# 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