Can anybody suggest which of these would be the best for pursuing a Bachelor’s degree in Math?
Most Interested in Pure Math topics like Differential Equations, Analysis, Algebraic number theory.
But also like intersection of Math with other fields like Mechanics, Electrical Engineering, Computer science, etc.
Also would love if I could minor in Computer Science/Machine Learning. So I would prefer a college among these that is not only great for Mathematics but also decent for CS, Engineering, etc.
Which college has the best teachers? Which one has most reputed faculty?
My son is also thinking about a double math/CS major. We haven’t researched Duke much. CMU’s math department is more oriented towards topics related to applications and computer science and less pure math, but they have pure math courses as well. Yale is ranked a bit higher and harder to get into than Cornell, but both would be great for you.
Cornell, Duke, and Yale are all excellent options for math, and I’ve met impressive mathematicians from all three. (My partner is a math lecturer at a top private university.) I haven’t run into anyone from CMU, but it’s obviously a good option for anyone interested in CS.
The schools differ far more in nonacademic factors (setting, size, feel/atmosphere, etc.) than in the quality of their math departments, at least at the undergraduate level. Relatively few students prefer small town Cornell and urban CMU equally.
You might want to compare the online faculty biographies and course offerings (not just the catalog listings but the term-by-term lists of courses that actually are offered).
You can find a few math program rankings online. USNWR does one. AFAIK, they all focus on graduate programs, but presumably there is trickle-down benefit to undergrads if the graduate program quality is high.
Also, using the NSF/WebCASPAR database, you can generate comparative statistics on alumni-earned math/stat PhDs. Since school and program sizes differ, you may want to use the IPEDS database to pull the number of math majors in each program, then calculate the ratio of alumni-earned doctorates adjusted for the number of majors.
For what it’s worth, here are the numbers I get for Cornell, Duke, Yale, and CMU (as well as for a few schools with similar or higher ratios):
PhDs …Majors … Ratio … School
52 … 138 … 0.377 … California Institute of Technology
33 … 96 … 0.344 … Harvey Mudd College
59 … 174 … 0.339 … Princeton University
26 … 130 … 0.200 … Williams College
38 … 194 … 0.196 … Cornell University
44 … 259 … 0.170 … Stanford University
66 … 451 … 0.146 … University of Chicago
58 … 397 … 0.146 … Massachusetts Institute of Technology
25 … 176 … 0.142 … Yale University
65 … 523 … 0.124 … Harvard University
23 … 208 … 0.111 … Duke University
34 … 346 … 0.098 … Carnegie Mellon University
The “PhDs” column represents the number of math/stat PhDs completed by alumni in the years 2012-16 inclusive (source: WebCASPAR).
The “Majors” column represents the cumulative number of math/stat majors who graduated from each college in the years 2010-14 inclusive (source: IPEDS).
Lots of caveats apply to data tables like this. For example, many students in excellent math programs don’t choose even to pursue math/stat PhDs. Also, 2010-14 may not be the very best window of time to represent the number of math majors for those who earned PhDs in 2012-16. And (maybe most importantly): nobody else reviewed these numbers before I posted them.
To me, assuming I got the numbers right, the take-away message is that all 4 of the cited colleges (CMU, Duke, Yale, Cornell) seem to generate roughly 100-200 math/stat PhDs per 1000 math/stat majors. Cornell is a little higher than the other 3 (for whatever reason); none of them generate as many per thousand as the tip-top producers (Caltech, Mudd, Princeton). However, all 4 are roughly in the same ballpark, by this metric, with some other universities (like Harvard) that seem to have very strong math programs.
tk21769, that is a lot of research! Well, as you said, there are many caveats to data tables like these. I think CalTech and Harvey Mudd are ranked highly for being small sized prestigious universities, hence a high PhD/BS ratio.
I feel this gives me an indication of how good the research and PhD program is, and not so much about the undergraduate experience. Like CMU seems to attract IMO medalists a lot these days, but doesn’t offer that great a PhD program in pure Math fields.
I sort of don’t trust graduate school rankings apart from the speciality rankings in USNWR. For example, NYU is highly ranked for Applied Math & Analysis because of Courant. I love both fields and checked out the CIMS website to find out about the UG program in Math. I sent a mail to the admissions officer; turns out, Courant is just for graduates!!
But I feel the speciality rankings are good nonetheless because I found out about Stony Brooks- a very underrated Math school-which has a few Fields Medals affiliations and is in Top 10 for Topology and Geometry.
Nonetheless, thanks for the data.
I’ll surely check out professor profiles at each Math department.
Could anybody still talk about first hand experiences about undergraduate programs in Math-related fields at these universities?
@NeoAnderson23 I’m a math major at stony.
Just to be clear, those statistics represent the number of alumni from each listed college - undergrads - who go on to earn math/stat PhDs.
Here’s another ranking you might find interesting:
https://thebestschools.org/features/best-mathematics-programs-in-world-today/
The narrative descriptions of each program may be more valuable than the rank order (which is quite different from the USNWR ranking in some cases.)
You can Google for other rankings (NRC, etc), maybe just to see which schools seem to show up near the top most often. The one I just linked seems to offer some of the most detailed descriptions.
Thanks!
If this were just math, it would be straightforward, but the inclusion of computer science, esp machine learning and the intersection would lean to CMU, actually a heavy lean. CMU is ahead of the other three colleges in that area, considerably ahead. Only Stanford and MIT, maybe Berkeley are in CMU’s class.
Hey theloniusmonk, what would be the straightforward choice for bachelors in pure math according to you?
Here is a math ranking based on highly competitive NSF undergrad research awards (over 10 years) normalized by number of graduates.
Cornell, Duke and Yale are close enough to be considered equal and CMU comes out lower.
CTech 20 0.74
Princeton 25 0.71
Reed 3 0.43
Mudd 13 0.41
MIT 36 0.38
Stanford 19 0.31
Harvard 39 0.25
Cornell 9 0.21
Duke 10 0.21
Williams 5 0.19
Yale 9 0.19
Oberlin 4 0.18
Tufts 3 0.18
UChicago17 0.15
Bryn Mawr 4 0.14
G Tech 5 0.13
Dartmouth 3 0.11
RPI 4 0.11
Columbia 8 0.09
ND 4 0.07
St Olaf 3 0.07
UNC 8 0.07
UMCP 9 0.07
CSOM 3 0.07
Michigan 12 0.06
Wash U 3 0.06
Pitt 5 0.06
U Ill Chicago 3 0.06
CMU 5 0.05
And here are the winners of the Putnam awards for the last 10 years. “It is widely considered to be the most prestigious university-level mathematics competition in the world, and its difficulty is such that the median score is often zero (out of 120) despite being attempted by students specializing in mathematics”
1st > > > 5th place
2007 Harvard Princeton MIT Stanford Duke
2008 Harvard Princeton MIT Stanford Caltech
2009 MIT Harvard Caltech Stanford Princeton
2010 Caltech MIT Harvard UC Berkeley Waterloo
2011 Harvard Carnegie Mellon Caltech Stanford MIT
2012 Harvard MIT UCLA Stony Brook Carnegie Mellon
2013 MIT Carnegie Mellon Stanford Harvard Caltech
2014 MIT Harvard RPI Waterloo Carnegie Mellon
2015 MIT Carnegie Mellon Princeton Stanford Harvard
2016 Carnegie Mellon Princeton Harvard MIT Stanford
2017 MIT Harvard Princeton Toronto UCLA
link: https://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition#Top-scoring_teams