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Division of Natural Sciences & MathematicsDepartment of Mathematics

Degree Programs

Degree Programs

Doctor of Philosophy

Degree Requirements

This degree requires:

  • completion of at least 135 graduate-level credits beyond the BA or BS degree,
  • passing of preliminary examinations,
  • completion of a tool requirement,
  • and completion of a written dissertation.

Although a master’s degree is not a prerequisite for acceptance into the PhD program, each student is required to obtain a master’s degree in mathematics before completing 80 credits in the PhD program.

Course Requirements

Of the 135 credits, a minimum of 36 credits of MATH courses must be completed 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 the student’s academic advisor.

(See the catalog of MATH courses.)

Preliminary Examinations

Every student admitted to the PhD program is expected to pass a written preliminary examination in analysis and a written preliminary examination in algebra. Both preliminary examinations are designed to test whether students in the PhD program have the adequate undergraduate preparation to continue in the program with a reasonable chance of success.

Both examinations are offered twice per year: during the week immediately preceding the first week of the fall quarter, and during the first week of the winter quarter. A student must pass both exams by no later than the end of the winter quarter of his/her second year in the program unless the graduate committee grants an extension of this deadline for exceptional and documented reasons.

(For more information about the preliminary examinations, see the preliminary exams page.)

Tool Requirement

It is strongly recommended that students satisfy their tool requirement by demonstrating the 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,
  • a significant laboratory experience involving mathematics.


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.

Please refer to the Office of Graduate Education manual for thesis and dissertation formatting guidelines.

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."

Questions regarding graduate admissions should be sent to the Graduate Coordinator, Prof. Paul Horn.