When planning which University to attend as an undergraduate, the issue of which programs there are strongest is actually secondary. The most important criterion is whether you’re a good fit. If you like the academic competitiveness, the culture, and the setting, that’s the place to go. Rankings are much more of an issue for graduate study, and the graduate department rankings are usually the best measure of an institution’s strength.
The list of top schools to do math at is populated heavily with what one might call “the usual suspects” – those institutions that excel in almost every field: Massachusetts Institute of Technology (MIT), Harvard, Princeton, Stanford, University of California – Berkeley, University of Chicago, California Institute of Technology (CalTech) and Yale, in that order, from very strongest to the slightly less strong. In the US News and World Report rankings, these schools are almost all tied for the top spot, and there is no serious distinction between in terms of strength.
At the graduate level, each will be stronger or weaker in various subspecialties, but this will have no bearing on a student’s undergraduate experience, or on the student’s ability to be admitted into a math graduate program after graduation.
The top-10 schools are, unsurprisingly, extremely difficult to get into. Although some academic superstars can be assured admission to them, most aspiring math students should look elsewhere, to lower ranked schools that have comparable undergraduate programs. Also, students of limited financial means ought to consider public universities, which will generally have much lower tution and fees, and will also have more opportunities to get merit based financial aid and grants. A sampling of alternative schools: Northwestern University, University of Texas – Austin, University of Wisconsin, University of Minnesota, Rutgers, University of California – San Diego, Duke, and Johns Hopkins.
The aspiring math graduate student should major in math or physics at the undergraduate level, make sure to study long and hard for the Graduate Record Examination (GRE), and build a rapport with professors who can write him or her a good recommendation letter to the graduate schools.
More information on rankings and the methods used to determine them here. Details on a particular university’s math department can usually be found by googling the university’s name and “math.” Course choices and major requirements can be found by googling the university’s name and “schedules,” “major requirements,” “general education requirements” and other similar queries.