Pure Math Schools

My son is a strong math student with executive function/organizational issues. He has been advised to seek a school that offers support for students with strong academic abilities (math especially, but he’s strong in every subject) and lopsided strengths. He just graduated HS and decided to take a gap year to mature before settling down with a full college load. His last 3 years of HS he took math at Michigan (185 Hon Calc I, 296 Hon Math II - Spivak Calculus/Linear Alg, 395/396 Hon Analysis I/II - Manifolds) and did very well. Last year his UM advisor recommended Hon Alg or repeating Hon Analysis because each year a different professor teaches the course with their own emphasis. He loves the process of learning vs getting through the classes as fast as he can so he chose to retake 395/396 and was very happy he did. He learned a lot of different material and it steered his interest toward Representation Theory. For his gap year he is doing an independent study/tutorial course at Oxford focusing on Representation Theory.

We are looking for schools where he will be able to continue his studies in Pure Math/Representation Theory as a freshman. Michigan and U Chicago are his top choices, but we would like him to have other schools as backups. He loves the math dept at UM and he really liked how the U Chicago admissions officer spoke about wanting students with an intellectual curiosity.

Maybe check out Rochester Institute of Technology…they also have a Spectrum Support Program.
http://www.rit.edu/~w-ssp/

For crying out loud! What other schools do you want to have as backups? Stanford or Princeton? MIT?

Your kid has been a successful math student at a very high level, while still in high school, at one of the top universities in the world. He will be admitted to Michigan, and (as long as you can afford it) that’s a superlative choice. I assume it’s close to home, so that makes it easy to manage his other issues. But if he’s doing a gap year, or even a gap term, at Oxford, it looks like that’s not a huge concern.

Chicago’s great for math. As are lots of other brand-name institutions, to any of which he has a decent chance of getting admitted given his experience at Michigan. Berkeley, UCLA, Wisconsin – which have a lot more slots to play with than other universities of comparable quality, except Michigan – should be virtual locks.

If you want to look for smaller, more intimate environments, Harvey Mudd or Williams, but they aren’t meaningfully easier to get into than the big obvious names on his list (or that should be). And, honestly, even if you thought he needed a smaller, more intimate environment – which seems not to be the case – I think it would be a mistake to exclude the top research universities. He’s a math star, and the math communities at any of these places will be small and intimate enough to give him the support he needs.

Cost constraints?

Given how advanced he is in math, he should look for a school with a strong PhD program in math (including the specialties that he may be interested in), since he will likely want to take graduate level courses and do graduate level research as an undergraduate. Faculty rosters (which indicate research interests) and course listings can help him determine how suitable a school’s math department may be.

Besides Michigan and Chicago, many of the usual midwestern suspects like Wisconsin, Minnesota, Illinois, Northwestern can be worth considering, assuming the cost and math department specialties are suitable.

Or Carnegie Mellon math dept is excellent also.

I’d say the important issue for this kid is support for his organizational/executive function issues. Clearly he’s a math star, but it sounds like he might need good support so the rest of his life doesn’t fall apart. Probably with his mental health profile, he’s at increased risk for depression and/or anxiety.

A good friend of mine has an Aspy son who is a math superstar. She was glad that her son ended up at a top school that was close to home, when he spiraled into depression one year. He was an academic standout, but he needed help for his mental health issues. She was glad she was nearby to spot the problem and help address it.

I suggest a college that is close to home. If the OP is in Michigan, then Michigan is probably the right place for this kid.

Holy cow - I’m well aware of the challenge of this highest initial honors sequence at Michigan. Completing that while in high school is incredible. I think JHS’s advise is spot on.

kids with spectrum disorders can take a long time to feel comfortable in new surroundings.
Send him to Michigan where he is already a known quantity and can continue his studies without the disruption of having to start at a strange new place.

Add Wisconsin to the mix- also a strong math department.

I already did.

I would hope all colleges he considers would want students with an intellectual curiosity.

I wouldn’t narrow cast so quickly to representation theory - once he gets exposed to even more, he may find other areas to explore.

The real point is to find a school that provides a high level of flexibility in that exploration.

In order, you should explore:
Harvard
Stanford
UC Berkeley
MIT
U Chicago

I would have added CalTech and Princeton to the list for their exceptional math quality, but due to other requirements, may be less flexible in creating the program he wants.

U Chicago has very little curriculum flexibility. The Core takes up a good chunk of the schedule. If he really wants to read Aristotle and Marx, 1 year of language, and 2 quarters of Biology, then by all means keep it on the list.

If he wants to focus on math, take it off the list.

I had a friend at UChicago, a math superstar, who finished his requirements for an MA in math as a junior. Did not receive his BA for another year though as he had to finish the core courses (which he detested).

This is true of MIT as well. The GIRs require 17 subjects* (though 2 are math subjects* that the OP’s son has no doubt completed already, leaving 15):

http://web.mit.edu/firstyear/2019/subjects/
http://wiki.mitadmissions.org/General_Institute_Requirements

*MIT uses “subject” for what most others call a course (e.g. 18.01 = single variable calculus), and uses “course” for what most others call a major (e.g. course 18 = math major).

My first thought would be to keep him at Michigan. Why rock the boat when he’s doing so well? And the math department certainly has ample resources to continue to guide and challenge him. On the other hand, as a full-time undergrad he would also need to meet distribution and foreign language requirements, etc., so it wouldn’t just be a continuation of his experience to date.

