Course Recommendations

Graduate Course Recommendations

  • MATH 555, MATH 601 and MATH 631 are strongly recommended for most students.
  • The Fall of your first year, you should plan to take MATH 771 (required) and three additional courses.
  • The Spring of your first year you should plan to take three or four courses.

Typical graduate course sequences for various focus areas are listed below.  (Some, but not all, of these courses are qualifying eligible.) Discuss your course selections with your mentor/advisor before registering each semester; the guidelines below are general, your mentor/advisor will help you identify the high priority courses.

Applied Mathematics & Numerical Analysis

  • First Year:
    • MATH 553 Asymptotics and Perturbation Methods
    • MATH 555 ODE
    • MATH 561 Numerical Linear Algebra, Optimization and Monte Carlo Simulation
    • MATH 557 Intro to PDE
    • MATH 563 Applied Computational Analysis
    • MATH 575 Mathematical Fluid Dynamics
    • MATH 577 Mathematical Modeling
    • MATH 631 Real Analysis
    • MATH 641 Probability Theory
  • Second Year: 
    • MATH 541 Applied Stochastic Processes, 
    • MATH 553 Asymptotics and Perturbation Methods, 
    • MATH 575 Mathematical Fluid Dynamics, 
    • MATH 641 Probability Theory
    • MATH 651 Hyperbolic PDE
    • MATH 661 Numerical PDE I
    • MATH 663 Numerical PDE II
    • MATH 653 Elliptic PDE
    • MATH 690-40 Topics in Probability

Algebra & Number Theory

  • First Year:
    • MATH 601 Groups, Rings and Fields
    • MATH 602 Commutative Algebra
    • MATH 605 Algebraic Number Theory
    • MATH 611 Algebraic Topology I
    • MATH 631 Measure and Integration
    • MATH 633 Complex Analysis
    • MATH 636 Analytic Number Theory
  • Second Year:
    • MATH 603 Representation Theory
    • MATH 612 Algebraic Topology II
    • MATH 620 Smooth Manifolds
    • MATH 621 Differential Geometry
    • MATH 625 Riemann Surfaces
    • MATH 627 Algebraic Geometry

Analysis

  • First Year: 
    • MATH 545 Stochastic Calculus
    • MATH 555 ODE
    • MATH 557 Intro to PDE
    • MATH 631 Real Analysis
    • MATH 633 Complex Analysis
    • MATH 641 Probability Theory
  • Second Year:  
    • MATH 545 Stochastic Calculus
    • MATH 553 Asymptotics and Perturbation Methods
    • MATH 635 Functional Analysis
    • MATH 641 Probability Theory
    • MATH 651 Hyperbolic PDE
    • MATH 653 Elliptic PDE

Geometry & Topology

  • First Year: 
    • MATH 555 ODE
    • MATH 631 Real Analysis
    • MATH 601 Groups, Rings and Fields
    • MATH 602 Commutative Algebra
    • MATH 611 Algebraic Topology I
    • MATH 620 Smooth Manifolds
    • MATH 621 Differential Geometry
    • MATH 633 Complex Analysis
  • Second Year: 
    • MATH 603 Representation Theory
    • MATH 612 Algebraic Topology II
    • MATH 653 Elliptic PDE
    • MATH 627 Algebraic Geometry
    • PHYSICS 781 Quantum Field Theory
    • MATH 527 General Relativity
    • MATH 690-20 Topics in Differential Geometry
    • MATH 605 Number Theory

Probability

The essential Probability courses are 

  • MATH 541 Applied Stochastic Processes
  • MATH 545 Stochastic Calculus
  • MATH 631 Real Analysis
  • MATH 641 Probability Theory

Other important courses connecting to probability include 

  • MATH 553 Asymptotics and Perturbation Methods
  • MATH 555 ODE
  • MATH 557 Intro to PDE
  • MATH 561 Numerical Linear Algebra, Optimization and Monte Carlo Simulation
  • MATH 633 Complex Analysis
  • MATH 635 Functional Analysis

Students should select other courses in Analysis, Applied Mathematics and Numerical Analysis based on their interests. For example students working in Stochastic Analysis should take courses in PDE. In general, strong computational skills are valuable.


Also see the list of Math Graduate Courses in the Graduate School Course Bulletin.