Mathematics in the undergraduate level are of very similar quality everywhere.
That being said, there are exceptions to this rule … (like CalTech, etc.)
Anyways, if your son is more into mathematics,
Literally (and I am not kidding), all of the top “20” universities in the US News ranking for undergraduate are superb places for studying this field (and especially MIT, CalTech, Harvard, Princeton, Stanford, UChicago). And outside these 20 universities, you can also add Williams and Harvey Mudd. Though these are liberal art colleges, they also seem to be very highly reputed for mathematics.
Going by USNews:
- Princeton: “John Nash”, “Terrence Tao”. I think this one is self-explanatory.
- Harvard: Well, it’s Harvard…
- Yale: Could pretty much say the same as #2 but with “it’s Yale”
- Columbia: Could say the same as #2
- Stanford: Could say the same as #2
- UChicago: Could say the same as #2
- MIT: Could say the same as #2
- Duke: This school seems to do really well on Putnam Exams and seem to send many of their math students to top grad schools.
- UPenn: This school has Wharton. Arguably the best business school in the world. Pretty self explanatory
- CalTech: Now this is one I should warn. Yes, the math department here is outstanding like the rest BUT they force every student to take theoretical series for Calculus 1 to up. If your son doesn’t like proofs (and are weak at it), I strongly suggest against this university. Yes, the education is top notch but this university is known to make students study like 70-80 hours a week outside class (just an exaggerated stereotype) and if your son detests proofs, this is going to be the worst 4 years of his life. That said,
this school is more for the pure math oriented students planning to later work in the academia. - Dartmouth College: Yay! Seems to be a superb math program. I mean, I use their pdfs for homework help
- Johns Hopkins: For a university known for hospitals, this university is pretty much fantastic all around.
- Northwestern University: Easy to double major and very “fun”. At least that’s what my friends say.
- WUSTL: Well, they do do well on the Putnam considering their math department for graduate studies isn’t that strong. That being said, I will say this school uhmm… is more oriented towards statistics students and not for pure math majors. And to be quite frank, WUSTL math from Calc 1 to Calc 3 is a joke. After that, it seems to differ but ya… it’s still a fantastic school but… in comparison to rest of the top “20 usnews” schools, not so sure… (it’s famous for med school though so the math researches are usually going to be bio related)
- Cornell University: Superb math program.
- Brown University: It’s applied math program is superb.
- U of Notre Dame: Now here is a tough one. If you are planning applied math, I’m sorry to say but cross this off. Now if your son is into pure math and is going to take the honors sequence (the one with 4 semesters of Algebra), it is also a fantastic school for studying math as it seems to place its students very well to top grad schools
- Vanderbilt University: Nashville, undergradaute oriented, fun, fun, fun! Still a fantastic place for undergrad math.
- Rice University: If you ever have to decide between WUSTL, U of Notre Dame, Vanderbilt, well, this school is so much better for mathematics all around. Quality of education here is exceptional and competes with places like U Chicago. Also, it’s #1 happiest student! I truly envy students attending here. If your son has the opportunity to study here! Wow. But I must say, its applied math is more into computer science research… (that said, it’s fantastic for math undergrad all around)
Now, I’m sure what I just listed is obvious. Of course those universities are all fantastic for undergraduate math. They are the top 20 overall for undergraduate studies (at least in accordance to USNews). Well, the thing is, I just wrote this to show you that anywhere will be fantastic place to study for your son.
That being said, since those above schools are super obvious and had been a waste of your time, here are some which I also hold in high regards while the school isn’t necessarily big:
- Williams (pretty much Harvard but for undergrad)
- Harvey Mudd (well, this school is a STEM freak school. It’s not business oriented but for applied math/statistics in the more engineering route or pure route, :). It would be awkward doing business-mathish thing here. Not that the school is bad at it but like…the atmosphere is like all hardcore STEM techies…)
- Pomona/Swathmore/Grinnell/Weselyan ( )
- Carleton (It’s like a somewhat middle between what I said for Reed and Harvey Mudd)
- Reed (if your son is absolute on getting Phd in the more PURE math/stats (not business). Otherwise, ignore it)
??. St. Olaf: I know top students here getting into MIT and it seems to have positive reviews for math but…not so confident with this one. I know academics are rigorous though
- Though I really really don’t want to say this but for math/stats, try avoiding liberal art colleges. Students tend to exhaust all the courses before they graduate and some colleges don’t have the resources for grad level math/stats.
Other universities I didn’t mention:
- NYU (Courant): Yes! Yes! Yes! Business oriented applied math!!! Arguably the best Applied Math for business in the WORLD. Now, the financial aid… is a crapshot (ouch!)
- Carnegie Mellon: Uhmm, it’s undergrad business is tops and its more applied math is quite famous. Although the more applied side seems to be discrete math (Comp Sci oriented math). That said, still great place for applied math/stats study.
- College of William and Mary: Uhmm… Does your son like colonial life? Just kidding. But hey, at least classes are rigorous and you get to ride horses. Though I must admit, this one is a really weird public university. (it’s a fantastic school nevertherless)
- U of Rochester: I think someone said this
- Brandeis: Uhmm… Well, Mitch Albom ^^. Though I don’t know about its math department, I know it is a fantastic school for undergrad education all around.
- Boston College: Reasoning in #4
- After this point, I don’t want to be rude but I think your flagship state universities (I don’t know where you live but…) offer better opportunities than most privates.