Mathematics, PhD

The Doctor of Philosophy degree is awarded for superior accomplishment, the attainment of a high level of scholarship and the demonstrated ability, through independent study and research, to carry out an original investigation and present the results of such investigation.

Course Requirements

Until the student has selected a major professor, the graduate advisor will assist in planning the doctoral program. The program will be designed to provide the student with competence in several major areas of mathematics and to provide for intensive study and research in the area of specialization. The student will be expected to complete approximately 90 hours of graduate work in mathematics beyond the bachelor’s degree, of which about half should be in courses numbered above 6000. Included in this work, the student will be expected to take (or previously have taken the equivalent of) the following core sequences:

In addition:

The student is required to take at least two 6000-level courses in each of the areas of algebra, analysis and topology.

Foreign Language Requirement

PhD candidates must demonstrate proficiency in a foreign language approved by the department (normally chosen from French, German, Spanish and Russian). See the Doctoral Degree Requirements section of this catalog for additional information.

Qualifying Examinations

Before enrolling in the dissertation seminar, the student must pass qualifying examinations over two areas chosen from algebra, topology, real analysis, complex analysis, probability and statistics, and applied mathematics. The doctoral advisory committee is appointed upon successful completion of the qualifying examinations.

Dissertation and Final Examination

The candidate must submit a dissertation exhibiting independent research on a topic approved by the doctoral committee. After the completion of the dissertation, a final comprehensive oral examination that will be primarily a defense of the dissertation will be given.