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
- reading proficiency in one foreign language, usually French, German, or Russian
- 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
- reading proficiency in French, German, or Russian
- passing marks on the Preliminary Examination consisting of three four-hour written and one one-hour oral 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).
The preliminary exams are intended to check that a student has a broad breadth of mathematics. The exam consists of three four-hour written examinations, usually in Algebra, Analysis, and Topology, followed by a one-hour oral. They are taken in one five-week period, either in the Spring or Fall.
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.
For both the M.A. and the Ph.D. degree one foreign language is required: French, German, or Russian. Students whose native language is not English are not required to present an additional language. Language skills will be tested by examinations administered by the department or may be demonstrated by the satisfactory completion of appropriate courses approved by the department. Any foreign language other than the ones listed above must be approved by the department.