Abstract math for an average student [HS junior, 3.5 GPA, multivariable calculus completed, <$45k]

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Hey all,

My teen is a junior this year and is very talented in math. He’d like to pursue a degree in abstract math. His GPA is 3.5, and he just took the PSAT and we expect a high math score (740+) and a lower english score (550). He very smart, but doesn’t test great.

So we’ve ruled out top programs like MIT - and we’re on the hunt for a college program that would be interested in a smart, dedicated kid who loves math (he completed AP Calc BC as a freshman and recently completed multivarible calc at Harvard extension school).

We’re looking locally at UMass Amherst - but it doesn’t seem to have a very strong abstract math program, and Tufts (which seems to have a decent program).

So: looking for recommendations of what schools we should be looking at outside of these two. We’re looking at WPI but I don’t think it will work for him given his love of math vs. engineering.

Any thoughts/help greatly appreciated - happy to provide more data as required.

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Has he taken any math course focused on proofs and theory (e.g. UMass Amherst MATH 300, or an honors college math course, or perhaps a discrete math course) to confirm his interest in pure math?

Do you have cost constraints? Are there other constraints or preferences in a college or university?

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The Tutorial Program at Ohio University would allow them to go beyond classroom material and to take graduate classes as an undergrad. Honors Tutorial College | Ohio University

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Purdue also allows for undergrads to take graduate level classes and has a very strong math department. They are test required though.

RPI would be another school to consider.

Any chance that your son’s GPA will go up junior year?

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Utah is a great option for strong math students with lowish GPA (3.5UW will definitely be enough to get admitted). The top students often win national awards like Churchill scholarships. Not too expensive either, given the option to get instate tuition after freshman year.

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This topic may offer you suggestions to research further: For Students Seeking a College Strong in Mathematics.

As an additional idea, look into Grinnell.

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Thanks for the additional questions.

  • He completed multivariable calc at Harvard Extension and is now doing differential equations with a tutor (no other math option for us in person), but hasn’t gone beyond that yet. He certainly explores those areas on his own (e.g. discrete), but hasn’t taken a formal class.
  • Cost constraints: we’ve got money put aside that should cover about 50-60% of his undergrad - obviously spending less is better but we also know it can be critical to have a degree from the right program for grad school.
  • No constraints of college vs. university.
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We’re hoping his GPA and SAT scores go up this year - he’s certainly working hard but the poor kid just gets so flustered at test taking! I’ll look at both Purdue and RPI. Thank you for the thoughts!

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50-60% of expensive private undergrad or 50-60% of in-state public undergrad?

Have you used net price calculators on various possible colleges to check if financial aid will result in an affordable net price at each college?

So no preferences on location or anything else other than pure math academic offerings and cost?

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Here are the top PhD feeders. If you look at the right side, it’s the per capita. You might look at some of these - and look at their math curriculums.

When you note you’ve ruled out a school like MIT, a 3.5 with even a 1400 isn’t going to get you into strong math schools - like UMD. That’s just a reality. I don’t know the student’s rigor outside of math - so that could hurt too.

But Earlham is on the list of top feeders as is Oberlin, Kalamazoo, Whitman, St. Olaf, Beloit, Hendrix, Juniata, Willamette, and Puget Sound. Kalamazoo gives great merit but more importantly has a flexible curriculum. It sounds like a student who might want to “avoid” certain subjects? I could be wrong there.

It may be at some schools the student walks in with a lot of credits - I don’t know.

As for budget, when you say you have 50% set aside - so you have about $45K a year set aside? Some schools will be $45K or less including big publics. Others with merit, etc.

A U Florida about hits budget but is likely a reach as would UGA be and likely Florida State too. A Stony Brook might work for a big school - both $$ and admission wise. UMN would be a stellar flagship. If the GPA stays at 3.5 and the SAT comes in high, you’ll have cheaper options in the South if needed.

Math is a great major and I think one can do well from most anywhere, especially job wise.

But given the stats that you’ve put up, I think your options will be more limited at the “top level” than you think.

