gorcee wrote:If I'm not mistaken, Swiss/European students typically begin university around age 20, right?
Right, 19/20. In the US?
By the way, all our classes are proof based.
College typically starts at 18 in the United States. The ordinary incoming freshman oriented towards math, sciences, or engineering will come in knowing analysis up through the Fundamental Theorem of Calculus.
Just for lulz, here is the recommended schedule for (pure) math majors at Carnegie Mellon (my alma mater, although I took the honors track):
1st semester: differential and integral calculus, physics 1 (mechanics), computer programming, biology, rhetoric
2nd semester: differential equations and approximation, formalistic foundations, "matrix theory", physics 2 (electromagnetism), humanities elective
3rd semester: discrete math (or combinatorics or graph theory), multidimensional calculus, chemistry, two electives
4th semester: ODE, abstract algebra, three electives
Junior year: two semesters of real analysis, probability, and linear algebra
I should make clear that those electives are largely but not fully expected to come from the humanities in the first three semesters, although one could focus on mathematically "practical" branches of the liberal arts like philosophy, economics, or statistics for the most part.