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 described earlier in this bulletin, 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
In the first two years of study 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 four 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.
The Ph.D. Examinations
The preliminary examinations are offered each year at the beginning of the Fall, Spring, and Summer terms. Each examination consists of a written component followed by an oral component at the option of the examiners. A syllabus for each examination is available in the departmental office. The student must successfully complete the examinations in four of the following seven areas: algebra, complex analysis, real analysis, probability, applied statistics, mathematical statistics, topology. At least two examinations should be completed by the beginning of the second year of study and it is expected that all four examinations will be completed after no more than five semesters of study.
Within three semesters after the completion of the preliminary examinations, an oral qualifying examination will be administered to test the student's preparation in the area of specialization and readiness to begin work on a dissertation.
Research Tool Requirement
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 and also have proficiency in a standard computer language. Both requirements are to be satisfied by departmental 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 (12 credits) taken in each of two sessions, or in a regular session and a summer session, not necessarily consecutive, which must be completed satisfactorily.
Graduate assistants holding a full assistantship may meet the full-time residency requirement by completing one academic year in such a position, including the satisfactory completion of a minimum of 9 credits per term plus satisfactory completion of assigned duties.
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;
- Approval of proposed dissertation topic.
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 the student's advisory committee and defended publicly.
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.