are the most recommended; the first is mandated by the Department, and the second is almost non-negotiable. My students need to know topology, but in place of the third the qualifying exam in Real Analysis or Combinatorics may be acceptable.
Later Years: You should be taking/auditing one or two courses every semester. This may be your last chance to learn some great mathematics - don't squander it! More or less mandatory:
but all other graduate courses are worthwhile given your interest. Especially for your later life when you may be required to teach these subjects in a college, you might consider