Typical graduate course sequences for different focus areas in mathematics
For Fall of first year, 3 courses are recommended, for Spring, 4 courses)
Applied Mathematics/Numerical Analysis
First year
Fall
Math 224 Scientific Computing I
Math 231 ODE
Math 241 Real Analysis
Spring
Math 225 Scientific Computing II
Math 232 Intro to PDE
Math 245 Complex Analysis
Math 287 Probability Theory
Second year
Fall
Math 216 Applied Stochastic Processes
Math 226 Numerical PDE I
Math 233 Asymptotics and Perturbation Methods
Math 282 Elliptic PDE
Math 288 Topics in Probability
Spring
Math 227 Numerical PDE II
Math 228 Mathematical Fluid Dynamics
Math 229 Mathematical Modeling
Math 281 Hyperbolic PDE
Math 287 Probability Theory
Courses in the third year might include Math 242 Functional Analysis,
Math 282 Elliptic PDE, or Topics in Partial Differential
Equations. Other courses of interest in connection with applied mathematics
are listed by the
Center for Nonlinear and Complex Systems.
Analysis/Probability
First year
Fall
Math 215 Mathematical Finance
Math 216 Applied Stochastic Processes
Math 231 ODE
Math 241 Real Analysis
Spring
Math 219 Stochastic Calculus
Math 232 Into to PDE (PDE I)
Math 245 Complex Analysis
Math 287 Probability Theory
Second year
Fall
Math 215 Mathematical Finance
Math 216 Applied Stochastic Processes
Math 242 Functional Analysis
Math 282 Elliptic PDE
Math 288 Topics in Probability theory
Spring
Math 219 Stochastic Calculus
Math 249 Topics in Functional Analysis
Math 287 Probability Theory
Algebra/Geometry
First year
Fall
Math 231 ODE
Math 241 Real Analysis
Math 251 Groups, Rings and Fields
Spring
Math 245 Complex Analysis
Math 252 Commutative Algebra
Math 261 Algebraic Topology I
Math 267 Differential Geometry
Second year
Fall
Math 253 Representation Theory
Math 262 Algebraic Topology II
Math 272 Riemann Surfaces
Math 282 Elliptic PDE
Spring
Math 268 Topics in Differential Geometry
Math 273 Algebraic Geometry
Math 274 Number Theory
Courses in the third year might include Math 236 General Relativity,
and Number
Theory or Algebraic Geometry.
Geometry/Mathematical Physics
First year
Fall
Math 231 ODE
Math 241 Real Analysis
Math 251 Groups, Rings and Fields
Spring
Math 245 Complex Analysis
Math 252 Commutative Algebra
Math 261 Algebraic Topology I
Math 267 Differential Geometry
Second year
Fall
Math 236 General Relativity
Math 253 Representation Theory
Math 272 Riemann Surfaces
Math 282 Elliptic PDE
Spring
Math 268 Topics in Differential Geometry
Math 273 Algebraic Geometry
Math 274 Number Theory
Courses in the third year might include Algebraic Topology II,
and Number Theory or Algebraic Geometry. Students interested in
mathematical aspects of string theory will be encouraged to take additional
physics courses, including Quantum Field Theory.