math/Stat majors… PhD rate for math majors
Rice…42…3810…0.011… 5%…18%
CMU…20…6223…0.003…5%…5%
Duke…17…6495…0.003…2.6%…8%
ND…16…8371…0.002…2.9%…5%
NU…15…8459…0.002…3.4%…4%
WashU…12…7303…0.002…3%…4%
Tufts …7…5176…0.001…1.2%…9%
JHU…8…6023…0.001…2.4%…4%
Vand…9…6796…0.001…4.8%…2%</p>

<p>Calculating PhD productivity based on the number of math majors (math program size) is difficult; the number of graduating math majors for 2006-10 perhaps cannot very reliably be projected from the percentage of math majors shown in recent CDS section J entries. However, it does appear that Rice significantly out-performs the other schools in math/stat PhD production, either in absolute numbers or in the per capita rates. I suppose it’s possible that for some reason, Rice alumni are getting doctorates from weaker programs compared to other alumni. I suppose it also is possible that a small school like Rice is a relatively poor target for recruiting by firms offering lucrative jobs in fields like finance, business consulting, or IT (which may be luring more math majors at some of the other schools). Or, more math majors at some of the other schools may be drawn into medicine. Etc.</p>

<p>Nevertheless, I don’t think we can discount the possibility that, for whatever reasons, Rice is doing a better job of motivating and preparing math students for graduate work in mathematics. That doesn’t necessarily mean Rice has the “best” undergraduate math program. It may mean Rice has a relatively strong program (compared to these other schools), or more conducive atmosphere, for the kinds of students who want to earn math/stat PhDs . </p>

10

<p>I would check the us news on the rankings of pure math and applied math. Somehow these schools don’t pop up as the good in math on the next tier down. They are selective but have strength in different area.</p>

11

<p>I agree work DrGoogle that something is off. Rice and CMU and Duke are good but I’m not sure just picking non ivy with SAT scores above X who send some percentage to grad school means anything. It’s a start but you may miss some very good schools.</p>

<p>As long as this is really in the process, check out which schools do well in the Putnam exam, an annual math competition at the college level. Harvard and MIT trade first and second place but see what schools have 1)a large number taking the exam and 2) what schools fill out the top ten. It won’t necessarily tell you which school sends the most into PhD programs but you will know where top math students, defined by high competition scores, go to school.</p>

12

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<p>My son sat in on the Multivariable Honors math class. I think
it was the same one as this:</p>

<p><a href=“http://www.ratemyprofessors.com/ShowRatings.jsp?tid=223950”>http://www.ratemyprofessors.com/ShowRatings.jsp?tid=223950&lt;/a&gt;&lt;/p&gt;

<p>his opinion was that it was truly amazing. He was astounded at
how good the prof was. Ask him in a year if he agrees
that Rice Math has other outstanding teachers, but there appears
to be at least one. :)</p>

13

<p>Stanford also is zero tier for math, I think US news gave it a rank #5.
NYU, UCLA, Uof Wisconsin, UCSD, and University of Maryland are good. One of the Google founders went to University of Maryland for Math major(IIRC).
<a href=“Sergey Brin - Wikipedia”>http://en.wikipedia.org/wiki/Sergey_Brin&lt;/a&gt;&lt;/p&gt;

14

<p>@tk21769‌
That looks like about what I saw before. For whatever reason, Rice definitely stands out by those criteria. </p>

<p>@DrGoogle‌
Thats a good point. The top 50 math programs according to us news are:</p>

