5: Graduate School of Arts and Sciences

General Information | Programs and Degrees Offered | Admission Information
Financial Assistance | Graduate Academic Regulations
Requirements for Specific Graduate Degrees | Departments and Programs | Faculty

Non-Departmental | Anthropology | Art | Asian and Middle Eastern | Asian Studies | Astronomy
Biochemistry | Biology | Biological and Physical Sciences | Biophysics | Cell and Molecular Biology
Cell Biology | Chemistry | Classics | Commerce | Drama | Economics | English | Environmental Sciences
French | German | Government and Foreign Affairs | Health Evaluation Sciences | History | Linguistics
Mathematics | Microbiology | Molecular Physiology and Biological Physics | Music | Neuroscience
Pharmacology | Philosophy | Physics | Psychology | Religious Studies | Russian and East European Studies
Slavic | Sociology | Spanish, Italian, and Portuguese | Statistics | Surgery

Department of Mathematics
Course Descriptions | Departmental Degree Requirements

Departmental Degree Requirements

Programs of Study   The Department of Mathematics administers programs leading to the degree of Master of Arts, Master of Science, and Doctor of Philosophy. These programs provide diverse opportunities for advanced study and research in algebra, analysis, topology, and mathematical physics.

The Master of Arts and Master of Science degrees are normally completed within two years, though 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 requires specific courses in algebra, analysis, and topology. In contrast, the course requirements for the M.A. degree are flexible and based on individual needs. The M.A. candidate has two options, one requiring an expository paper for a thesis, and the other substituting additional course work 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 masterís level. The most important addition is the Ph.D. dissertation, which is based on original research performed under the supervision of a faculty member.

All full-time graduate students are required, as part of their graduate program, to gain teaching experience by assisting the instruction of undergraduate courses.

Master of Arts Degree
Course Requirements   (a) Thesis option: 24 credits of approved courses at the 500 level or above (some courses from other departments and thesis research can count towards the 24 credits). (b) Non-thesis option: 30 credits of courses at the 500 level or above (no reading or research courses), which must include MATH 531, 532 (or replacements from among MATH 731, 732, 734) and MATH 551, 552 (or replacements from MATH 751, 752), and cannot include more than 9 credits from other departments.

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

Examinations   A passing grade on the final masterís exam (or both parts of the general examination); specific content of the exam should be agreed on by the student and the examiners well in advance. The candidate must be a registered student at the time of the exam, and must finish the degree requirements within three years of passing the exam.

Language   Facility in reading mathematical literature in one foreign language (French, German, Russian, or a substitute acceptable to the department) as confirmed by an examination administered by a member of the department. Two years of undergraduate credit in one of the languages will meet this requirement.

Doctor of Philosophy Degree
Course Requirements   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 analysis, algebra, and topology, and satisfactory performance on the qualifying examination.

General Examinations   The general exams are written exams which are set and graded by the graduate committee. They test whether the student has the inventiveness and command of basic material to pursue a Ph.D. degree, and are usually taken in the second year of graduate study.

Qualifying Examination   The qualifying exam is an oral exam or presentation set by a committee (consisting of the studentís major advisor and at least one other faculty member). It tests whether the student is ready to embark on dissertation work in a specific area and is usually taken during the third year. Acceptance as an advisee is conditional upon satisfactory performance on this exam.

Language   Facility in reading mathematical literature in two languages (French, German, Russian, or a substitute acceptable to the department), as demonstrated by an exam administered by the department, in which students are required to translate passages from mathematical works in the given language.

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 two other faculty members (one from within the department and one from outside) must approve the dissertation and defense in order for the dissertation to be considered accepted by the faculty.


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