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Well, I should be more specific. I think once you get into the sort of number theory where you prove things about modular arithmetic, and the sort of analysis w

by lacker 7y ago

Well, I should be more specific. I think once you get into the sort of number theory where you prove things about modular arithmetic, and the sort of analysis where you are talking about abstract spaces rather than n dimensions of real numbers, those courses are notably different from high school courses, and all the focus on proofs is intellectually stimulating to advanced kids. The courses which are typically boring for advanced kids are calculus, linear algebra, differential equations, probability, statistics, combinatorics. Most of an undergrad math degree usually falls into this bucket but it really varies by university. Also, there’s a big difference between colleges. Not because of the curriculum as much as the other students who will set the pace of the class. Often the same kid who could attend Ohio State at 14 could also attend Princeton at 18, and that makes a difference even if the course titles are the same.

nostrademons 7y ago
Ah, I'd agree with that. Calculus/probability/statistics/combinatorics were usually freshman courses at Amherst, and you could often place out of them with APs. Linear algebra was taught proof-based; it and DiffEq were usually sophomore-level courses. The rest of the major was all proof-based.
JackFr 7y ago
>The courses which are typically boring for advanced kids are calculus, linear algebra, differential equations, probability, statistics, combinatorics. Most of an undergrad math degree usually falls into this bucket but it really varies by university. That's just not true. That's the freshman/sophomore curriculum. And there are big differences between the diff eq, stats & linear algebra course which are which are 'proof' vs. those which are 'practical'.
chongli 7y ago
I think once you get into the sort of number theory where you prove things about modular arithmetic That’s one small part of the intro algebra course at my university, which all math and CS students take in the fall of first year. The first year calculus courses are considerably proof-based as well, and lots of first years end up failing despite being a high 90s student at their high school. A more typical high school student who got 80s in their sleeves and calculus courses would fail everything and be asked to withdraw.

by lacker 7y ago

nostrademons 7y ago

Ah, I'd agree with that. Calculus/probability/statistics/combinatorics were usually freshman courses at Amherst, and you could often place out of them with APs. Linear algebra was taught proof-based; it and DiffEq were usually sophomore-level courses. The rest of the major was all proof-based.

JackFr 7y ago

>The courses which are typically boring for advanced kids are calculus, linear algebra, differential equations, probability, statistics, combinatorics. Most of an undergrad math degree usually falls into this bucket but it really varies by university. That's just not true. That's the freshman/sophomore curriculum. And there are big differences between the diff eq, stats & linear algebra course which are which are 'proof' vs. those which are 'practical'.

chongli 7y ago

I think once you get into the sort of number theory where you prove things about modular arithmetic That’s one small part of the intro algebra course at my university, which all math and CS students take in the fall of first year. The first year calculus courses are considerably proof-based as well, and lots of first years end up failing despite being a high 90s student at their high school. A more typical high school student who got 80s in their sleeves and calculus courses would fail everything and be asked to withdraw.