I can think of several, including my alma mater.
Ok. I’ll take it back. But I’d still think it’s encouraged, if not required.
I did mean the type of maths he is interested in. But I’m taking his desire to study “only math[s] and nothing else” for granted, given OP was so specific about the parts of the subject he wants to study.
And yet in the UK, the exception is “Natural Sciences” at Cambridge as opposed to selecting single subject Physics, Chemistry or Biology at Oxford and elsewhere (and even then for NatSci you specify in advance if you are a physical scientist, doing Phys/Chem, or a biological scientist, doing Bio/Chem - you don’t do all three).
I do agree that there are many interesting problems at the boundaries of the different science subjects. Some people like to find and solve those problems, some prefer to focus on going into depth within one particular subject. Its really up to OP’s son to decide whether he prefers depth or breadth.
No, it is when the instructor does not grade on a curve and makes the assignments and tests too hard for the pre-set grading scale.
Of course, that may be a slightly different kind of stress than the stress of competition created by grading on a curve.
If OP’s son wants to study “only math and nothing else”, then I’d agree that his options are limited to those UK schools and a few US colleges with open curricula.
Requires only physics and math courses for the major, although the college or division may have general education or core requirements in non-physics sciences:
https://ua.princeton.edu/academic-units/department-physics
https://handbook.fas.harvard.edu/book/physics
Requires non-physics non-math science courses for the physics major (beyond any general education or core requirements of the college or division):
Since graduate level courses may represent a part of your son’s college education, you may want to consider graduate department rankings for mathematics:
https://www.usnews.com/best-graduate-schools/top-science-schools/mathematics-rankings
As an opinion, departments with peer assessment scores of ~3.4 or higher should offer sufficient breadth to a potential undergraduate who would be unlikely to know at this time how their interests may develop.
5 Likes
If he is quite certain he only wants to study math and is unlikely to change his mind, then he should be looking at Oxford or Cambridge. Large universities in the US will have distribution requirements. But he is young and there is a chance his interests will expand. A friend of my daughter’s seems very much like your son. She was focused on math at an early age, but decided to attend Bowdoin to get a liberal arts education. She excelled in math there and went straight to a PhD program at the University of Minnesota after she graduated from Bowdoin. If he is willing to look at an LAC (at the risk of running out of math), it might be worth it to wait to go all in on the math.
2 Likes
Okay, but the existence of “a pre-set grading scale” is usually assumed. Most people just call it a standard.
OP here. I want to thank everyone for their time and input— I’ve learned so much in 5 short days— my son and I are grateful for your generosity. What a fantastic community!
To answer a few questions which have come up: my son, at this point anyway, is definitely drawn to “pure math”— by which I mean the proofs, the larger abstractions, the way it all fits together “behind the scenes”—that abstract beauty— rather than solving real-world problems with computations or applications… I’m not a math person myself, so I may be using the terms incorrectly.
My son has also voiced a preference for studying only (pure) math— which his dad, especially, has some qualms about— but I thought I’d relay my son’s preferences in my original post. He may, of course, attend a college with breadth requirements— but all other things being equal, he’d prefer taking fewer non-math classes.
He’s also skipped around a bit in his education— he took MVC at UCB, which wasn’t so very fun/interesting for him, but he knew he needed the foundation. And then he skipped up to abstract algebra when my brother (a mathematician) encouraged him to reward himself with something “fun”. He’s taking complex analysis at UCB now for the same reasons— because it seems interesting/fun— without first taking intro to analysis or intro to proofs or linear algebra. He’s picked up enough in his own reading to be all right in the class, but i assume that at some point he’ll need to back up and take the classes he’s skipped over.
All that to say: I don’t think he’ll enter college as the course-equivalent of a junior, because he’s missing some earlier courses. At the most, he’ll have taken 5 UCB math classes, one of which was an intro course (MVC).
I’m also assuming that there exist honors/ abstract/ “pure”/more difficult versions of the classes he has taken at UCB, that might be interesting for him, even if he’s already taken them at UCB? Is that right? I’m not sure about that… just applying my own experience— a Shakespeare class at one university is not the equivalent of a Shakespeare class somewhere else, especially if someone brilliant is teaching it. Would that hold in math, as well?
