A place to study pure math— for the love of it

Hi everyone,
This is my first time posting so I hope I’m doing it right! Thanks in advance for any advice.

My son, a junior, found his passion very early in life— pure math. All he wants is to study math— he’s drawn to proofs, the abstract, the big picture (but of course can do the computational stuff too). Not that drawn to contests— he loves math for its beauty, and doesn’t really enjoy competition. He reads math papers and proofs for pleasure, just on his own.

We’re looking for a college where he can study math to his heart’s content, but where the “vibe” is more cooperative or laid-back, and where the emphasis is on theoretical math, rather than computational or applied math. Right now he especially loves number theory.

His background:
His high school did not allow any sort of math acceleration, so after his sophomore year, on the advice of his counselor, he left the math department behind. He studied calculus on his own and scored a 5 on the the AP Calc BC exam. We live near UC Berkeley, so he’s taken multivariable calculus and advanced algebra there— earned A+ in both courses. This semester he’s taking complex analysis. He took AA without having the prerequisites but seems to have figured it out as he went along; hopefully that will hold for complex analysis too.

His stats: all of his scheduled testing so far has been canceled, due to Covid, so we don’t have much to post. He took the PSAT as a sophomore and scored 1390, but that was without any preparation, so I’m pretty sure he could bring that up.

He has a 4.0 (his high school doesn’t do weighting); he took AP chemistry last year (scored a 5), and is taking AP computer science, AP US History, and AP English, and AP bio this year. He plays piano, does speedcubing and chess. No sports; no “leadership” in EC. He’s shy, awkward, and sweet.

So far in his search, he’s been drawn to Oxford, because he’d get to study only math, and he likes the sound of the tutoring system. Also UC Berkeley, because he already knows the department— but I’d love him to be in a less anonymous space. I just don’t know how happy he’d be in a highly competitive or high-pressure environment, which so many good math colleges seem to have. But he’s been fine at Berkeley so far, so maybe that’s just a mom issue. Socially, he’s shy— he has one friend at the moment— so a smaller college seems like a good match, but I’ve also read on these forums that some of the small colleges might run out of math for him to take if he’s already taken as much as he has (he plans to take another 3 classes at UCB before graduating high school.)

Any insights are much appreciated!

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For a range of U.S. schools to research further, look into those that appear in a Princeton Review sampling, “Great Schools for Mathematics Majors,” such as Harvey Mudd, MIT, UChicago, Caltech, Harvard, Brown, Rice, CMU, Pomona, Haverford, Amherst, Hamilton, Williams, Bowdoin, Reed, Carleton, Grinnell, Macalester, URochester and St. Olaf.

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From the description of the courses, they are MATH 53, 113, and 185, the latter two being upper division courses usually taken by college juniors or seniors. Listed prerequisite for 185 is 104 (real analysis). Math courses are listed at Mathematics (MATH) < University of California, Berkeley .

UCB may seem more anonymous overall, but upper division (and graduate level) pure math will be considerably less anonymous (and this tends to be true for other large research universities). UCB does have about 100 pure math majors per year, but also about 300 applied math majors per year (statistics is a separate department; at some colleges, statistics is part of the math department).

There are some posters who are very pro-LAC (liberal arts college) here, but many LACs have relatively small math departments with limited upper division offerings and no graduate level offerings, so they would be less suitable for your very advanced-in-math student who will have taken probably five upper division math courses by the time of high school graduation. Having him take a look at catalogs and schedules for math courses at any college under consideration is highly advisable.

But note that most colleges do have general education requirements; even many of those with more flexible curricula have limitations on the percentage of courses in any one department or division (i.e. so that a student could not take 100% math courses). Some colleges have notably heavy general education requirements (e.g. MIT, Harvey Mudd, Chicago, Columbia).

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Foreign language? Many colleges look for that in admissions.

For PhD study in math, a reading knowledge of French, German, and/or Russian (enough to read and understand math research papers written in those languages) is desirable or required. Obviously, it can be a matter of luck whether a 7th-9th grade student chooses (or is able to choose) one of those languages for high school foreign language… If he needs to take foreign language in college for a general education requirement, he may want to consider these languages.

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Mathematics, Wesleyan University - Wesleyan University

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I would argue, as a formerly shy, mathy kid, that a larger university is a better match. There’s a higher probably of finding one’s peeps when there’s more students.

It’s going to be hard to beat Berkeley. Only MIT, Stanford, Harvard, Oxford and Cambridge are ranked higher for math. He won’t run out of math at a large university, but he very well might at a smaller institution. Larger institutions will have lots of courses in both theoretical and applied math.