<h1>1 Massachusetts Institute of Technology</h1>

<h1>1 Princeton University</h1>

<h1>3 Harvard University</h1>

<h1>3 University of California—​Berkeley</h1>

<h1>5 Stanford University</h1>

<h1>5 University of Chicago</h1>

<h1>7 California Institute of Technology</h1>

<h1>7 University of California—​Los Angeles</h1>

<h1>9 Columbia University</h1>

<h1>9 New York University*</h1>

<h1>9 University of Michigan—​Ann Arbor</h1>

<h1>9 Yale University</h1>

<h1>13 Cornell University</h1>

<h1>14 Brown University</h1>

<h1>14 University of Texas—​Austin</h1>

<h1>14 University of Wisconsin—​Madison</h1>

<h1>17 Duke University*</h1>

<h1>17 Northwestern University*</h1>

<h1>17 University of Illinois—​Urbana-​Champaign</h1>

<h1>17 University of Maryland—​College Park</h1>

<h1>17 University of Minnesota—​Twin Cities</h1>

<h1>17 University of Pennsylvania</h1>

<h1>23 Rutgers, the State University of New Jersey</h1>

<h1>23 University of California—​San Diego</h1>

<h1>25 Johns Hopkins University*</h1>

<h1>25 Stony Brook University—​SUNY</h1>

<h1>25 University of Washington</h1>

<h1>28 Georgia Institute of Technology</h1>

<h1>28 Ohio State University</h1>

<h1>28 Pennsylvania State University—​University Park</h1>

<h1>28 Purdue University—​West Lafayette</h1>

<h1>28 Rice University*</h1>

<h1>28 University of North Carolina—​Chapel Hill</h1>

<h1>34 Carnegie Mellon University*</h1>

<h1>34 Indiana University—​Bloomington</h1>

<h1>34 University of California—​Davis</h1>

<h1>34 University of Illinois—​Chicago</h1>

<h1>34 University of Utah</h1>

<h1>39 CUNY Graduate School and University Center</h1>

<h1>39 Washington University in St. Louis*</h1>

<h1>41 Brandeis University*</h1>

<h1>41 Texas A&M University—​College Station</h1>

<h1>41 University of Arizona</h1>

<h1>41 University of California—​Irvine</h1>

<h1>41 University of Notre Dame*</h1>

<h1>46 Boston University*</h1>

<h1>46 Michigan State University</h1>

<h1>46 University of California—​Santa Barbara</h1>

<h1>46 University of Colorado—​Boulder</h1>

<h1>46 University of Southern California</h1>

<h1>46 Vanderbilt University*</h1>

<p>I probably mislabeled some, but the ones with * are private, non-zeroth tier, non-ivy colleges. In order, they are:</p>

<h1>9 New York University</h1>

<h1>17 Duke University</h1>

<h1>17 Northwestern University</h1>

<h1>25 John Hopkins University</h1>

<h1>28 Rice University</h1>

<h1>34 Carnegie Mellon University</h1>

<h1>39 Washington University in St. Louis</h1>

<h1>41 Brandeis University</h1>

<h1>41 University of Notre Dame</h1>

<h1>46 Boston University</h1>

<h1>46 Vanderbilt University</h1>

<p>Only Tufts appears on my list but not this one, but NYU, Brandeis, and Boston are all on this list but not mine.
Usual us news disclaimers apply. </p>

<p>@SlackerMomMD‌
Duke, CMU, Rice, and NYU are the only ones to make any notable appearances in the competitions history, in that order (satisfying the previous criteria). Out of those, only Duke and CMU have placed in recent years. </p>

15

<p>It looks like NYU was the only notable university I missed. Are there any others that belong in the group I mentioned?</p>

<p>On the other side of the spectrum, most rankings place Tufts, Vanderbilt, and Notre Dame below the others for math. Is it accurate to say that their specialties lie outside mathematics?</p>

16

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<p>It seems that Harvard and MIT have dominated the winner’s circle in recent years, with Caltech and a few other schools bringing up the rear. Of the 19 Putnam Fellows since 2008, 11 have been MIT students. 4 have been Harvard students. Since 1990, 23 Harvard teams have finished in the top 5; 18 MIT teams have finished in the top 5. (<a href=“William Lowell Putnam Mathematical Competition - Wikipedia”>http://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition&lt;/a&gt;)</p>

<p>If you are looking for math programs a tier or two down from Harvard and MIT, I doubt Putnam results will be all that helpful. There are too few winners representing too few colleges. The data on PhD completions represents a much larger number of good outcomes (if you’re trying to compare more than a few super selective schools.)</p>

17

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<p>It appears you are looking only at research universities. In case you also want to consider small liberal arts colleges, you might want to consider the following schools:</p>

<p>42 Harvey Mudd College
21 St Olaf College
20 Williams College
19 Swarthmore College
17 Reed College
16 Carleton College
13 Oberlin College
13 Wheaton College (Wheaton, IL)
12 Whitman College
10 Pomona College</p>

<p>These LACs (and apparently no others) generated 10 or more math/stat PhDs from 2008-2012, according to NSF data. The first column shows the number of math/stat doctorates earned by alumni during this period.
Compare these numbers to the numbers for the 9 research universities listed in the original post. Except for Rice, all those universities are much larger schools than these LACs. Reed alumni earned as many math/stat PhDs as Duke alumni in this 5 year period (even though Duke enrolls more than 4X as many undergraduates as Reed). </p>

