Is set theory taught in middle school in the US? I recently learned that one of my cousins who is a 7th grader in the United States is learning naive set theory (sets, maps, 1-1, onto maps, relations).  Is this part of middle school math curricula in the US?  So would your average American high school graduate know what a bijection is?
 A: At present, there is no standard US curriculum. The mathematics taught before college in public schools varies by the state, the district, the city, the school, and even the classroom.
There is a movement to create national standards ("Common Core State Standards for Mathematics") which have been adopted in most of the states, but they do not presently have a corresponding curriculum.
Historically speaking, you might be interested in reading about New Math, which included a fair amount of naive set theory in its approach to mathematics curricula. Another term worth looking up is SMSG.
Generally speaking, however, the answer to both your questions is no. Naive set theory is not a standard topic in public schools, and the term "bijection" is almost certainly unknown to the vast, vast majority of high school students in the United States.
A: In my own (junior) high school (between $5$ and $8$ years ago), there was a mild introduction to these things, but nothing at all on the order of even undergraduate mathematics. As an example, it amounted to having sets $A=\{1,2,3,4\}$ and $B=\{1,2,3\}$ and asking if there could exist a $1$-$1$ map, etc. (This was in a public school, by the way).
From students I've tutored in the past, there also seems to be a similar curriculum, but again, I emphasize that it was not anything extraordinary. This seemed a little long for a comment, and this is my own personal experience. I hope it goes somewhat toward answering your question.
A: I was taught 1-1, onto, and 1-1 and onto functions in high school.  I don't recall learning the terms injection, surjection, or bijection but it's certainly possible (35 years ago!). I was just thinking that bijection was 1-1, but it's 1-1 and onto! As I am an above average graduate, I guess that answers your question!  Even above average high school graduates in the USA do not know what bijection is.  I certainly hope this helps someone.   Thanks for the education!
