<p>Many of the math topics you have seen in high school and the lower division college math courses will reappear in upper division college math courses as you prove them (e.g. in real analysis, you will be writing proofs for calculus theorems).</p>
<p>But the options you have in pure and applied math do determine which upper division college math courses you will take as within-major electives. You can check the math department web sites of various universities to get an idea of what types of courses are suggested for the various options.</p>