Thank you again for all this conversation.
UCB does offer honors versions of 53, 113, and 185 (with H prefix, so H53, H113, H185). Other honors math courses at UCB include H54, H104, H110. For regular courses that are large (53, 54, 110), the honors courses are much smaller.
https://math.berkeley.edu/courses/choosing/honors-courses
It is probably not worth the time to repeat a course with the honors version, since the regular versions are considered sufficient to go on to the next course (including graduate level courses listing them as prerequisites; note that all of the above courses are required for both the pure and applied math majors at UCB). However, if he wants to take other math courses for which there is an honors course, he may want to consider the honors course. Note that 104 (real analysis) is considered one of the more difficult courses to begin with, while 110 (linear algebra) is often recommended as the first upper division math course for math majors (so it may not be as difficult).
Re: skipping around
Presumably, he has had single variable calculus (AP calculus BC or UCB Math 1A and 1B). The remaining lower division math courses at UCB would be 54 or H54 (linear algebra and differential equations, sophomore level) and 55 (discrete math). Beyond that, https://math.berkeley.edu/programs/undergraduate/major/pure describes the upper division math courses for the pure math major. As advanced as he is, he will probably take more than the minimum, probably including graduate level courses.
2 Likes
If he is studying complex analysis at UCB right now and getting along well in it, please forget about LACs.
It is very rare that a LAC will offer honors versions of the standard early sequence (mvc, linear algebra, intro analysis), as I wrote somewhere above, Swarthmore does, but really he is going to run out of courses at a LAC.
The standard level courses at even the top LACs will not be taught at a higher level than at UCB, likely a lower level depending on the school and specific courses being compared, although it will be a full professor for sure at the LAC.
Another plug for the Budapest program. Sounds like your son may not have been exposed to too much number theory and combinatorics, and there’s probably no better place to study those topics than in Hungary.
2 Likes
Forgot to address the idea of stress and competition— what I meant to convey in my original post was that I think my son really appreciates, and desires, depth, hard thought, and rigor. In fact, he thrives on it. What I think would work less well for him would be a competitive vibe, and/or too many laborious/repetitive problem sets, so that it becomes more about endurance/labor without as much new learning/insights…?
1 Like
That generally describes upper division pure math.
It is unlikely that upper division pure math courses anywhere will be that way. “Competitive vibe” is something that would be more common among pre-meds and courses which pre-meds take (e.g. biology and chemistry).
3 Likes
This is great advice. I think he would love the honors versions of these courses, and we have looked. However, he can only attend classes that don’t conflict with his high school schedule, and so far there haven’t been any honors courses that meet in the afternoon or evening. But we will keep hoping!
1 Like
Proofs are part of any math (at least at the advanced level), but It’s clear from your descriptions that he prefers purer math for their abstraction, perhaps their elegance due to their axiomatic approaches. However, taking that complex analysis course and finding it interesting and fun seem to be the only thing that’s inconsistent with that picture.
Not sure I follow. The fun part of complex analysis is visualizing Riemann surfaces and such like in your head. Very different from the plug and chug way in which many lower level calculus courses are taught. My take away from OP’s comments above is that her son presumably enjoys the visualization part of abstract mathematics and solving the sort of problem that comes to you in a flash lying in bed half asleep rather than as a result of spending a few days writing a computer program.
As one of my friends noted, you need 2 hours of inspiration in the course of 3 years to get a PhD in pure maths.
2 Likes
OP did say in her post that her son didn’t find calculus to be interesting or fun. Subjects fall under analyses have similar flavors, even at different levels. I actually consider visualization to be the opposite of abstaction and algebraic structures to be more abstract than analytic functions.
But perhaps that may have more to do with the difference between lower division (frosh/soph level) math courses (with significant computational / application emphasis, due to being shared with other majors like engineering majors, physics, chemistry, etc.) and upper division (junior/senior level) math courses (mainly taken by math majors, mostly with a greater emphasis on proofs and theory). Honors courses at any level will further increase the emphasis on proofs and theory.
4 Likes
It may be. But OP described several times that her son loves math for its beauty and abstraction, and she contrasted his reactions to the two different types of courses he took (one of which fits the definition of beauty and abstraction; and the other doesn’t).