Degree Requirements

The requirement consist of the following:

• a minimum of 135 quarter hours beyond the BA or BS degree,
• passing of preliminary examinations,
• completion of a written dissertation,
• completion of a tool requirement.

In addition, although a masters degree is not a prerequisite for acceptance into the PhD program, each student must have completed a masters degree in mathematics before completing 80 quarter hours of the PhD program.

See also the University's official Graduate Bulletin for the Department of Mathematics (or download it here [PDF]).

Required courses

Of the 135 quarter hours, at least 36 must be at the 4000 level. Up to 35 credits may be taken in other relevant disciplines, as approved by the Mathematics Department Graduate Committee. Courses should be chosen in consultation with, and are subject to the approval of, the student's advisor. (See the catalog of MATH courses.)

Preliminary examinations

Preliminary exams are for students admitted to the PhD program. For more information about the exams, see the preliminary exams page.

Dissertation

The dissertation must make a significant contribution to the research literature in mathematics.

After the dissertation has been completed, the student must defend it in a final examination, as specified by the Office of Graduate Studies.

You can download the LATeX template for a PhD dissertation.

Tool requirement

It is strongly recommended that students satisfy their tool requirement by demonstrating an understanding of, and ability to use, a modern computer typesetting system. Other options include

• reading competency in two languages selected from French, German, and Russian,
• a series of outside courses in another discipline
• significant laboratory experience involving mathematics.

Transfer Credit

The Department of Mathematics adheres to standard transfer credit policy outlined by the Office of Graduate Studies. (See Graduate Policy Manual, p. 51-52)

"With approval from the student’s advisor and the chairperson of the department, doctoral students may reduce the required hours for a doctoral degree by up to 45 hours with an earned master’s degree from a regionally accredited university.

The student must initiate in writing the request for posting the master’s degree through the program of study and is responsible for seeing that the department, appropriate student services office of the college, school, or department and the Office of Graduate Studies have approved the request.

An official transcript must be on file in the Registrar’s office and must demonstrate that the student earned a “B” average or better in his/her master’s degree program.

The student’s DU academic department must fill out the Transfer of Credit form and provide a statement that the student’s master’s degree is appropriate and adequate background for the doctoral degree being sought.

Fifteen additional quarter hours may be allowed to be transferred provided the credits have been earned after the master’s degree was awarded and it does not conflict with the doctoral residency requirement that requires enrollment at DU in at least six quarters (four semesters), including at least two consecutive quarters (one semester) of full-time attendance."