I know you said you’re not looking for other suggestions but…Brown has upgraded their financial aid formula and is now quite generous (plus will often meet the packages provided by other Ivies and perhaps other peer institutions like MIT. They no longer consider home equity and they are a no-loan institution. They provide a grant for full tuition for families earning $125k of less, with typical assets.
If your son might be interested, here is a link to Brown’s course catalog. If he types in APMA in the keyword search, he will see the APMA offerings for this semester. (or MATH for math or CSCI for computer science or PHIL for philosophy, etc).
Not sure about their math department, but their Applied Math (APMA) is extremely well regarded. No GEs, so a student who wants to explore widely as well as deeply can do so.
An AO at an info session we attended recently pointed out something very similar. She said please don’t tell me some basic facts and then ask me to assess your chances. I can’t know that until I actually read your full application.
And I think that is the right way of thinking about it from at least a certain perspective. Everyone’s chance are either 100% or 0% in the end, it is a process of discovery for the college to figure out which.
Of course it is still helpful to divide schools into categories of selectivity for the purpose of guiding application mixes. But we should avoid the illusion of precision. It is fine to observe that MIT is generally harder to get into than CMU. But if you try to turn that into an assessment you have an individual 4% chance at MIT, 10% chance at CMU, you are already way out on a conceptual limb.
And for that matter, if you assume those are independent probabilities, you are sawing off that limb. But that is a whole other subject.
Respectfully, Williams doesn’t sound like a fit for OP in terms of large urban school. Would also say that if one has an academic interest in math (i.e. planning for PhD), math is one of the few areas where an LAC, even a very top one, puts you at a disadvantage. If one wants to do math ug to pursue another field or career after, a top LAC would be great. But students competitive for math PhDs at top programs generally have several grad courses under their belt in their desired area (analysis, geometry, number theory etc.) from ug when they apply for grad school. LAC’s do not offer the range or level of math courses that universities with big math grad programs do. They also do not generally have the breadth of connections, and in math PhD admissions connections between the ug letter writers and supervisors at top programs play a significant role.
And truly top ones publish a few papers. This may still be doable at a LAC, I presume, but the flip side of LAC professors putative focus on teaching vs research is there may also be fewer opportunities to become involved in cutting edge research leading to publications.
Would a school like Wesleyan, a liberal arts college that offers a PhD in math, be an exception to the liberal arts college rule because of its grad program? Or because its grad program is not a HUGE one (compared to something presumably like a big state college), would it still be at a disadvantage?
Are these connections assumed based on continuing research? My impression is that due to the tightness of the academic job market, people earning doctorates from top programs are ending up at all kinds of schools and thus would have connections with those programs and the people they studied with who ended up elsewhere. Is that incorrect?
And as we don’t know what other colleges OP’s son is considering, in general, how would you sort the factors below in terms of importance for a student wanting to study math and eventually earn a PhD?
Prestige of university’s overall name
Prestige in math
Depth of math study offered (doctorate/master’s/bachelor’s)
Prestige of overall name is less important than prestige of the math program. Many state flagships have large active math departments with great reputations. Top math programs include Harvard, MIT, Princeton, Stanford, Berkeley, Chicago, UToronto etc… But Rutgers, SUNY Stonybrook, Ohio State, Michigan, Texas A&M have terrific math programs that place their top ugs at top schools.
Universities with prestigious math programs have a lot of professors and students, multiple seminar series, prestigious post-doc positions and named lecture series that are constantly bringing people to the department for exchange of ideas. You want that culture of inquiry, excitement, collaboration, rigour. There will be a lot of options for math fields to pursue and Honours math students will take grad courses and be part of that culture.
For effective letters, ongoing research collaborations, and continued connections through speaking at conferences allow the diaspora of top PhD math programs to send their top students back to top programs from excellent mid-level programs. There are more good mathematicians than good programs so many excellent faculty are not in good places for math. Top LAC’s do send a rare math student to top programs, but Wesleyan, because it has a math grad program, has a better track record.
These are my thoughts for an 18 y.o. with academic ambitions in math. But many students talented in math ultimately pursue consulting, finance, or other sciences, all areas where LAC’s have better placement records than they do in math.