I’m an international student very determined to choose pure math as my major, with a GPA of 4.0 and composite score of 36 in ACT.
I’ve already had some idea for my 1st choice university to apply for (Princeton), but I found it difficult to make a subsequent list of schools (maybe 3 to 6 schools) that are relatively easier to get into (with an acceptance rate higher than, say, 15% or 20%), but still somewhat fit my preferences.
I’m planning to study mathematics until I get a PhD (if I can), and I’ve already had a fairly well acquaintance on real analysis and abstract algebra (of the college level of abstraction and rigor), so I really wanted to find some school that allows math majors to get into the fresh, solid and rigorous mathematics as quickly as possible (instead of wandering in dull things like calculus or matrices for a long time). And for the more advanced math courses provided by the school, a higher rigor and quality will also only be more welcomed.
However, I don’t like the idea of getting into a school that’s mainly or almost only focused on STEM (e.g. MIT, Caltech, Harvey Mudd), because many areas of humanities, among them literature, history and art history, are also greatly attractive to me. I would consider choosing any of them as my minor if I can, or at least choose quite a few courses in these fields.
For these reasons, schools with both a strong math department and a solid background of liberal arts education attracts me most.
I’m not very outgoing, and don’t quite like both doing sports and being very social. Tuition is not a big problem, and the size of the school is also not a main consideration. I prefer to live in cities or towns better than rural areas (like Ithaca). Research universities and liberal arts colleges are both okay for me, as long as I can get an education that fits my preferences there.
If cost really is no issue ($75,000 per year), then some of the better state flagships might be good safeties. If you find two that you like, then you can take some shots at some of the bigger names.
I have a family member who got a PhD in applied math with a degree from Pomona so as long as you go somewhere “linked” with graduate programs it should be okay.
With that said the top feeder schools for math PhDs are
CalTech, Harvey Mudd, UChicago, MIT, Harvard, Pomona, Rice, Princeton, Swarthmore.
You should also consider Carnegie Mellon, Cornell, Northwestern, UCs, Case Western, JHU, and Virginia Tech
You’ll probably have a better chance at a research university with a good graduate math program where you can take graduate-level classes. Check U.S.News Best Graduate Mathematics Programs. For example, NYU is the ultimate urban school and easier to get into. Berkeley has one of the top math departments in the world, it’s still quite competitive to get in but less so than Princeton. U. of Michigan has a great math program if you’re OK with the location.
The Princeton Review prints a sampling, “Great Schools for Mathematics Majors.” Of the colleges included, UChicago, Harvard, Rice, URochester, Haverford, Reed and, with consortium options, HMC would meet most of your criteria, or would at least provide you with a few suggestions to screen further.
I thought the op was looking for ideas for schools with slightly higher chances than Princeton. I don’t think Pomona or cal tech qualify. I added Chicago because it’s a bit less but that the extreme end.
A student who has seen real analysis and abstract algebra in high school needs a research university with graduate level offerings in courses and research opportunities. I.e. the OP is the type of student for whom most LACs would not be good fits.
Perhaps Stony Brook, Rutgers, Minnesota, Illinois, and some other state flagships may be suitable as somewhat less selective alternatives, assuming affordability at list price. More selective, but not as selective as Princeton would be those like Berkeley, Michigan, UCLA, etc…
You sound like a good candidate for the University of Toronto and the University of Waterloo. They are much more straightforward in admissions than US universities.
By my calculations, the following are the 25 undergraduate institutions with the highest rates of alumni per capita PhD completions in math/stats over a recent 5 year window:
Harvey Mudd College (apparently, about 40% of graduating math majors earn PhDs)
California Institute of Technology
Princeton University
Swarthmore College
Oberlin College
Cornell University
Whitman College
Williams College
Haverford College
Amherst College
University of Chicago
Smith College (women only)
Stanford University
Massachusetts Institute of Technology
Grinnell College
University of Puget Sound
Rice University
Yale University
Harvard University
Bowdoin College
Georgia Institute of Technology-Main Campus
St Olaf College
University of Notre Dame
Lafayette College
University of Pennsylvania (apparently 10% of graduating math majors earn PhDs *)
Data Sources:
NSF/WebCASPAR (for PhD completions, 2011-2015 inclusive)
IPEDS (for graduating math majors, 2010-2014 inclusive)
The number of math majors for these schools ranged from 62 for Whitman to 523 at Harvard for the 5y period.
Expect big differences in course offerings, etc., across departments of such varying scale.
Keep in mind that many factors other than math instruction quality may be influencing these results
(“selection effects” as well as “treatment effects”). It may be the case that many alumni from some of the strongest schools choose more lucrative career paths than academia; small private schools may have higher concentrations of high income students who more easily can delay careers. Also, my “majors” window (2010-14) isn’t necessarily the best available representation for the number of alumni feeding my “completions” window (2011-15).
