1, Harvard-MIT Mathematics Competition (HMMT) is a high school mathematics competition jointly organized by Harvard University and MIT. Up to now, it has a history of 19, and it is one of the most influential math competitions for senior high school students in the United States.

2. The University of California, Berkeley Mathematics Competition (BMT) is organized by the Department of Mathematics of the University of California, Berkeley. The purpose of this paper is to pay attention to mathematical problems with novel and interesting contents, advocate encouraging students to go beyond the limitations of the classroom through competitions, and cultivate students' unique mathematical thinking and innovative ideas, as well as the sense of cooperation and mutual assistance among teams.

3. Duke University Youth Mathematics Conference (DMM) is an annual mathematics challenge for middle school students sponsored by Duke University Mathematics Department and undertaken by Duke University Mathematics Federation. DMM emphasizes mathematical thinking ability, reaction ability and flexibility, and pays attention to students' teamwork ability.

4. The Mathematics Competition of Princeton University (PUMaC) has been held by the Mathematics Club of Princeton University since 2006, and the whole process has been organized by students of Princeton University. It is a math competition for international high school students and one of the world-famous math competitions.