Mathematics Degree Requirements
Requirements for the M.A.
- at least two units in 500 or 600-level graduate mathematics
- at least two additional units in graduate mathematics
- at least two additional units in graduate mathematics or an allied field
- completion of an M.A. thesis
- passage of an oral final examination in the area of the thesis
The M.A. is most commonly completed in a two-year period during which the student takes two courses each semester for a total of eight units, at least two of which are devoted to research on and writing of the M.A. thesis. All M.A. candidates are required to write a thesis. An M.A. thesis may be based on original research, expository, or a combination of the two.
An undergraduate student enrolled in the A.B./M.A. Program must meet these same requirements with the exception that up to two units may be taken for dual undergraduate and graduate credit.
Requirements for the Ph.D.
- at least 12 units in mathematics, providing a broad foundation of study
- passing the Preliminary Examination
- completion of a Ph.D. dissertation
- passage of an oral final examination in the area of the dissertation
Although it is not required, we recommend that most students first complete an M.A. degree, before continuing on to the Ph.D.
The twelve units generally include many units of Supervised Work (Math 701).
A Ph.D. student in Mathematics may enter the Preliminary Examinations after demonstrating proficiency in three general principal areas of mathematics, which will typically have been shown through the student鈥檚 regular graduate course work and through additional required work, if needed. In the Preliminary Examinations themselves, the Ph.D. student demonstrates advanced proficiency in one or two topics as formulated by the student and their potential advisor and approved by the Department. The Preliminary Examinations consist of the following components:
- the student will deliver a short course of 3-4 lectures (addressed to graduate students and faculty in mathematics);
- for a written examination, the student will submit a written component (comprised of lecture notes and substantial responses to a set of prompts, which may be worked on, untimed, at any time over the first four weeks of the examination period); and
- for an oral examination, the student will participate in a conversation with the Supervising Committee (for the committee to gain further clarification on prompts and responses and for the candidate to share additional knowledge).
All Ph.D. candidates must complete original research the results of which must be presented in a well-crafted dissertation that is worthy of publication. The oral final exam is a standard dissertation defense consisting of a presentation of the dissertation material, questions from a general audience, then further questioning by the committee, after the rest of the audience is excused.
Our graduate students may specialize in any of the broad divisions of mathematics represented among our faculty (see our faculty research interests). In certain circumstances, arrangements have been made for graduate students to work with faculty at other institutions. In all cases, students are expected to acquire a well-rounded understanding of mathematics as a whole.