The general aim of the program leading to the Ph.D. in mathematics is to prepare students to become productive research scholars capable of communicating their knowledge to students and to the mathematical community. The program is planned to develop in the student a fundamental understanding of certain basic fields of mathematics, a deep understanding of the major field of interest, the ability to formulate and recognize significant research problems, and the ability to analyze problems and reach solutions and to transmit ideas to others.
The program of study and research requires at least three academic years of full-time study and research, or the equivalent over a longer period, beyond the baccalaureate and, typically, may involve as many as four years.
Requirements for Admission
In addition to the general University requirements for admission to doctoral study, an applicant's undergraduate major preferably should have been in mathematics. Students who are deficient in their mathematical preparation must make up such deficiencies.
Program of Study
To satisfy our breadth requirement the student acquires a general education in mathematical science through a program of coursework planned in conjunction with the Graduate Director. During this period the student completes preliminary examinations in three areas and at least two courses in areas not examined.
Following the preliminary examinations, the student completes the general education requirement and begins the process of specialization. As soon as possible, the student selects a dissertation advisor. A committee consisting of the advisor and three other faculty members is formed to guide the student's subsequent progress toward the degree. Readiness to begin the dissertation is marked by completion of the qualifying examination, which should take place in the third year of study.
Upon completion of the qualifying examination and satisfaction of the appropriate research tool and communication skills requirements, the student is advanced to candidacy and begins work on the dissertation.
Program Requirements for the PhD in Mathematics:
- Credits: A minimum of 60 graduate credits in mathematics as approved by the advisor, with an average of B or better.
- Breadth Requirement: All students must show proficiency in four of five areas: algebra, topology, complex analysis, real analysis, probability & statistics. Students are required to successfully pass written preliminary examinations in three areas and satisfactorily finish one breadth sequence in an additional fourth area. The preliminary exams should be completed by the end of the third semester of study.
- The written preliminary examinations are offered each year at the beginning of the Fall and Spring terms and in June. A syllabus for each examination is available in the departmental office and on the departmental webpage. At least two examinations shall be attempted by the beginning of the second year of study and it is expected that all three examinations shall be attempted after no more than four semesters of study. A student who fails one of the preliminary examinations may retake the examination one more time. Only two tries are permitted in each subject. Any deviation from this policy requires approval of the Executive Committee and the Graduate Studies Committee.
- Breadth Sequence: Two semester sequence in an area complementary to the student’s choice of preliminary exams areas. Allowed sequences are: Mat 511 & 510A, Mat 524 & 520A, Mat 540A & 540B, Mat 513A & 513B, and Mat 554 & 555. Only a sequence in an area not covered by the student’s choice of written preliminary examinations will be accepted for fulfillment of this requirement. Passing a fourth written preliminary examination will also satisfy this requirement.
- The written preliminary examinations are offered each year at the beginning of the Fall and Spring terms and in June. A syllabus for each examination is available in the departmental office and on the departmental webpage. At least two examinations shall be attempted by the beginning of the second year of study and it is expected that all three examinations shall be attempted after no more than four semesters of study. A student who fails one of the preliminary examinations may retake the examination one more time. Only two tries are permitted in each subject. Any deviation from this policy requires approval of the Executive Committee and the Graduate Studies Committee.
- Successful Completion of the Oral Qualifying Examination: Within a month of completion of all the breadth requirements, the student shall select a faculty member as his/her dissertation advisor. At this time the student begins specializing in the areas on which the student will write his/hers PhD dissertation. Within two semesters of selecting the advisor, an oral qualifying examination shall be administered to test the student's preparation in the area of specialization and readiness to begin work on a dissertation. At this point, an Advisory Committee is formed to guide the student's subsequent progress toward the degree. It consists of four faculty members: the PhD advisor who chairs the committee together with three members selected by the PhD advisor, in consultation with the PhD candidate. The examination is not open to the general public.
- Completion of a Research Tool: The student must display a reading knowledge of French, German, Russian, or another foreign language appropriate to the area of specialization and approved by the department. This requirement is to be satisfied by departmental examination and shall be completed before the oral qualifying examination.
- Full Time Study in Residence:Each student in a doctoral program must engage in full-time study beyond the master's degree or equivalent at the University in at least two sessions after admission to the advanced program. This requirement is designed to insure for each doctoral student a sustained period of intensive intellectual growth. For this purpose a student will enroll in full-time study (9 credits) taken in each of two sessions, or in a regular session and a summer session, not necessarily consecutive, which must be completed satisfactorily.
- Continuous Registration of Doctoral Students: All students enrolled in the doctoral program must maintain continuous registration for each fall and spring session, until they have completed all program requirements. Minimum registration consists of 3 credits of approved course work or registration for dissertation load (899 courses only). When this is not possible, a student should apply for a leave of absence for up to four semesters. The duration of a leave does not count against deadlines for the comprehensive exam or degree requirements. Being on leave means a student is not working with University personnel to complete his/hers degree. A student who simply "drops out" and tries to return may have difficulty obtaining retroactive leave and readmission. Note: Students with a full assistantship must be registered with full-time status for the duration of the assistantship. International students must be registered full-time for the duration of their studies.
- MAT 899: Students must be registered for Doctoral Dissertation, MAT 899, during the semester in which the degree is conferred. Credits for this course do not count toward the 60 credits mentioned in item 1.
Admission to Candidacy
A student is admitted to candidacy for the degree of Doctor of Philosophy upon the following:
- Satisfactory record in course and research study;
- Completion of the University residence requirements;
- Satisfactory completion of research tool requirement;
- Satisfactory completion of the comprehensive and qualifying examinations.
Dissertation
The dissertation is based on independent research by the student and should constitute a significant original contribution to mathematics or statistics. The dissertation must be approved by a majority of the student's Advisory Committee and the Chair of the Department. It must conform to university thesis requirements for preparation and submission. More information is available at the Graduate Admissions office. A copy of the dissertation should be given to each member Advisory Committee and displayed in the Department of Mathematics Lounge at least three weeks prior to its defense. The dissertation is defended publicly.
Ancillary Duties
In addition to the completion of course requirements, satisfactory performance in some ancillary teaching, research, or practicum duties contributing to the academic development is required, whether or not the student receives financial support from this institution. These duties will be assigned with educational objectives in mind.