Ph.D. Degree Program & Requirements

The Mathematics Department at U.C. Santa Cruz offers programs leading to the Ph.D. degree. Ph.D. students are required to complete all of the following:

Ph.D. Degree Requirements

Students are required to complete all of the following:

•  Obtain a first-level pass on at least one of the three written preliminary examinations, and a second-level pass on at least one other. Students must complete the full sequence in the track associated with the preliminary examination they did not achieve a first-level pass;

•  Satisfy the foreign language requirement;

•  Pass the oral qualifying examination;

•  Complete three quarters as a Teaching Assistant;

•  Complete six graduate courses in mathematics other than 200, 201, 202, 204, 205, 206, 208, 209 and 210. No more than three courses may be independent study or thesis research courses.

•  Write a Ph.D. thesis.

Students admitted to the Ph.D. program may receive a Master's degree en route to the Ph.D.; students admitted to the M.A. program may transfer to the Ph.D. program upon passing the required preliminary examinations at the Ph.D. level.

Graduate Advising


Robert Boltje
Graduate Vice Chair
Phone: 459-5001

Graduate Program Coordinator
Phone: 459-5461

Entering graduate students are advised initially by the Graduate Vice Chair, and then assigned a faculty mentor who will be an ongoing advising resource for the student. Within the first two years, and typically after passing the preliminary examinations, the student selects a faculty advisor in the area of the student's research interest. This is done in consultation with the Graduate Vice Chair. Each graduate student is expected to consult with his or her advisor to formulate a plan of student and research. The student's advisor ultimately will be the student's thesis advisor.

Degree Timetable

Requirement Targeted Time
Preliminary Exam End of second year
Language Exam End of third year
Oral Qualifying Exam
(Advancement to Candidacy)
By 7th quarter,
but no later than 12th quarter
Dissertation Defense Four to six years

Preliminary Exams

 Ph.D. students should complete the preliminary exams and introductory sequence requirements by the end of the 2nd year in order to make satisfactory progress.  If a graduate student does not fulfill the above requirement by the end of the 2nd year, depending on the student's progress, he/she can be placed on academic probation.  If a graduate student has not fulfilled the above requirements by the end of the 3rd year, he/she is subject to dismissal from the program.

Advancing to Candidacy

To make satisfactory progress, a Ph.D. student should advance to candidacy by the end of their fourth year. A Ph.D. student who has not advanced to candidacy by the end of the 4th year will be placed on academic probation or be subject to dismissal from the program.


Ph.D. students are expected to obtain their Ph.D. degree in 4 to 6 years.