Nevertheless, this list may be helpful in suggesting colleges you might not have considered. St. Olaf, for example, is less selective than many of the others, yet seems to have a strong math department. But also keep in mind that course offerings at St. O. and some of the other LACs may be relatively limited compared to what you’d get at a bigger school. Oh, and I don’t think I have any way to compare the quality of grad schools where these alumni are earning their doctorates.
Universities where 5%-10% of math majors earned PhDs for the same tracking periods:
Columbia (~8%)
NYU
CMU
NC State-Raleigh
UC Berkeley
UC Santa Cruz
UFlorida
Ohio State
Arizona
Rochester
Utah
Colorado-Boulder
UC-Irvine
UC-SD (~5%)
Agreed, and OP’s preference for (sub)urban schools rules out quite a few LACs regardless.
It’s worth noting that math and humanities courses will be quite small even at the largest universities (<30 students at the largest, and probably a great deal smaller on average), thus negating one of the biggest advantages of LACs. Students majoring in disciplines like math and languages at universities get the best of both worlds – a wide array of course offerings, lots of research opportunities and resources, and small classes and faculty attention.
NYU sounds like a good fit. It’s very strong in math and, while still selective, is a bit easier to get into than the Ivies. It’s top-notch for art history too, though admittedly more so at the graduate level.
I agree with the posters above that the major public universities like Berkeley, UCLA, Michigan, UT Austin, etc. are well worth a look for math as well as the humanities, since cost doesn’t seem to be an issue.
Toronto in Canada is an excellent and cheaper alternative to the US (barring substantial financial aid at Princeton and comparable schools).
Carnegie Mellon could be a good low-match - they’re very reachy for certain majors (CS, musical theater) but for pure math I would think you’d be in good shape with your stats. They take the Putnam competition very seriously and like to have a competitive math cohort. They also have solid liberal arts. And a nice urban location in Pittsburgh. They accept lots of international students - 23% of their undergrad population.
If you don’t like the STEMminess of Mudd, you can major in math at any of the other four colleges and still take Mudd math classes. The art history, literature, and history offerings are excellent. And unlike most LAC’s, the 5C’s have a graduate division, Claremont Graduate University, from whose offerings qualified undergrads can also select classes https://www.cgu.edu/school/institute-of-mathematical-sciences/
Toronto is also an excellent suggestion that fits all of your criteria.
I like U of Maryland’s math program. Maryland is very strong in applied math, physics and CS as well, in case you change your mind and its right on a subway line to Washington DC. https://www-math.umd.edu
Beware that MIT limited international students to only 10% of freshman class, so its about a 0.1% chance there, but depends on factors like, did your parents attend college, being an underrepresented minority, gender, etc
Also do not overlook New York University Courant Institute ! https://cims.nyu.edu
Courant Institute is ranked number 1 in the USA for applied mathematics PhDs, ahead of Princeton.
Pure math is also outstanding at NYU, but Princeton is a fantastic choice. Check if Princeton limits international students in the freshman class. If they do, you need matches, for your stats and international status.
I love Gatech’s math program. Its got really strong discrete math, and combinatorics groups, if you
want to be on the intersection of CS and math, its truly one of the best. GaTech welcomes freshman to do
research in math, if you are ready. check out the Big O Theory Club at Georgia Tech:
If you major in math, its less crowded at GaTech than if you major in theoretical CS. Undergrads can major
in theoretical CS, and all undergrads pick two “threads” with theory as one of the options.
Note that both MIT and Caltech (and I think Mudd, but am not sure) require an average of one humanities/social science course per term. For MIT that would be a minimum of 8 classes and 12 for Caltech (semesters vs. quarters). MIT’s offerings in these areas are reportedly excellent. Caltech’s offerings are narrow, but sound interesting (https://catalog.caltech.edu/current/courses). Caltech also has a reasonably extensive program in the history and philosophy of science that is separate from the history and philosophy course listings.
In contrast, a number of other schools that have been mentioned have fewer requirements in the humanities and accept various types of AP and IB credit. For example, if my son had chosen CMU instead of Caltech, he would have been required to take only one humanities course in his entire 4 years.
Of course, many of the colleges listed here are especially reachy for internationals. Good luck!
If the OP is looking for a happy medium between small college ambience and the depth of a larger university, Wesleyan (17%) might make a less crap-shootey alternative to Princeton. A very theoretical department (don’t let the co-heading with CS fool you) that leans toward topology, Wesleyan - unusual for a LAC - awards its own doctoral degrees. Graduate courses are readily available to majors who burn through the course catalogue.
Any of the top public universities would be safety/matches for you as they tend to focus on stats more. So just choose two/three of them plus whatever other colleges you might want to try.