Some schools require you to apply to one specific subject and only study that subject during your time there. It is my understanding that most universities outside America are like that. Other universities have minimal constraints, like Brown where there’s no core curriculum and you can take however many classes you want pass fail. The only constraint is the requirements for your major. But some American schools fall in between, like University of California and CMU where you have to apply to a specific school.
I personally have excelled at math in high school and will have a much better chance of getting into a school to just study math, but I really want to go somewhere that I can explore other subjects. Any ideas about some good places for me?
In general, US universities expect students to take some courses outside of their majors, possibly as required general education, possibly as free electives. Liberal arts majors like math tend to consume about 35-50% of the total course work for courses in the major, leaving the rest for general education and free electives.
However, access to majors and courses depends on whether math and the other subjects you are interested in are oversubscribed at the schools you are considering. The problem is that if the subject is oversubscribed, admission to the major may be additionally competitive beyond getting admitted to the school, and access to the courses by non-majors may be difficult.
@Broses, it sounds like a liberal arts college would be ideal as many have well regarded Math programs with many having as much as 10% of the students as Math majors; Bowdoin, Hamilton , Harvey Mudd, Swarthmore and Williams are some examples - there are many others.
For freedom-of-movement across most arts & science subjects (including math), it doesn’t necessarily matter much whether the school is a LAC or a research university. It’s more a question of how the liberal arts curriculum is structured. There are research universities (like Brown) where distro requirements are minimal; there are a few LACs where everyone enrolls in virtually the same courses (St. John’s) or major (College of the Atlantic). There are research universities (like UChicago or Yale) with only one undergraduate school/division; there are a few LACs (like the University of Richmond or Oberlin) that do have distinct undergraduate schools (for business/music/etc.)
Chances are, a prospective math major will enter the college of arts & sciences not an engineering school. Within that a&s division, you shouldn’t have major problems switching majors (or exploring subjects outside the major) as long as you can manage the prerequisites and distro/core requirements.