The department's graduate programs include a PhD program in mathematics and MA programs in mathematics and in computer science. The research emphasis at Wesleyan at the doctoral level is in pure mathematics and theoretical computer science. One of the distinctive features of our department is the close interaction between the computer science faculty and the mathematics faculty, particularly those in logic and discrete mathematics.
Among possible fields of specialization for PhD candidates are algebraic geometry, algebraic topology, analysis of algorithms, arithmetic geometry, categorical algebra, combinatorics, complex analysis, computational logic, data mining, elliptic curves, fundamental groups, Galios theory, ergodic theory, geometric analysis, graph theory, homological algebra, Kleinian groups and discrete groups, knot theory, logic programming, mathematical physics, model theory, model-theoretic algebra, number theory, operator algebras, probability theory, proof theory, topological dynamics, and topological groups.
Graduate students at Wesleyan enjoy small, friendly classes and close interactions with faculty and fellow graduate students. Graduate students normally register for three classes a semester and are expected to attend departmental colloquia and at least one regular seminar. The number of graduate students ranges from 18 to 22, with an entering class of three to six each year. There have always been both male and female students, graduates of small colleges and large universities, and United States and international students, including, in recent years, students from Bulgaria, Chile, China, Germany, India, Iran and Sri Lanka. All of the department's recent PhD recipients have obtained faculty positions. Some of these have subsequently moved to mathematical careers in industry and government.
Requirements for the degree of doctor of philosophy. The doctor of philosophy degree demands breadth of knowledge, an intense specialization in one field, a substantial original contribution to the field of specialization, and a high degree of expository skill. The formal PhD requirements consist of the following:
Courses. At least 16 one-semester courses are required for the PhD degree.
Several of the courses are to be in the student's field of specialization,
but at least three one-semester courses are to be taken in each of the three
areas: algebra, analysis, and topology. First-year students
are expected to take the three two-semester sequences in these areas.
However, students interested in computer science may replace course work in
one of these areas with course work in computer science, with the permission
of the departmental Graduate Education Committee. One of the 16 courses must
be in the area of logic or discrete mathematics, as construed by the
departmental Graduate Education Committee.
- General preliminary examinations. The general preliminary examinations occur in the summer after the candidate's first year of graduate study and cover algebra, analysis, and topology (or computer science, in the case of students including this option among their three first-year subjects).
- Language examinations.
Students must pass reading examinations in any one of the languages
French, German, or Russian. It is strongly recommended that PhD
candidates have or acquire a knowledge sufficient for reading the
mathematical literature in all three of these languages. Knowledge of one of these three languages is required.
- Special preliminary examination. For a graduate student to become an official PhD candidate as recognized by the department, he/she has to pass the Special Preliminary Examination, an oral examination that must be passed by the end of the student's third year of graduate work. The student's Examination Committee determines the subject matter content of the Special Preliminary Examination. This committee is chaired by the student's dissertation advisor and must include at least two additional faculty members of the department. The Special Preliminary Examination will be based primarily, but perhaps not exclusively, on the student's field or specialization. Specific details of the form and content of the examination shall be determined by the Examination Committee at the time the subject matter content is discussed.
- Dissertation. The dissertation, to be written by the PhD candidate under the counsel and encouragement of the thesis advisor, must contain a substantial original contribution to the field of specialization of the candidate and must meet standards of quality as exemplified by the current research journals in mathematics.
- Selection of dissertation advisor. A graduate student should select a dissertation advisor by the end of the student's second year of graduate work. Defense of dissertation. The final examination is an oral presentation of the dissertation in which the candidate is to exhibit an expert command of the thesis and related topics and a high degree of expository skill.
Five years are usually needed to complete all requirements for the PhD degree, and two years of residence are required. It is not necessary to obtain the MA degree en route to the PhD degree. Students may choose to obtain the MA in computer science and the PhD in mathematics. Any program leading to the PhD degree must be planned in consultation with the departmental Graduate Education Committee.
Requirements for the degree master of arts. The requirements for the master of arts degree are designed to ensure a basic knowledge and the capacity for sustained, independent, scholarly study. The formal MA requirements consist of the following:
Courses. Six one-semester graduate courses in addition to the research units
MATH591 and 592 or COMP591 and 592
are required for the MA degree. The choice of courses will be made in
consultation with the departmental Graduate Education Committee.
Thesis.The thesis is a written report of a topic requiring an independent search and study of the mathematical literature. Performance is judged largely on scholarly organization of existing knowledge and on expository skill, but some indications of original insight are expected.
- Final examination. In the final examination, an oral presentation of the MA thesis, the candidate is to exhibit an expert command of the chosen specialty and a high degree of expository skill. The oral presentation may include an oral exam on the material in the first-year courses. A faculty committee evaluates the candidate's performance. Three semesters of full-time study beyond an undergraduate degree are usually needed to complete all requirements for the MA degree. Any program leading to the MA degree must be planned in consultation with the departmental Graduate Education Committee.