## Requirements for the Ph.D. Degree

In order to qualify for the Mathematics Ph.D., all students are required to:

- Complete eight term courses at the graduate level, at least two with Honors grades.
- Pass qualifying examinations [1] on their general mathematical knowledge;
- Submit a dissertation prospectus;
- Participate in the instruction of undergraduates [2];
- Be in residence for at least three years;
- Complete a dissertation that clearly advances understanding of the subject it considers.

All students must also complete any other Graduate School of Arts and Sciences degree requirements [3] as they appear in the Programs and Policies bulletin.

The normal time for completion of the Ph.D. program is five years. Requirement (1) normally includes basic courses in algebra, analysis, and topology. The Honors grades of (1) must be achieved within the first two years. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term. All qualifying examinations must be passed by the end of the second year. There is no limit to the number of times that students can take the exams, and so they are encouraged to take them as soon as possible.

The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)–(5) and obtaining an adviser.

In addition to all other requirements, students must successfully complete MATH 991a, Ethical Conduct of Research, prior to the end of their first year of study. This requirement must be met prior to registering for a second year of study.

**Master’s Degrees**:

The M.Phil. and M.S. degrees are conferred only en route to the Ph.D.; there is no separate master’s program in Mathematics.

**M.Phil.** Please refer to the Graduate School Degree Requirements [3]

**M.S.** A student must complete six term courses with at least one Honors grade, perform adequately on the general qualifying examination, and be in residence at least one year.