<p>Besides PhD production and Putnam winners, another indicator you might want to consider is undergraduate research activity. Look for lists of senior thesis titles, student publications, etc., if available.
<a href=“http://www.math.duke.edu/news/awards/research.html”>http://www.math.duke.edu/news/awards/research.html&lt;/a&gt;
<a href=“http://academic.reed.edu/math/theses.html”>http://academic.reed.edu/math/theses.html&lt;/a&gt;
<a href=“http://library.williams.edu/theses/dept.php”>http://library.williams.edu/theses/dept.php&lt;/a&gt;&lt;/p&gt;

18

<p>For the OP who has already taken junior/senior level college math courses like real analysis (mentioned in another thread), evaluation of math departments must include checking whether they have enough advanced and graduate-level offerings to keep the OP interested. This is especially with small LACs.</p>

19

<p>Here is a list of 22 advanced math courses at Vanderbilt:
<a href=“http://as.vanderbilt.edu/math/undergraduate/course_descriptions/”>http://as.vanderbilt.edu/math/undergraduate/course_descriptions/&lt;/a&gt;&lt;/p&gt;

<p>Here is a list of math courses at Williams:
<a href=“http://math.williams.edu/courses/”>http://math.williams.edu/courses/&lt;/a&gt;&lt;/p&gt;

<p>By my count, Williams offers 47 math courses at the 200 level or above, not including the Senior Thesis, Independent Study, or statistics courses. Now, colleges don’t offer every course in the catalog every term.You can look up term by term offerings here:
<a href=“http://catalog.williams.edu/catalog.php?&subjinfo=math”>http://catalog.williams.edu/catalog.php?&subjinfo=math&lt;/a&gt;
By my count, in Fall 2014 Williams offers 12 math courses at the 200 level or above (again, not including the thesis, independent study, or statistics courses.) That’s far more courses than anyone could take at one time, although of course they do not necessarily cover every advanced topic in mathematics that might be available at other schools. Keep in mind, though, that the faculty at LACs like Williams have no grad students, so they are relatively free to commit time to thesis and independent study courses.</p>

<p>Here’s a list of the ~19 Mathematics faculty members at Williams:
<a href=“Faculty & Staff – Mathematics & Statistics”>http://math.williams.edu/faculty/&lt;/a&gt;
That’s ~19 Mathematics professors for 68 graduating Math majors between July 1, 2012 and June 30, 2013 (according to the 2013-14 Common Data Set). Those faculty members all hold PhDs (from Stanford, Princeton, Texas, Wisconsin, Rochester, Penn State, JHU, Brown, Oregon, Florida, Caltech, and Michigan.) With a professor for every ~3.6 graduating math majors (and no grad students), I would expect that (unless the OP is a truly extraordinary young mathematician) the faculty has enough knowledge and time to cover his interests in independent study or thesis courses, in case those interests are not already covered in the regular offerings. </p>

<p>Williams is an exceptionally rich college. Few other LACs (not even all the other 9 listed above) will offer the same level of resources. If you do want extensive advanced course offerings, ucbalumnus is right to suggest that you should carefully check the course listings (and faculty rosters).</p>

20

<p>

IPEDS conveniently gives us the number of math/stats majors produced by each school from the class of 2010 to the class of 2013.</p>

<p>CMU: 55, 54, 73, 72
Duke: 33, 37, 47, 38
JHU: 32, 35, 39, 43
Northwestern: 59, 63, 54, 59
Notre Dame: 43, 28, 35, 52
Rice: 25, 33, 34, 52
Tufts: 22, 19, 14, 17
Vanderbilt: 28, 21, 19, 30
WUStL: 31, 33, 42, 34</p>

<p>Totals for the 4 years:</p>

<p>254 CMU
235 Northwestern
158 Notre Dame
155 Duke
149 JHU
144 Rice
140 WUStL
98 Vanderbilt
72 Tufts</p>

<p>PhD totals for the 4 most recent years (2009-2012):</p>

<p>CMU: 6, 6, 2, 5
Duke: 4, 5, 4, 3
JHU: 1, 1, 2, 1
Northwestern: 4, 2, 0, 4
Notre Dame: 3, 1, 2, 4
Rice: 10, 9, 7, 1
Tufts: 1, 2, 1, 2
Vanderbilt: 5, 0, 2, 0
WUStL: 3, 6, 1, 5</p>

<p>Totals for the 4 years:</p>

<p>27 Rice
19 CMU
16 Duke
15 WUStL
10 Northwestern / Notre Dame
7 Vanderbilt
6 Tufts
5 JHU</p>

<p>Percentage of math students earning a math PhD:</p>

<p>18.75% Rice
10.71% WUStL
10.32% Duke
8.33% Tufts
7.48% CMU
7.14% Vanderbilt
6.34% Notre Dame
4.25% Northwestern
3.36% JHU</p>