In the USA, do college courses deeply differ from high school courses? I'm interested in school systems, and I have a question regarding the &quot;college&quot; level. (I have a French background).
When I look at college math or physics books, it seems to me that there is no big difference with what is taught at the high school level.
By comparison, in France, first year university math or physics books dramatically differ from high school books.
To put my question in a provocative way: what is the purpose of teaching at the college level what students already know from their high school courses? Or don't they? Or, is my vision of college contrary to actual facts?
First of all, the US has no university system.  It has somewhere around 1500 community colleges offering 2 year degrees and 3500 colleges and universities offering 4-year degrees, all of which run with more independence than an ordinary French university.  (Keep in mind the federal government has established only a tiny handful of universities; public universities are nearly all set up by the individual states.)
Second, you should understand that there is no high-school leaving exam like the bac.  Basically anyone who is willing to sit in the classroom and do a minimal amount of work can get a high school diploma.  Harvard is incredibly selective and it's about as hard to be admitted to Harvard as it is to be admitted to the ENS.  The top 100 or 200 of US universities are all selective, and the average student would not be admitted.  However, most universities and all community colleges will allow anyone with a high school diploma to attend.  (My university officially has admission requirements based on high school grades, but high school grades have been inflated to such an extent that these requirements are almost meaningless, and the admissions office routinely gives waivers to these requirements anyway.)  About 85% of Americans earn a high school diploma and can attend community college.  (Another several percent obtain a GED.)  Only about 45% of French take and pass the baccalaureate general and can attend university.
At a community college, you should expect that many students do not actually know what you might think they should have learned from high school, and a significant number of students will have trouble with upper elementary material such as adding fractions.  There will even be a few students who are functionally illiterate.