Degree Programs and Requirements

THE MASTER OF ARTS AND MASTER OF SCIENCE DEGREES are normally completed within two years, during which time the student fulfills course requirements and passes a final examination. In some cases, these degrees can be completed in one calendar year (two semesters and a summer session). The M.A. and M.S. programs differ mainly in course requirements. The M.S. degree in mathematics requires specific courses in algebra, analysis, and topology. In contrast, the course requirements for the M.A. degree in mathematics are flexible and based on individual needs. The candidate for the Master's degree in mathematics has two options, one requiring an expository paper for a thesis, the other substituting additional coursework in place of a thesis.

The Doctor of Philosophy degree is normally completed within five years. Candidates for the Ph.D. must fulfill certain course requirements and examinations beyond the Master's level. The most important addition is the Ph.D. dissertation, which is based on original research performed under the supervision of a faculty member.

In all programs, students may take approved courses from other departments.

There is a teaching requirement for advanced degree programs in mathematics: all full-time graduate students receiving financial aid are required, as part of their graduate program, to gain teaching experience by assisting in the instruction of undergraduate courses. Normally the student simultaneously fulfills the teaching requirement and obtains financial aid by teaching or directing discussion sections for undergraduate courses. Teaching is evaluated, and a good record is an asset to graduates seeking academic employment. Some students obtain their financial support by serving as computer assistants (CA's) after receiving appropriate training (provided by the department).

Graduate students gain teaching experience by assisting in the instruction of undergraduate courses.

Requirements for the
Doctor of Philosophy Degree in Mathematics

Course requirements: 72 hours of coursework at the 500 level or above (which may include 18 hours of non-topical research: MATH 897, 898, 997, 999). A student must do satisfactory work in two semesters of analysis (MATH 731, 734), algebra (MATH 751, 752), and topology (MATH 577, 780), or the equivalent.

Examinations: Passing grades on two General Examinations, chosen from Algebra, Analysis, and Topology, and satisfactory performance on the Second-Year Proficiency Examination.

General Examinations: The General Examinations, set and graded by the Graduate Committee, are written exercises. They test whether a student has the inventiveness and command of material basic to the pursuit of a Ph.D. degree. The examinations cover the following material: Algebra (MATH 751 and 752), Analysis (MATH 731 and one additional course selected from 734, 736, and 725), and Topology (MATH 577 and 780). They are offered two times a year, in January and August. A student is expected to take these examinations at the first opportunity following completion of the corresponding two-course sequences, that is, at the beginning of the second year of graduate study. In any case, these exams must be satisfactorily completed by January of the student's third year. A student is allowed at most a total of four sittings for exams (taking one exam is one sitting).

Second-year proficiency examinations: Students take an informal oral examination on material from two or three selected second-year courses. The exact content of the exam is determined by a panel of faculty members in consultation with the student. Its purpose is to gauge the student's readiness to begin carrying out research in the student's chosen area. It is normally taken in May of the second year. If any deficiencies are noted, the examining panel will make recommendations on how to fix the detected problems and meet again with the student in August.

Language: Facility in reading mathematical literature in one language (French, German, Italian, Russian, or substitutes acceptable to the department), as demonstrated by an examination administered by the department, in which the students are required to translate passages from mathematical works in the given languages. The language requirement should be satisfied by the end of the student's fourth year, or by the date of the Ph.D. defense, whichever comes first.

Students pursuing research in the history of mathematics are required to pass a written translation examination in two foreign languages, typically French and German, although the languages required will depend on the student's research interests. These language requirements should generally be satisfied by the end of the student's third year in order to enable the student to do primary source reading in the pertinent languages.

History of Mathematics Program: The requirements for the Ph.D. in the history of mathematics are the same as for the Ph.D. in mathematics, with the exception of the additional language requirements described above. Also, students entering the program must exhibit a strong reading comprehension in two foreign languages, preferably French and German. Students interested in pursuing a Ph.D. in history of mathematics should contact Professor Karen Parshall before submitting their application.

Dissertation and defense: Written under the supervision of the major advisor, the Ph.D. dissertation must contain original contributions to the field of mathematics. The main results of the dissertation are presented at a public oral defense. A committee consisting of the major advisor and three other faculty members (two from within the department and one from outside) must approve the dissertation and defense in order for the dissertation to be accepted by the faculty.

Time limit: The Ph.D. may be completed in as few as three years but must be completed within seven years.

Requirements for the
Master's Degrees in Mathematics

Course requirements: (a) Thesis option: 24 credit hours of approved courses at the 500 level or above (some courses from other departments can count toward the 24 hours). (b) Non-thesis option: 30 hours of courses at the 500 level or above (no reading or research courses), which must include MATH 531, 533 (or replacements from among 731, 732, 734) and MATH 551, 552 (or replacements from 751, 752), and cannot include more than 9 hours from other departments.

Thesis (option (a) only): The Master's thesis is an expository paper written under the supervision of a faculty advisor.

Examinations: For the M.S. degree, students must pass one General Examination chosen from the areas of analysis, algebra, and topology. For the M.A. degree, the student may satisfy the examination requirement by either a passing grade on one General Examination or a passing grade on a Final Masters Examination, the scope of which must be agreed upon in advance by the examiners in consultation with the student. Masters candidates must be registered students at the time of the examination and must complete the degree requirements within three years of passing the examination.

Time Limit: Minimum one year, maximum five years.

The requirements for the M.S. degree are the same as for the M.A. degree, except that the program must include MATH 731, 734, MATH 751, 752, and MATH 577, 780 (or higher substitutes).

Transfers
With the approval of the Department and the Dean of the Graduate School, up to one session of the required three sessions of graduate work may be completed at another graduate school.