Ph.D. Degree Program Overview

The objectives of the Mathematics Ph.D. program are to prepare students for a career in academia, industry, or teaching. At the end of their studies, students will possess the ability to solve problems and communicate solutions in rigorous mathematical language, to communicate mathematical concepts effectively, and to conduct independent research.

Ph.D. students are expected to obtain their Ph.D. degree within six years. Students admitted to the Ph.D. program may receive a master's degree en route to the Ph.D.

Ph.D. Degree Requirements

Students are required to complete all of the following:

  1. 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*;
  2. Satisfy the foreign language requirement;
  3. Pass the oral qualifying examination;
  4. Complete three quarters as a Teaching Assistant;
  5. Complete the required coursework: Math 288A** plus six graduate courses in mathematics other than Math 200, 201, 202, 204, 205, 206, 208, 209 and 210. No more than three courses may be independent study or thesis research courses.
  6. Write a Ph.D. thesis (dissertation).
*Requirements may be met through the following three combinations:

| 1st level pass | 1st level pass | 1st level pass |

| 1st level pass | 1st level pass | Sequence |

| 1st level pass | 2nd level pass + Sequence | Sequence |

**Required for all cohorts entering the program Fall 2019 and later. 

Degree Timetable

Requirement Targeted Time
Preliminary Exams End of second year
Language Exam End of third year
Oral Qualifying Exam
(Advancement to Candidacy)
Between seventh and twelfth quarters
Dissertation Defense Four to six years

Graduate Advising

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.

Annual meetings with the Graduate Vice Chair and the Graduate Advisor and Program Coordinator are conducted with each student on a one-on-one basis. These meetings serve to notify the student of their current progress within the program and outline expectations for the continuation of normative progress toward the Ph.D. degree.

Graduate students are encouraged to review the Graduate Student Mentoring Packet for resources on how to get the most out of the graduate student-mentor relationship.


Francois Monard, Graduate Vice Chair | 831-459-1525

Gina Hernan, Graduate Advisor and Program Coordinator

Preliminary Exams

Ph.D. students should complete the preliminary exams and introductory sequence requirements by the end of the second year in order to make satisfactory progress.  If a graduate student does not fulfill the above requirement by the end of the second year, depending on the student's progress, they can be placed on academic probation.  If a graduate student has not fulfilled the above requirements by the end of the third year, they are 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 fourth year will be placed on academic probation or be subject to dismissal from the program.


Each graduate student in the Ph.D. program is required to write a Ph.D. dissertation or thesis on a research topic in mathematics. Ph.D. students are expected to obtain their Ph.D. degree in four to six years.

Applying for Graduation

Ph.D. students must complete the Application for the Doctor of Philosophy Degree form by the appropriate quarter’s deadline listed in the current Academic calendar.

The form can be found on the Graduate Division website or can be provided by the Mathematics Department. The form should be turned in to the Graduate Advisor and Program Coordinator for review and submission to the Graduate Division.