My son has some very good acceptances for his math intended major. Not interested in the financial sector for future job. Princeton is the closest to home and the best financial offer. Dream school since he was 7. All of the schools in the list are within budget. We are thinking any of the other alternatives will give him potentially a better undergraduate experience since he is good for math but not a world medalist or anything like that. The question is would Princeton math give him the support and the possibility of growing in the field at his pace or is it just going to be an uphill battle from the beginning? He is taking successfully calc bc, linear algebra and Cs math based MIT independent course as a senior.
Calling @neela1.
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Math can be an uphill battle anywhere.
I don’t know if I am qualified to answer :-). My kid is a CS major at Princeton with significant interests in math. He is not a math major. He has taken the first year math sequence that incoming math majors take, and feels closer affinity to the math community on campus than to the CS community. He is on the border. So you should take my opinion for what it is worth.
He is a regular kid – hasn’t had the prep that some of the competition kids have had. After Calc BC in 10th grade he did number theory and discrete math in 11th, and a hodge podge of stuff in 12th grade – lin alg, multi var, vector calc etc. He also had experience working through a bunch of TCS papers by hand the summer of 11th grade – starting with the original Turing paper on “Computable numbers …”
Then he prepped the summer before going into P by working through the infinite napkin ( you can google this)-- self study.
So when he went into P, he had a half an hour conversation with Gunning (since retired) to start with the main Math sequence meant for Math undergrads, about his mathematical maturity. Gunning gave him stuff to prove, and satisfied himself that he wouldn’t bomb the course. This course was 15-20 hours of homework a week. The department beats you down on rigor. This two semester course sequence is baptism by fire. If you survive these, things become easier. The kids work communally. They are encouraged to work together. But you should attempt to work through everything on your own before you go into the communal session for each homework pset. Otherwise you will bomb the midterm and the finals. The proof standards are very high. If you miss one line, you’d get a zero etc. This is the book used for the two semesters: An Introduction to Analysis | Mathematical Association of America
The book is used for the math sequence called MAT 216-218.
For kids who come in with less exposure to proofs, the department suggests starting with MAT 215-217, which is a slower introduction to the same ideas.
At the end of the first year my son pivoted into CS, and focused on graph theory, combinatorics etc. He said that it is not interesting to stay in math if you are going to confine research to a narrow area of math down the road. He said you need to be a god to be fluent in multiple areas of math eventually after PhD. Since he is not god, he pivoted. The Math kids stayed in math – algebra, number theory, topology, algebraic number theory etc. Things become more manageable after the first year because the learning curve is less steep – except perhaps for complex analysis in third semester, and algebra. The TCS community and the Math community overlap in areas like Probability, Combinatorics and Graph theory, and some self-study algebra where needed in CS. This year the math department (my son’s cohort who stayed in math) placed exceptionally well into grad school. Really top notch.
Half the math department goes into grad school. The other half goes into Quant Finance.
I would say that this is doable. If my kid can do it, anyone can. It just needs a healthy attitude to put your head down and work through the pset, unaided the first time around, without any baggage, however long it takes.
This is the top 1-2 math department in the country. You are not supposed to let go of admission here and go somewhere else :-). You are supposed to come here and make it work. It is just work. You get used to it.
The department teaches the courses targeting the top 10% of the class. The rest of the class steps up over time. The real genius level kids skip out of the entry level sequence that I mentioned above and take the next set of courses. No kid is genius level in all areas of math coming in. They all have particular interests and tend to be good in areas that interest them.
There is also applied math at Princeton offered through the ORFE department – that is a different cup of tea. Not as demanding. ORFE is not part of the math department. The math department doesn’t want anything to do with applied math :-). I am not kidding.
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Is close to home important to the student ?
You said Princeton has always been the dream. But now that’s he into these schools, has he visited ?
I’m guessing with this list there’s no wrong answer. Obviously the sizes and geographies are different. Rice may have a bit more breadth…for example if he later wanted to pivot and to do business.
But Williams and Amherst are the top LACs and Princeton maybe the top school. Amherst has added value if he’s worried about remoteness with UMASS close by.
I’m sure academically all can and will deliver.
Best of luck.
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These are all good programs, with Princeton better than the others.
I’m sure you know this but the math high schoolers see or even engineers is not the math that math majors love. My daughter is considering adding a math minor to her CS major and she’s finding it interesting and challenging and very different than Calculus 1-3.
