Welcome to College Confidential, @droskill!
I am not a math expert, but in looking at College Navigator (the feds’ website), I focused on schools with a good number of students in general math programs (as applied to financial math, applied math, statistics, etc.) as a very high-level gauge as to what type of options might be available for a student interested in pure math. In terms of assessing the math content of a school, I would rely heavily on @Twoin18’s knowledge as well as @ucbalumnus and tagging in @hebegebe.
UMass-Amherst is a great option and will be tough to beat since you have in-state pricing. But it’s always nice to have choices, so here are some additional schools your family may want to investigate:
Will Meet Budget
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Central Michigan: About 10k undergrads, offers through a PhD in math (2 conferred in SY23-24) and has no differential for out-of-state students. @2plustrio has a kid here.
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Iowa State: About 25k undergrads
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Northern Illinois: About 11k undergrads, offers through a PhD in math (3 conferred in SY23-24), and no differential cost for out-of-state students.
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Southern Illinois – Carbondale: About 8200 undergrads and this school really tends to punch above its weight in terms of the number of students going on to earn doctorates in a variety of academic fields.
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U. at Albany (NY): About 12k undergrads and the tuition would be the same as at UMass due to their flagship match program (which is now applicable for students from all states, not just a select few!).
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U. of Utah: Seconding this school of about 27k undergrads
Highly Likely to Meet Budget
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Clarkson (NY): About 2500 undergrads. This is a STEM-focused school and offers through a PhD in math (4 math doctorates were conferred in SY23-24). Tends to be very generous in doling out merit aid.
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Ohio U.: Seconding this school of about 19k undergrads
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U. of Iowa: About 22k undergrads
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U. of Missouri: About 24k undergrads
Potential to Meet Budget, but Less Likely
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Binghamton (NY): About 14k undergrads and the sticker price is about $50k. But they are trying to attract more out-of-state students, so maybe there’s the possibility of a modest scholarship to bring this within budget?
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Brandeis (MA): About 3700 undergrads here. Run the Net Price Calculator to see if this might fall within budget. If it doesn’t meet the budget via need-based aid, I doubt your son would receive sufficient merit aid to meet your price target.
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Stony Brook (NY): About 18k undergrads. Sticker price is about $51k, but perhaps your son might receive enough merit aid here.
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U. at Buffalo (NY): About 20k undergrads and a sticker price of about $49k. I suspect this school might be more likely to offer merit than Binghamton or Stony Brook, but that is just a guess on my part.
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U. of Connecticut: About 19k undergrads. If your son was interested in double majoring in something like Applied Data Analysis, Mathematics/Actuarial Science, Mathematics/Actuarial Science/Finance, or Statistics (all of which sound not like abstract math) then he could qualify for the Tuition Break program (formerly the New England Regional Program) and pay 175% of UConn’s in-state tuition (source).
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U. of Minnesota – Twin Cities: About 40k undergrads. This school may have one of the most robust math programs on this list, and its NPC does give a merit estimate to see if it will fall within budget.
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U. of Vermont: About 12k undergrads and I have heard that their NPC is pretty accurate with respect to estimating merit aid.
Rutgers, Maryland, and Wisconsin are some other schools that are reputedly very strong in math, but I am less optimistic about them coming close enough to budget. I could, however, easily be wrong. 