What about Cambridge? Admission is strictly by intended field of study, and the emphasis is on going deep in one’s chosen field, rather than breadth. And the Oxbridge tutorial system and the cloistered atmosphere of a Cambridge college might suit him well. It would require aligning him with the right college and the right mentor, but it sounds like this kid is a borderline math genius, if not an outright genius. And what aspiring mathematician wouldn’t want to study in the same shaded groves of academe where Sir Isaac Newton once romped?

https://www.lsa.umich.edu/students/academicsrequirements/lsadegreesrequirements indicates that University of Michigan’s foreign language requirement is that of fourth term equivalency (16 credits if starting from the beginner course, fewer if the student can start in a higher level course based on high school language courses or heritage knowledge). There are also various other general education requirements described on that page.

Math departments commonly require PhD students to have a reading knowledge of French, German, and/or Russian, since math research papers may be published in those languages. It appears that the typical expectation is that one can read a math research paper written in such a language and understand the math, as opposed to general fluency and literacy that is the usual goal of language courses.

This, of course, is absolutely silly as general advice, while retaining a grain of truth. Chicago has a higher proportion of math majors than any of its peers (other than technical institutes). It’s one of a handful of colleges – all or almost all of which should be on the OP’s list – that is truly set up to handle incoming students with extraordinary math ability, and it does in fact regularly enroll and educate such students. It’s a place where students like that can find peers, which is pretty much the most important thing one could ask for with the student described.

So, one way or another, Chicago educates and satisfies a whole bunch of math students. It does so notwithstanding its core requirements (one of the benefits of which is that everyone there, including English and theater majors, has a healthy respect for and interest in math). As far as I know, all of its peers have general education requirements that are not a whole lot less demanding than the core, although they may be more flexible, and somewhat easier to meet with AP credits. You would have to go to Brown, which is at least a couple of rungs down the math ladder, to dispense with general education requirements, or of course go to Oxbridge.

If the OP’s son really wants to study math and math alone, then that’s an option, or maybe he should look carefully to see just how many courses he would have to “waste” on non-math at various colleges. But the vast majority of educationally ambitious students don’t think that way, even at Brown. They like knowing something about fields other than their own field of concentration. They like knowing people with a variety of interests, and having some common ground on which to meet them.

If you have 5s on a lot of APs in high school some schools (Carnegie Mellon) will let you out of nearly all the Gen Ed requirements while others will let you out of only a limited number (Tufts) or none at all (Dartmouth). Personally it’s good for kids to get at least some exposure to things other than their major.

There is a reason for undergrad college requirements to include breadth courses. A well rounded education is so much better than only having knowledge in one area. I wouldn’t be sure a second language is required for math PhDs (or any other field) anymore given the prominence of English and the translating capabilities of computers in today’s world. Remember that despite your kid’s intense interest and ability in math he needs to learn about the rest of the world around him. Going away to college would be good for him. Socially and to see how things are done elsewhere.

Wis75 made an excellent point. Undergraduate degrees do include a breadth of requirements. While it is really exciting to think about all of schools with excellent math programs, a college major contains a relatively small number of credit hours relative to the number of hours to graduate and requirements in all areas must be satisfied. When looking at college catalogs, don’t just turn to the pages on math because those classes/options are already enticing. Instead, look at the general requirements and talk with your son about all the kinds of classes he may encounter. Are there areas with core requirements that are interesting and some that are personally yucky. Would he prefer psychology over sociology? If so, would a class in experimental psychology be more appealing. I would start talking to your son from the very beginning that he needs to limit his math coursework to perhaps one class per term. Just this idea may start getting him to focus on other requirements beyond math. What would be ultimately very distressing is your son taking all the math classes and doing extremely well, but not have enough credits in other requirements to cobble together a degree. Even if it could be possible to substitute math classes for general requirements, that does not give him the broader world view in which to locate math socially and ethically.

Practically too, assuming he is likely to earn a Ph. D., he still has to meet admissions criteria and relevant standardized tests. He needs to be beyond his high school understanding and level in reading, writing, and other areas for the admissions tests. Graduate classes are very often interesting and no more challenging than college-level classes so I wouldn’t worry about them.

Writing, even when the dissertation is short because of the topic or field, challenges many qualified students who end up ABD, Depending on the field in terms of percentage, a huge number of individuals don’t finish because of life challenges like money and time as well as more clearly academic concerns such as writing and data analysis–drawing and writing conclusions within the constraints of data.

Issues with executive functioning and organization could have an important impact on writing a dissertation. I found the dissertation no big deal. However, I spent hours reading and thinking and sorting through information to hone in on a topic and then to flesh out what I wanted to do and how to do it. I had my own little cubby at the university to work in, but it was only me and my interest in working independently in that space that got me through. Faculty and other grad students are interested in what you are doing and may provide tips, but you don’t have a mentor keeping tabs on you and your progress.

Final point on the dissertation or other papers and theses in grad school: After your earn your degree you are free to pursue whatever you want. The dissertation is only a hurdle. If your committee chairs, says type in green on peach paper (not literally this example, of course), do it. If s/he says concentrate on this aspect of your topic, do it. Whatever, do it. Your goal is graduation and nobody is much interested in your dissertation after you are done. You don’t need to alienate any support system that may come your way.

I hope all works out for your son. If he is Aspie, he might look at Temple Grandin as an example of a highly educated person with Aspergers. She earned a doctorate at Illinois and now teaches at Colorado State. She has mastered independent learning, teaching, speaking and writing to the degree that she completed a dissertation and was appointed faculty (hired) at an excellent school.

More reasonable would be two courses in one’s major per term. Although the student in question is very advanced in math and can probably finish a math major with 8 or fewer semester-long math courses, taking two math courses in some semesters should not be too much of an issue in leaving enough schedule space for breadth while allowing for more exploration in math.

It also does not appear that the OP has indicated that general education or core curriculum requirements would be a particularly troublesome issue for this particular student (“strong in every subject”, although exceptionally strong in math), so perhaps this whole discussion about general education may not be that relevant.