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<p>Most colleges’ math major degree programs are designed so that a student starting in calculus 1 can complete them easily in eight semesters. However, many of the top math majors start in calculus 2 or a more advanced math course, based on the availability of advanced math courses in their high schools or nearby colleges. In a few cases, brilliant-in-math students with dual-enrollment opportunities at a nearby major university may reach junior level math courses like real analysis or abstract algebra while still in high school.</p>
<p>So the summary is, the amount of math taken in high school that you describe is more than enough for an incoming math major, but such a student, if attending a school with a large and good math department, will likely encounter even more advanced students in math. With the described amount of math in high school (though multivariable calculus, assuming it is a dual-enrollment course that gives transferable college credit), the student would enter college taking linear algebra and differential equations, and possibly a proof-techniques and/or discrete math course, then move on to junior/senior level math courses.</p>