Many of the LACs will have great math and music courses that will challenge him. He can ask his school counselor if there is a copy of Rugg’s Recommendations. Rugg literally gets feedback from students at every college you can think of on how they feel about their majors. Students rank on many aspects of their experience and Rugg compiles all this info, so your son can see which colleges are recommended for which majors. My kid used RR extensively in deciding which colleges to apply to, as she has many areas of interest. You will not be able to see RR online, and either have to buy it, refer to it at a library, or see it in your counselor’s office. It’s a great resource.
St. Olaf is very well known for its math department. Take a look into it.
A relative is starting at University of Michigan this fall in an honors math program which sounded very interesting. Even though it is a very large school, the number of students in the program is small. He will certainly not be repeating coursework he has already done in high school.
I think many LACs will fit your son’s needs.
Personally, I attend University of Richmond where I’m a math and CS double major, music and dance double minor. I really like the environment here. I’ll also mention that I’m on a full tuition scholarship for music that only requires minoring in music.
I came in taking linear algebra, with the Calc sequence done in high school. I did not receive credit for Calc 3, since it was not AP or dual enrollment, but was able to place out. I have never not gotten a class I want, but have sometimes needed an override from the department due to them filling before my registration time (since I’m ahead). Quick painless email and I get the go ahead to register within a few hours. There is also a great breath of classes offered, so you won’t run out.
Most LACs will allow no majors to participate in the arts. Our dance, theater, and music minors/majors are non audition and open to anyone. Music ensembles are open to anyone (placement audition required for many, although you’re guaranteed a spot in an ensemble. Orchestra may send musicians to band if we have too many winds, jazz ensemble will place overflow in one of the Jazz combos) and theater productions also have auditions that anyone can go out for. I’m also involved with theater, but mainly behind the scenes (I’m choreographer for the first show this semester).
I know people have mentioned Williams bc it is award winning in Math but did you know they also have a top notch Opera workshop - sounds like this would be right up his ally-
The Williams Opera Workshop pairs student singers with young professionals to prepare operatic scenes and partial operas or operettas. This group offers singers the opportunity to further develop skills in stage acting, character development, and the incorporation of foreign language while working as part of an ensemble.
The workshop culminates in a final semi-staged performance in late January. Acceptance into the workshop is by audition only, with individual auditions taking place in September, around the time of the music department’s open house.
Penn (although a little larger probably than he would want) has many many different types of music performance groups and connections with Opera Philadelphia and other opera initiatives http://sites.sas.upenn.edu/opera/
also has reciprocity with Curtis for courses not found at Penn… doesn’t get better than that for music
BTW almost half of Opera Philadelphia is a young audience http://billypenn.com/2016/05/06/half-of-opera-phillys-audience-is-under-35-heres-how-they-did-it/
I posted a few back about St. Olaf and its strong math program. Forgot to mention its stellar, renowned music program.
http://wp.stolaf.edu/music/ensembles/
"The strong tradition of ensemble music-making at St. Olaf College dates back to 1893, when the St. Olaf Band presented its first concert at the Northfield City Park. F. Melius Christiansen, founder of the music department and the famed St. Olaf Choir, assumed leadership of the St. Olaf Band in 1903 and led the group on its first tour in 1904. Christiansen took the band to Norway in 1906, thus making it the first American college musical organization to conduct an overseas concert tour.
Today St. Olaf College is home to six choirs, two bands, and two full orchestras — including the internationally acclaimed St. Olaf Band, St. Olaf Choir, and St. Olaf Orchestra. St. Olaf ensembles perform regularly at state and national music conventions, and faculty members appear as presenters, clinicians, and conductors at conferences and festivals around the world. Additional performing opportunities include three jazz bands, Early Music Singers and Collegium Musicum, two handbell choirs, and numerous chamber ensembles."
OP, it’s crazy hard to get into, but MIT fits the bill. Awesome music there! My son graduated from MIT, and he spent considerable time pursuing music via classes, his own production company and doing musical theater. The students and their interests are incredibly diverse, and it’s not so huge.
