Program and Courses
Graduate students pursuing a Ph.D. in Mathematics usually spend the first two years completing an M.A. degree, including writing a thesis with a faculty adviser. During this time they take a variety of graduate courses, helping to prepare them for the preliminary exams (usually in analysis, topology, and algebra) that are a required step in completing the Ph.D.
Along with a range of research seminars and independent studies, we offer our core graduate courses, usually once every two years, including two semesters each of Graduate Algebra, Real Analysis, and Topology and one semester of Complex Analysis. Most of our graduate students also take a semester of undergraduate topology, supplemented with additional work for graduate credit and some take additional undergraduate courses, similarly supplemented. Students may also take courses at the University of Pennsylvania.
A distinctive aspect of the graduate program at Bryn Mawr is that the students in the Graduate School of Arts and Sciences at Bryn Mawr are graded on a Satisfactory/Unsatisfactory basis, with a narrative evaluation written by the instructor of each course.
Course list:
| 501,502 503,504 505,506 511,512 515,516 521,522 523,524 563,564 601,602 603,604 605,606 615,616 701 702 |
Real Analysis I and II Algebra I and II Topology I and II Complex Analysis I and II Geometry I and II Dynamical Systems I and II Number Theory I and II Lie Algebras I and II Topics in Analysis Topics in Algebra Topics in Topology Topics in Geometry Supervised Work Research Seminar |
Selected undergraduate courses:
| 303,304 311 312,313 322,323 351 390 |
Abstract Algebra Partial Differential Equations Topology Theory of Functions of a Complex Variable Chaotic Dynamical Systems Number Theory |
Degree Requirements
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
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.
Exams
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.
Graduate Research
Thesis and Dissertation Requirements
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.
