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.

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