My son had finished dif equations by sophomore year, so he also was looking for schools that offered high level or graduate level math classes. (Ironically, he never took advantage of graduate math classes, as once he was done with his math reqs, he focused on taking CS classes)
He did not apply to any small schools other than Harvey Mudd and Caltech-loved Mudd, hated Caltech. He was deciding amonth Princeton, Mudd and MIT in the end. He had a hard time deciding between Mudd and MIT, but wanted a larger school in a big city, so MIT it was.
Have him look at Bowdoin. One of my daughter’s close friends is a serious math student and she is thriving there. Lots of chances for independent study for self-motivated students, and good faculty mentoring.
Consider Williams or Hamilton, which both attract math majors with their well regarded departments.
Wow. This has been an extremely helpful series of answers! Thank you very much! I appreciate the careful reading of my questions as well as your generous and detailed answers! If there are any other thoughts, I am still reading (as is he), but I wanted you all to know our gratitude.
Here are the math course catalogs of several schools named in this thread:
Bowdoin: https://www.bowdoin.edu/math/programs/Math%20Courses.pdf
Caltech: http://pma.caltech.edu/courses/department/ma
Hamilton: https://www.hamilton.edu/academics/departments/Courses-and-Requirements?dept=Mathematics
Harvey Mudd: https://www.math.hmc.edu/program/courses/descriptions/
MIT: http://student.mit.edu/catalog/m18a.html
Saint Olaf: http://www.stolaf.edu/catalog/1415/academicprogram/math.html
Williams: http://math.williams.edu/courses/
For comparison, at some big state universities:
Alabama: https://catalog.ua.edu/undergraduate/arts-sciences/mathematics/courses/ and http://services.graduate.ua.edu/catalog/16400.html
Berkeley: https://math.berkeley.edu/courses/choosing/course-descriptions
Kentucky: https://math.as.uky.edu/math-courses
Minnesota: http://www.math.umn.edu/courses/
Stony Brook: http://sb.cc.stonybrook.edu/bulletin/current/courses/mat/
Ok, wow-I guess I’d never looked at MIT’s math offerings. That’s a whole lot of classes.
“bright kids who actually read and think, not more competitive kids”
The University of Chicago or Swarthmore could be good if he likes reading and contemplating things. In contrast, MIT or Penn could be more attractive if he is more of a hands on doer.
It sounds like he could be a candidate for these schools, but keep in mind that they will typically want to see some out of class achievement in addition to the gpa and test scores.
@listener76, I know Williams has been recommended several times on this thread for the excellence of its math program. I’d also like to reinforce that Williams has very strong music and theater departments. Double majoring is quite common and encouraged. Barring that, there are ample performance opportunities in music and theater for non-majors. The opera workshop mentioned by @runswimyoga is a good example. The Williamstown Theater Festival is one of the best known summer groups in the region and although it is run independently from the college, the energy rubs off.
I’m sure your son would be a person of interest to Williams, both for his academic achievements and for that fine baritone. 
Small schools are always looking for talented students who will contribute to the campus community.
You don’t infivsyr your financial situation. Many of the schools suggested in this thread are “need only.” They can be quite generous with need-based aid, but may not offer merit aid. If you need (or want) financial aid run a few net price calculators to make sure you’re covered.
Alternately, if you won’t be applying for financial aid, your son might want to consider applying early decision. If that’s a possibility try to do some visiting between now and mid-November. Small LACs have distinctive personalities that are hard to grasp without visiting.
Will the small schools without grad departments in math be able to offer the same courses as those with strong math grad schools do??? Someone mentioned Michigan. Wisconsin also has Honors for the math major, this can include grad level courses in math. Enough math majors to have students with diverse interests along with math. The opportunity for nonmusic majors to be in an orchestra. How many different mathematicians will a student encounter in a small college? I do not see a large school as being any more competitive than a small school, something mentioned as a negative for his HS.
Holy smokes! Everyone’s got a school or two to recommend.
It might not spring immediately to mind, but with the usual caveats about being a reach (as are many of the others mentioned): Yale. It feels like a small school (residential colleges), has enough classes to keep anyone interested, and has a thriving music/theater scene both academically and socially.
