Ph.D. in Mathematics

Candidates for the degree of Doctor of Philosophy with a major in mathematics will be required to earn not less than 60 semester hours of course credit beyond the bachelor's degree in mathematics and closely related fields. The number of hours and the courses for each student will be determined by the advisory committee. The candidate must fulfill the course requirements for the Master of Science degree in mathematics.

The basic requirement for the Ph.D. degree is the preparation of an acceptable dissertation. This dissertation must demonstrate the candidate's ability to do independent, original, and significant work in mathematics. It is required that this dissertation possess the degree of excellence of research papers ordinarily published in the leading mathematical journals.

A comprehensive examination is given each year during the weeks preceding the beginning of the fall and spring semesters. This examination is taken by all students in the graduate program who have completed the requirements for the M.S. degree, and who have not been admitted to candidacy for the Ph.D. degree. The examination serves as both a qualifying and candidacy examination. The prospective candidate for the Ph.D. will be allowed to take the examination at most three times. Two failures to qualify eliminates the student from the graduate program in mathematics. The comprehensive examination for the mathematics option consists of 3 of the following exams:

• Reals I and Complex I (RC)
• Reals I and Reals II (R)
• Complex I and Complex II (C)
• ODE and PDE (DE)
• Algebra I and Algebra II (A)
• Topology I and Topology II (T)

to be selected by the student in such a way that (i) at least one of (A) or (T) is taken, and (ii) (RC) is not taken with either (R) or (C). The Ph.D. examinations are not restricted to the content of the specific courses; however, the courses listed under the M.S. comprehensive examinations are good preparation for these examinations. Syllabi for the examinations, as well as copies of past examinations, are available from the graduate secretary.

In addition to extending knowledge by personal reading and research, a doctoral graduate in mathematics will normally communicate knowledge to others. Therefore each student in the Ph.D. program is required to acquire the equivalent of one semester of full-time experience in teaching; this requirement may be fulfilled by part-time experience over several semesters. Typically, teaching assistantship appointments will satisfy this requirement, but other similar experience may qualify as approved by the Department.