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The obvious answer is Oxbridge where he’d be able to study pure math to his heart’s content. The admission’s interview both at Oxford and Cambridge would be with math professors and about math. Basically they will be looking to see if they would want to have your son as their student. On top of lectures and other classes, students attend weekly tutorials with faculty fellows in very small groups of one to three students.

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If he has already taken and excelled in MVC and Algebra as a junior, my suggestion is to forget about LACs, as a number of posters have implied. Even Amherst and Williams will not have very much. The departments are just too small, nothing is leveled, and it is very easy to run out of interesting courses.

If you do try the LAC route, my suggestion would be to look at Amherst (availability of grad courses at UMass), Pomona (consortium with Harvey Mudd) and Swarthmore (historically very strong, and one of the few LACs with honors sequences for the talented students).

In terms of pure math, please don’t forget about Cambridge if you are considering Oxford. In no particular order, Harvard, Princeton, MIT, Chicago, Berkeley, UCLA and CMU would all be fine places to study pure math.

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Thank you! All of this is so very helpful. @ucbalumnus, he’s in his 3rd year of Spanish, and will take one more year as a senior. Thanks for suggestions about other languages.

@Mcastrellon, thanks for pointing out the LAC’s which have links to other institutions/ grad schools. That’s been hard for us to figure out.

It would never have occurred to me to think about him “running out” of math courses, but it sounds like it actually could be an issue. We’ll definitely keep that in mind!

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What you say about a larger place for a shy kid makes a lot of sense— thank you.

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@ucbalumnus, Yes, those are the course numbers. I meant abstract algebra, not advanced algebra, of course— mom mistake.

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Don’t forget the usual college planning stuff:

  • As the parent, do the financial planning to figure out the budget. Try the net price calculators on the web sites of various colleges under consideration to see if financial aid will be enough.
  • Be sure to find a safety with a suitable math department.
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Also, since he sounds like he is gifted in math, the math department will be filled with his people. There will be lots of collaboration and excitement with peers who are interested in the same thing he is. So it won’t be competitive so much as collaborative. I think it will be very unlike high school where kids often compete on a me v. you type approach. Collaboration is key. One of my kids is a math kid ( actually both, but one in particular), they decided that the math competition team wasn’t a good place. Not enough collaboration. Kid found it elsewhere in a STEM activity. For kids who breathe math, they need to find a place that supports “pure math”. I think most of the places were covered. He can also look through the curriculum and see what courses are listed and what excites him.

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Yes completely agree. He should register for STEP 2/3 and do that this June if at all possible. It requires a lot of natural ability and preparation. Getting an S in both is as near as you can get to an auto admit to Cambridge.

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I’d rate Berkeley above Stanford for pure math. And Cambridge is certainly better than Oxford :wink:

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If he really like the only math aspect of Oxbridge, I would skip UChicago. Much of your first two years are satisfying the Core requirements.

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Since you’re a CA resident, one program he should consider is the Math major at UCSB in the College of Creative Studies (CCS). See Mathematics | UCSB College of Creative Studies

CCS is sometimes called “grad school for undergrads”. Students in CCS can take any course at UCSB they want, undergrad or grad, if they feel ready for it. It’s an incredible program for the right student. And at CCS he might find the social mix he’s looking for. He’d know the kids in the relatively small CCS community, but also have the larger U available. It’s one of the few colleges in CA where everyone lives on/near campus so its easy to meet up with friends. The vibe at UCSB is pretty relaxed; shorts and a t-shirt, you’re good to go.

In these Covid times its hard to get to know colleges, but CCS is big on talking to prospective students. They want the kids for whom the program is a fit. So if he’s interested he should give them a call or send an email, they’d be happy to tell him more.

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A good compromise between a LAC and a behemoth institution like Berkeley, Wesleyan is the only co-ed LAC that grants math degrees at the Ph.D level (the other is Bryn Mawr) and probably the only one that does so at a robust level. And, with 3,000 students it’s significantly larger than Amherst and Williams, but still small enough not to lose track of a shy person in the shuffle. With 80 math majors and 16 full-time department members, I doubt DS will be in danger of running out of courses.

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If the CA schools are affordable for you, I think this is relatively easy. Apply to UCB and UCLA. Take his shot at Oxbridge. Then pick a few from Harvard, Princeton, MIT and Stanford. Then you just have to find a CA safety school in case the wheels come off. If he decides that he wants to develop more than just math, replace Oxbridge with UChicago.

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Pretty much any US university will allow him the option to develop more than just math (although the strength of other fields can vary). Colleges with heavy core curricula like Chicago, MIT, and Columbia will require him to develop specific other areas as chosen by the colleges in their core curricula.

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