[munchbunny]

My experience, also from an ivy league college, was that the beginner classes were taught well but often lacked rigor. But if you were looking for the level of rigor that introductory courses for dedicated majors would provide, you were going to have a bad time because those were often quite unforgiving.

For example, the 100 level math classes mostly did not touch proofs, just calculation. The 200 level math classes were almost exclusively proof based, but they didn't teach you how to write them. Either already knew how or you were going to have to teach yourself the mental framework on the fly. Contrast that with 100 vs. 200 level humanities courses in my college, where there really was a focus on teaching you how to argue points in writing.

[Jtsummers]

That's not unique to ivy league schools. Outside of math majors, most math is taught in an "application" approach, especially at the 100 and 200 level. You're taught enough to be able to use it. You can set up your physics problems in a way that uses calculus, and you know enough calculus to compute an answer (and maybe a bit of diff eq, but likely in Physics 1-3 you haven't formally taken differential equations so your skill there is limited). You know enough linear algebra to set up systems of equations and solve problems with it. But you will rarely find 100 and 200 level courses that, beyond a cursory evaluation, cover the fundamental theorems that really define calculus and linear algebra (as a non-major) unless you end up taking a 300 or higher level course. Same with probability and statistics. The 200 prob/stat class teaches you about applications, and enough to use normal and uniform distributions (guaranteed) and maybe a couple more. You can do some limited modeling, but you won't be able to derive various properties of those distributions or other distributions unless you take a 300/400 level stats course.

Which, it turns out, is sufficient for the vast majority of engineers and scientists.