Are there any competitions similar to the USAMTS open to college students?
Yes, there are! Perhaps the most famous is the Putnam Mathematical Competition. Started in 1938 and sponsored by the Mathematical Association of America (MAA), the Putnam is open only to regularly enrolled undergraduates, in colleges and universities in the United States and Canada who have not yet received a college degree. The Putnam exam takes place once a year, usually around the beginning of December. No individual may participate in the competition more than four times. The Putnam competition is divided into two sessions, morning and afternoon. There are six problems in each section and they are graded on a 0-10 point scale, for a maximum possible score of 120 points. The problems are difficult! For example, the median score on the 1998 Putnam exam was 10 points, so participants who worked one problem correctly scored in the top half of the entries. After the Putnam exam is given, the problems and solutions are published in the American Mathematical Monthly, a journal published b