Budapest Semesters in Mathematics (BSM) is an off-campus study program in mathematics, founded in 1985 by friends of Paul Erdös. Many Carleton math majors have attended BSM over the years. In fact, Carleton has sent more students to BSM than any other institution. Since BSM is a semester program, Carleton students usually go in the fall of their junior year. (Spring semester of BSM would overlap with both winter and spring terms at Carleton, and it may not yield enough academic credit for this to be a good choice. It’s possible to go in the fall of a student’s senior year, but that would limit the student’s choice of comps groups for their senior year.)
BSM has a summer program (BSM-Summer) and also has a sister-summer-program for students interested in the study of teaching secondary mathematics, Budapest Semesters in Mathematics Education (BSME-Summer).
Financial aid packages can usually be applied to cover the cost of a fall semester at BSM. Financial aid packages usually cannot be applied to BSM-Summer or BSME-Summer.
If you’re considering going to any of these programs, you should read about the recommended background, how to apply, math major electives, and Carleton credit. Feel free to ask people in the department for advice: current math majors who have gone to Budapest or math faculty are great resources.