I am a Canadian High school student and intend to take Putnam contest this year, a well-known annual mathematics competition for undergraduate students. According to the Mathematical Association of America (MAA): “An eligible student who has not yet received a high school diploma should be informed of this limit before participating,” which caused me some confusion about the word “eligible” and I also learn that there are people can take Putnam when they were in High school. Is it possible to take the Putnam exam when I’m still in High school? If the answer is yes, would someone be pleased to show me how can we participate or what requirements for high school students to take the exam?
I want to take part in the contest in order to advance myself about mathematic at College, and learn more from cooled people. Here is a link about Putman contest from MAA: https://www.maa.org/math-competitions/putnam-competition.
Your interest in the Putnam exam is very admirable! I handled the registration for my university's Putnam team for many years, so I believe I can answer your question.
While the posted eligibility critera could be clearer, the key sentence in the website's FAQ is: "The competition is open only to regularly enrolled undergraduates, in colleges and universities of the United States and Canada, who have not yet received a college degree." So to be eligible, you need to be a "regularly enrolled" student at a college or university.
This does not necessarily mean full-time enrollment. If you are officially registered for one college/university course, you are eligible to take the Putnam as part of that institution's group of Putnam-takers. Presumably you would find the Putnam contact at that insitution and contact them directly for more details.
Otherwise there are no elgibility requirements: you don't have to have taken specific math courses or have specific grades or anything like that (just as with the university students themselves).
If you end up not being able to take the Putnam this year, you can look forward to four Putnams as a university student! And the Putnam is posted online soon after it is given, so you can take any year's Putnam for fun on your own.