# Required Coursework

A three-course sequence in each of the three fields of algebra, analysis, and geometry-topology (manifolds) will be offered each year. Preliminary examinations will be given for each core sequence at the beginning, middle, and end of each academic year.

First-level passage of a preliminary examination satisfies the core sequence requirement for that field. Ph.D. students are required to complete the full core sequence in the field associated with the preliminary examination in which they do not achieve a first-level pass. The core sequences are as follows:

- MATH 200, Algebra I
- MATH 201, Algebra II
- MATH 202, Algebra III
- MATH 204, Analysis I
- MATH 205, Analysis II
- MATH 206, Analysis III
- MATH 208, Manifolds I
- MATH 209, Manifolds II
- MATH 210, Manifolds III

Students are also required to complete Math 288A* plus six additional courses in mathematics. No more than three courses may be independent study or thesis research courses.

**Required for all cohorts entering the program Fall 2019 and later. *