<p>It does not look like math PhD programs tend to have much in the way of specific graduate level math course requirements, although they do assume knowledge of various topics that an undergraduate math major should know, including real and complex analysis (tested in preliminary or qualifying examinations).</p>
<p><a href=“Coursework”>http://math.mit.edu/academics/grad/timeline/coursework.html</a>
<a href=“PhD Program | Department of Mathematics at University of California Berkeley”>PhD Program | Department of Mathematics at University of California Berkeley;
<a href=“Program Requirements | Math”>https://www.math.princeton.edu/graduate/requirements</a>
<a href=“Harvard Mathematics Department Graduate Information”>Harvard Mathematics Department Graduate Information;