Why is there such a big difference in math education between The Americas and (Europe and Asia) ? except for a few privileged who have the opportunity to access to math much earlier than the ordinary people.
The Question arises when in my first class in my topology class, my professor, who is russian, said that in Russia universities freshmen students take topology and geometry, measure theory and abstract algebra in their first semester. On the other hand, say in the US, most of students start taking calculus 1(with proofs removed) and a logic class on how to write proofs.
In third year when US undergrad math students are just learning the real math (topology, abstract algebra, and real analysis), Russian students are already taking courses such as algebraic geometry, differential topology, Category theory, Riemannian Geometry, etc.
Why is there such a brutal difference?