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The PhD degree indicates knowledge of mathematics and a demonstrated capacity to do original, independent scholarly investigation. Early in the doctoral program, the student will complete major concentration-area course requirements or their equivalents (including courses required for the area MS degree) and will arrange a major professor or co-director within the department to direct the doctoral research. Three to six additional members complete the supervisory committee so that it is mutually agreeable to the student, the major professor or co-director, and the department chair. The supervisory committee must include three or more graduate faculty members of the department as well as a University Representative appropriately drawn from outside the department. The student then satisfies the area, department, and university requirements for doctoral candidacy (MAT 8964) and writes and defends a dissertation of original and independent research. The candidate, the major professor or co-directors, two other supervisory committee members from mathematics, and the University Representative are expected to be physically present at the dissertation defense. Consensus of the supervisory committee is necessary for a pass of the dissertation defense.
Studies leading to the PhD are available in Pure Mathematics, Applied and Computational Mathematics, Financial Mathematics, and Biomathematics. Each area of study specifies its own course requirements. The PhD qualification and candidacy examinations together comprise the preliminary examination, MAT 8964. Course requirements are chosen to provide the student with a strong basis for research. Standard foundational material is covered in the 5000-level courses with more advanced material in topics courses and seminars. Some of the required courses may be offered by other departments. The student will be expected to actively participate in at least one of the seminar series offered by the department and to regularly attend the weekly mathematics colloquium.