Mathematics

M.S., Ph.D.

401.874.2709

Faculty: Professor Eaton, chair; Associate Professor Kook, director of graduate studies. Professors Finizio, Kulenovic, Ladas, Merino, and Pakula; Associate Professors Baglama, Kook, Medina-Bonifant, Thoma, and Wu; Assistant Professors Bella and Comerford; Professors Emeriti Datta, Driver, Fraleigh, Grove, Lewis, Roxin, Schwartzman, Suryanarayan, and Verma.

Specializations

Research activities are mainly concentrated in the areas of combinatorics and graph theory, complex dynamical systems, difference equations, numerical analysis, and applied analysis.

General Information

Programs of study can be designed for individuals who are employed on a full-time basis. However, all Ph.D. candidates must register full-time for two consecutive semesters prior to taking the doctoral comprehensive examination.

Master of Science

Admission requirements: bachelor’s degree with strong undergraduate background in mathematics. Applicants with deficiencies in mathematics may be accepted subject to taking certain undergraduate courses in addition to the graduate program requirements.

Program requirements: 30 credits (or 24 plus thesis), including at least 18 credits in mathematics of which at least 15 must be at the 500 level or above. A course requiring a substantial paper involving significant independent study and a written comprehensive examination are required for the nonthesis option. MTH 435 and 513 must be completed with a grade of A or B. Recommended courses include MTH 515, 525, 535, 536, and 562.

Doctor of Philosophy

Admission requirements: same as for master’s program.

Program requirements: Two tracks are offered: Pure Mathematics and Applied Mathematics. A total of 72 credits is required. Of these, 18 credits of dissertation work (MTH 699) are required. Within the first year of the Ph.D. program, the student, in conjunction with the Graduate Committee, will select a research advisor (major professor) from the graduate faculty of the Mathematics Department, including persons holding limited joint appointments. At this time, the student’s doctoral committee is selected and the program of study is carefully prepared by the student with his or her major professor. The program of study must be approved by the student’s doctoral committee, the department chairperson or graduate program director, and the dean of the Graduate School. Soon after that, in a similar manner, the dissertation proposal must be prepared and approved. The candidate shall successfully defend his or her dissertation in an oral defense. This is an oral exam, usually two hours long, administered by the candidates dissertation defense committee composed of the doctoral committee and two additional members approved by the Graduate School. This oral exam is in addition to the oral part of the comprehensive exam (see below).

The Department of Mathematics requires that doctoral candidates have reading proficiency in mathematical French, German, or Russian. The specific requirement to be satisfied is to be determined by the major professor.

For the pure mathematics track, required courses are MTH 515, 516, 525, 535, 536, and 562. For candidates without a master’s degree in mathematics, 1) subject to the approval of the department chair and graduate program director, at most 12 credits can be taken outside of the mathematics program (MTH); 2) the M.S. qualifying exam must be passed in MTH 435, 436, and 513. For candidates with a master’s degree in mathematics, 1) prerequisites MTH 435, 436, and 513 must be taken; 2) up to 30 credits from a master’s degree in mathematics may be applied towards the Ph.D.; and 3) all but at most 6 credits of their remaining credits must be for mathematics courses (MTH) at the 500-level or higher.

For the applied mathematics track, at least 30 of the 54 non-dissertation credits must be in mathematics (MTH). Areas of concentration are determined by and selected from among the research interests of the graduate faculty of the program, which includes members of other departments who are formally designated as graduate faculty in mathematics. Consult the Mathematics Department’s webpage for the current research interests of the graduate faculty. Up to 24 credits for courses in the student’s selected area of concentration may be applied to this degree. For candidates without a master’s degree in mathematics, the M.S. qualifying exam must be passed in MTH 435, 436, and 513. For candidates with a master’s degree in mathematics or a closely related area, 1) up to 30 credits from the M.S. in mathematics or an area closely related to mathematics may be applied towards the Ph.D.; and 2) all of their remaining credits must be for courses at the 500-level or higher; permission of the department chair is required if more than 12 of the remaining credits need to be taken outside of the mathematics program (MTH).

Ph.D. Comprehensive Examination. Shortly before the completion of formal course work, each doctoral candidate shall take the Ph.D. comprehensive examinations. These consist of a 10-hour written part to be taken over eight days and, on successful completion of the written part, an oral part (normally within four weeks). The exam is to be taken by the student within the first six semesters of enrollment in the Ph.D. program.

The rules governing the content of the written exam vary depending on which track is being pursued. For both pure and applied tracks, the written exam covers the material corresponding to 10 courses, which are selected by the student’s major professor. With the permission of the department chair and graduate program director, the exams for MTH 435 and 436 may be waived, in which case eight courses are required. The preparation, administration, and evaluation of the written comprehensive examination are the responsibility of the student’s research advisor, the doctoral committee, and other department members assigned by the doctoral committee. Unanimous approval of all members of the doctoral committee is required for passing.

The oral part of the comprehensive examination is two hours long and is conducted by the oral comprehensive examination committee, which consists of the doctoral committee with two additional members approved by the Graduate School. This oral exam is in addition to the oral defense of the dissertation (see above).

It is the responsibility of the major professor to request the permission of the dean of the Graduate School to schedule both the written and oral exams and to inform the Graduate School about the results. Consult the Graduate Student Manual, Section 7.57, for procedures that must be followed to schedule both parts of the comprehensive examination. In case of failing the whole or a portion of the comprehensive examination, the student may be permitted one re-examination if so recommended by the examining committee and approved by the Graduate School.