Suggested Curriculum

for a student wanting to write a PhD thesis with me in Algebraic Geometry.

First Year:

  • Analysis: M517, M518
  • Algebra I,II: M566, M567
  • Topology: M570, M571
  • Second Year:

  • Complex Analysis: M519
  • Algebra III, IV: M666, M667
  • Master's Paper
  • Projective Geometry M675E/M775E (if offered) or Riemann Surfaces M619 (if offered)
  • Qualifying Exams:

  • Basic Analysis (Part A) (Covering M517-518-519)
  • Algebra (Covering M566-567)
  • Topology (Covering M570-571)
  • 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:

  • Real Analysis: M617, M618
  • Differential/Algebraic Topology: M670, M675F when offered
  • 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

  • Combinatorics
  • Partial Differential Equations
  • Dynamical Systems/Ordinary Differential Equations
  • Numerical Analysis
  • Linear/Nonlinear Programming, Optimization