These highly selective LACs are listed in a Princeton Review sampling, “Great Schools for Mathematics Majors”:
Reed
Grinnell
Hamilton
Haverford
Carleton
Bowdoin
Harvey Mudd
Advanced mathematics students at these schools would be encouraged to spend a semester in Budapest to complement their own colleges’ offerings.
Penn-Curtis is really something of a one-way street. There are few, if any, courses offered at Curtis that are not offered at Penn, except for performance courses, and to take the performance courses you would have to qualify for them, which means essentially being admitted to Curtis. If you are serious enough about music to want to take Curtis performance courses and good enough to be admitted, you probably shouldn’t be at Penn. Meanwhile, of course, Penn has a lot of courses that Curtis doesn’t offer, and every once in a while a Curtis student takes one, if he or she can find time away from practicing.
I also think that as a practical matter it’s much tougher to take courses at Penn from Haverford, Bryn Mawr, or Swarthmore, than it is to take classes at UMass from Amherst or to cross-register at the Claremont Colleges. Not impossible, but there are a lot of schedule disparities, and daytime travel times are pretty consequential. You can’t just ride your bike over to the Penn campus from the suburban colleges.
CalTech and MIT are very intense schools. That doesn’t sound like what your son wants. I understand why students that attend TJ-type high schools may want to step back and explore. If you can give your children the gift of time fantastic. I do realize that some families need to push their children through education to a career.
Two ideas.
- Attend a school like Tufts with an excellent math program. The student can take advantage of art and music programs in the community. The student can also visit open events at several other colleges within the Boston area. He can establish a peer group outside the fishbowl of his academic peers.
- Pursue a school like Vanderbilt with generous merit scholarships. A larger school is very likely to have numerous club opportunities to pursue the arts. I cannot comment specifically on Vanderbilt, but most top universities that offer merit scholarships often link the opportunity for guaranteed research or internships to the award. A larger school can offer the opportunity to establish friends outside of his major.
With both choices he will need to establish peer study groups.
I know the 5C’s are one of the darlings of the CC community. My children would have bounced out of there within a month. Think about social fit as well as academic fit.
For those parents that don’t think college is a big race to the finish and all about pumping up the resume I think you are behind the curve. Students check their peers LinkedIn accounts to make sure they don’t miss this class or that opportunity. Parents check the LinkIn profiles of the peers of their children and insist they take the same classes.
It sounds like the OP’s son is legitimately advanced in math. I don’t think there’s any question that most – not all, but most – students like that wind up attending either a large public flagship university with a substantial math department, or a smaller private research university, often one that is very difficult to get into (because, frankly, not that many of them have meaningfully better math departments than lots of public flagships offer). The OP’s son should at least consider those options seriously without dismissing them. Public flagships are often huge institutions, but the math community within each is likely to be relatively intimate and manageable, especially for a student who doesn’t have to take basic calculus. For the rest, it’s sort of like living in a city – you don’t know everyone, but why would you think you ought to? You know the people you work with, you meet others randomly or doing other things that interest you, and it doesn’t really matter that there are 15,000 students in your graduating class.
The high-prestige private research universities are much more like liberal arts colleges day to day than they are like big public flagships. They may be 2-3 x the size of most liberal arts colleges, but they are a fraction the size of large publics, and, factoring in financial aid, they generally cost the same or often less than liberal arts colleges.
The advantage of going to colleges like that, as a math student, is that the math community there – while not large in absolute terms – is much larger than you will find at any liberal arts college (with the possible exception of Harvey Mudd). There will be lots more courses offered every year, and lots more talks given, and lots more people to hang out with and to learn from by osmosis. Going to an LAC that doesn’t have a substantial math department means essentially entering into a tutoring relationship with a couple of faculty members. That can be great, no question about it, but it’s not the most robust situation, and until you go to graduate school you will be constrained to learn what they available faculty can teach you. (That’s not such a terrible thing, by the way, and it may be the best way of being certain you are well prepared for graduate study.) People do that all the time, and feel satisfied by it – just not as many people as choose the other option.