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The content of many courses in the U.S., especially science and math courses, is pretty uniform. Often the very same texts are used. You can't take calculus at the University of Louisville and only be taught half as much as someone taking the equivalent course at an Ivy League school.


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In my experience teaching at elite schools and discussing teaching with mathematicians, scientists, and engineers elsewhere, this is dead wrong.

You can find many exceptions, but in general, mediocre schools do not have anywhere close to the same depth of curriculum as schools like Harvard, Princeton, MIT, etc. Almost all (over 95%) of the students taking freshman mathematics (Math 1) at Caltech have passed AP BC calculus or the equivalent in high school. The content of the course is not set by keeping pace with the other calculus classes in schools with students with weaker backgrounds. It is determined by the demands of later classes, which are also much more demanding at Caltech than elsewhere. The text books used at elite schools are sometimes the same, but sometimes very different.

Let's see. In one year, students in Caltech's Ma 1a (the first term of freshman mathematics) were required to be able to prove differentiability implies continuity, and to be able to rigorously derive Stirling's formula (from error estimates in Simpson's rule applied to a particular function; they also had to be able to derive the error estimates). By the way, this was not for mathematics majors. Many mathematics majors at Caltech would skip Ma 1, and would take classes like Ma 5, introduction to abstract algebra, which used a text used for graduate abstract algebra courses elsewhere. Please point to anything remotely resembling that, in a class called calculus, for non-majors, at a school where the average SAT math scores are under 600. The material you teach people you expect will become accomplished scientists and engineers is very different from the material you teach to future middle-level managers.

Some schools of all types align the calculus classes with the high school courses, to let students who have passed AP Calculus pass out of the lowest level calculus class(es). This often means that there is a college class designed to substitute for an AP class, which therefore does not cover as much material as a normal college class. These classes are not representative of the courses taught to students in later years.