The PhD distribution requirements are (a) **extent** passing 36 credits of 6000+ courses; (b) **breadth** completing sequences in two of the following four categories, two semesters in a third, and a semester in the fourth.

**Algebra, Combinatorics and Number Theory**

- MAS 6331-2 Algebra
- MAS 7396-7 Advanced Topics in Algebra
- MAD 6206-7 Combinatorics
- MAS 7215-6 Theory of Numbers

**Analysis**

- MAA 6616-7 Analysis
- MAA 6406-7 Complex Analysis
- MAA 7526-7 Functional Analysis

**Applied Mathematics**

- MAD 6406-7 Numerical Analysis
- MAP 6327-8 Applied Differential Equations
- MAP 6356-7 Partial Differential Equations
- MAP 6467-8 Stochastic Differential Equations and Filtering
- MAP 6472-3 Probability
- MAP 6487-8 Biomathematics Seminar
- MAT6932 Calculus of Variations/Optimal Control (Fall)+ MAP6208 Numerical Optimization (Spring)

**Topology and Foundations**

- MTG 6256-7 Differential Geometry
- MTG 6346-7 Topology
- MTG 6401-2 Ergodic Theory and Dynamical Systems
- MTG 7396-7 Advanced Topics in Topology
- MHF 6306-7 Logic

Additional courses may be offered which fulfill these requirements. Such courses will be approved by the Graduate Committee at the time they are offered.