**The requirements for the M.A.** are:

- at least 2 units in 500 or 600-level graduate mathematics
- at least 2 additional units in graduate mathematics
- at least 2 additional units in graduate mathematics or an allied field
- reading proficiency in one foreign language, usually French, German, or Russian
- completion of a 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.

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, thus
decreasing the total number of units required to get the two degrees.

**The requirements for the Ph.D.** are:

- at least 12 units in mathematics, as needed to provide a broad foundation
- reading proficiency in French, German, or Russian
- reading proficiency in a second of these languages or proficiency in an acceptable high-level computer language
- 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 examination usually consists of one test each of Algebra, Analysis, and Topology. The oral final exam is a standard dissertation defense consisting of a presentation of the dissertation material, questions from the 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 specialization). 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.

**Language Exams**

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.

**Preliminary Exams** (for Ph.D. Degree)

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 and Fall.

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. As an indication of the quality of our graduate students' work, in 2001, one of our M.A. students won the prestigious Master's Thesis Award from the Northeastern Association of Graduate Schools.

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.

As topics of these theses and dissertations, graduate
students may specialize in any of the broad divisions of mathematics
represented among our faculty.