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All four of these schools tend to be recognized for their undergraduate mathematics programs: For Students Seeking a College Strong in Mathematics.
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All are top notch and Williams is well renowned for Math. I don’t know about the others but Princeton seems to be more about theoretical math. @neela1 can speak to it and probably the others as well.
The good news about Princeton/Williams/Amherst is that there is the opportunity to try several areas for size and most kids find the right place for them.
FWIW many of the math majors hang out with the physics kids as well at Pton. Physics is a very collaborative group and there are courses they both take. My guess is that due to relative size of the colleges, there are many more potential peers at Pton-maybe 40 kids per year as math majors and 50 as physics? Just a guess.
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Physics is about 35 and Math is about 40 in 2021.
Physics kids also start with MAT 216-218 or MAT 215-217, as well as some alegbra later on. So they know each other.
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Perhaps the student should look at upper and graduate level math course offerings and faculty rosters at each school to see which department’s offerings look more interesting to him.
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Williams, especially, is known for its classroom experience:
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For the 40 undergrads that it graduates (and some grad students), Princeton has a 100 faculty in the math department. This is not counting the faculty that are at the Institute for Advanced Studies that Einstein worked at, that is separate from Princeton, but behaves as if it is attached to Princeton.
Between the two departments (PU and IAS) they have an outsized impact on Math as a field.
If you don’t find a course that you like, you can go talk to a prof and have him/her offer you a reading course. My son and some friends had a Prof offer a course on Lie Algebras freshman summer when their internships were cancelled due to Covid. For no charge. Or you can ask a Prof to guide you in one-on-one research if you have sufficient preparation.
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This. If he’s not interested in the financial sector then what does he want to do with a math major? It’s better to find out if you are cut out for a PhD by measuring yourself against the best in the field.
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There are at least two great mathematicians that said that hard work gets you very far in math – Terence Tao (PhD from Princeton at the age of 21) and Noga Alon (Princeton Prof). Noga is known to solve a few hundred problems of a certain kind in a day just to gain intuition about some aspect of math he is trying to understand. He is incredibly productive. Math is slow work. And competition math is not the same as doing research in math. Those are different skills. So even if you are coming from a low base, if you work hard, you can do great things in math. And serious math is collaborative. Not competitive.
I have friends in academia who tell me that successful mathematicians are divorced a bit more than average among academicians. Because their work tends to be consuming. So buyer beware :-).
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Years ago, a dear friend started at Princeton as a math major. While they did fine, they also felt that “having seen what true math genius” looked like in several classmates (and incidentally, friends to this day), they pivoted to applied math and economics. It was less a matter of keeping up than in their mind, measuring up.
This was long ago, but my sense was that my friend didn’t feel defeated or dissuaded and they did go on to get a graduate degree in a field requiring higher level math.
My guess is that your son will be appropriately guided at Princeton and that there are many options there. It may or may not be what he plans now but it’ll be an amazing place from which to work that out.
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Thank you so much for all the pertinent and experiential info. It is a relief to know that there is more of a collaborative environment. He is reading into those introductory courses and he is thinking he will start there. Thank you for the suggestions of doing some of the specific leg work during the summer. Do kids use tutoring and office hours actively or is it meanly study groups? And I hear you. If you get into Princeton, you go to Princeton! It is a little tell of be careful what you wish for.
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Mine used office hours and study groups a lot. Also just informal gatherings of kids sitting around trying to figure out a problem and grabbing any grad student or prof who wandered by for insight. As mentioned above, there are lots of affiliated fields to pivot to if one wishes-computer science, ORFE, physics, economics. Those kids place well into finance-consulting-tech or any employer who values quantitative skills.
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Congratulations on the great acceptances.
Your son has indicated he is not interested in the financial sector, but has he indicated what he wants to do with the math degree (recognizing this may change in the future)? Is it academia? Applied mathematics? Something else?
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Kids go to office hours freely — both with faculty and with TAs. Senior professors are very approachable. Freshman fall my son walked into a field’s medalists office hours and had him explain a paper written by someone else for a couple of hours.
Also on pivoting — some areas can be approached from multiple departments. For example, combinatorics can be approached from CS and Math ( although this year the CS kids in combinatorics placed less well than the Math kids in combinatorics into grad school), logic can be approached from both math and philosophy ( often you have math, philosophy, physics and CS kids taking these classes together), mechanism design is at the intersection of math, CS and economics, areas in physics such as fluid mechanics are very math adjacent etc.
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