[OJFord]

Yes you generally can in the UK too, just ask the lecturer as a courtesy at least, if there's capacity they'll probably be pleased someone's keen, but might ask you don't submit any problem sheets or whatever for grading.

That's not what GP means though: in the first year in the US, generally speaking, undergraduates aren't enrolled on a particular programme; they take a range of courses from different faculties for credit, and decide which area to 'major in' (and perhaps additionally 'a minor') later.