I would like to learn more about the student in English, Foreign Language, Social Science and Science too.

Top Feeders to Ph.D. Programs

Requirements for the Major or Minor – Math Department | Kalamazoo College

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However, with some of the smaller schools, a small math department may not have enough pure math offerings to satisfy a student who enters very advanced in math like the one in this thread. OP and the student should investigate carefully the math offerings at various schools of interest.

For example, Kalamazoo appears to have only about seven upper level pure math courses in its catalog.

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Cost constraints: Keeping it simple here - $45k per year.

Net Price Calculators: Have not done this yet - trying to figure out what the initial list of schools looks like to dig in on this.

Constraints: We’re based in Boston - he’d like to be relatively close to us (drivable) - but he also recognizes that may have to go far afield (e.g. Utah) to find the right program.

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This is actually my concern with a smaller school. That’s one reason why we’ve been looking a bit more at universities vs. colleges.

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That’s why I note - the OP would have to check. But if schools are top feeders to PhDs - they might be worth calls or informational interviews with the math department.

The lesser tier LACs will hit cost (assuming no aid). For big flagships, the student may need to leave.

Admissions may be an issue - but within range does a UNH, U Maine or URI type have enough heft? Or any SUNYs. Maybe Rutgers? Pitt will be over budget but how about Temple? For meets need privates, maybe a Rochester or Case Western (with a lot of interest) - but we don’t know if the family will have need.

I think there are certainly colleges in the Northeast without having to go to Utah - but at $45K, that might be the limiter. I’m guessing the meets need schools won’t be in play - most of them - unless the student has overall rigor.

Appreciate if you can talk about the classes taken outside of math - they’ll matter - but a math centric student not advanced curriculum wise in other areas likely won’t be admitted by top schools.

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That seems to cover in-state public universities in MA, assuming that is the state of residency. However, out-of-state flagships, which may be well represented among schools with large math departments that would not be unreasonably difficult to get admitted to, are unlikely to fall under that price limit without substantial scholarships (not all of them do offer substantial scholarships).

UMass Amherst’s math offerings are listed at Regularly offered courses : Department of Mathematics and Statistics : UMass Amherst

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Does the student meet the UMASS minimums? We know about math but nothing else.

UMass says this:

Minimum subject matter requirements must be met (see below).

Unit Requirements

  • English: 4

  • Mathematics (Algebra II minimum): 4 including math in the senior year of high school

  • Natural Science (3 labs): 3

  • Social Science (one course in US history): 2

  • Foreign Language: 2 of same language (waived for MA vocational tech high schools)

  • Electives (from areas above, arts and humanities, or computer science): 2

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Take a look at Union (NY) to see if it fits your requirements for courses and cost. They give merit.

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OP, this is an important comment by ucbalumnus. Your son is no doubt unusually advanced in math. But it is not until he takes a theorem-proving math class – typically a real analysis course or a proof-based linear algebra course – can he confidently say he is interested in pure math (or abstract math as you call it).

Many college students who scored 780+ in SAT math and who aced multivariable calculus, differential equations, and elementary linear algebra, struggle with proving mathematical statements from the ground up, using only axioms/logic and resisting the temptation to say “this is obviously true.” The theorem-proving mindset/process is quite different from “computing this derivative or integrating that function.” Most students don’t enjoy the process and don’t find it natural to them. Some even hate it.

Since your son is only a high school junior, he has time to figure out whether pure math is really for him, or applied math (or even engineering) actually suits him better. He doesn’t have to enroll in a real analysis class to find out. He can get a taste of pure math by googling “introduction to math proofs” and trying out on his own some of the elementary proof exercises contained in articles returned by the search. He may also read this article on how to do proofs written by a UC Berkeley math professor for beginners, and see how well he is able to follow.

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There is also the occasional student who is just ok in more basic math classes, but really blossoms once they find out that they love proofs.

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Top “feeders to PhDs” in STEM or generically in social science and humanities? I suspect these smaller schools are the latter because it’s typical to take as many upper level courses as possible and even some grad level courses before getting admitted to a STEM PhD.