Graduate Degree Programs & Requirements

The Mathematics Department at U.C. Santa Cruz offers programs leading to the M.A. and Ph.D. degree.

• M.A. Degree Requirements
• Ph.D. Degree Requirements
  • Foreign Language Requirement
  • Qualifying Examinations For Advancement To Candidacy
  • Dissertation For The Ph.D. Degree
• Degree Timetables
  

M.A. DEGREE REQUIREMENTS

Students are required to complete two of courses 200, 201, 202; two of courses 204, 205, 206; one of courses 208, 209, 210, and complete five additional courses in mathematics (or related subject, by approval.  In addition, students must do one of the following:

• Pass an M.A. level preliminary examination
• Write a Master’s thesis

Ph.D. DEGREE REQUIREMENTS

Students are required to complete all of the following:

• Obtain a Ph.D. level pass on two of the three written preliminary examinations, or a Ph.D. level pass on one and a Master’s level pass on the remaining two. Students who opt for the Ph.D. level pass on two of the three preliminary examinations must complete the full sequence in the track associated with the preliminary examination they did not 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 and 206. No more than three courses may be independent study or thesis research courses.
• write a Ph.D. thesis and present the thesis defense.

Students admitted to the Ph.D. program may receive an M.A. degree in 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.

Foreign Language Requirement

Graduate students in the Ph.D. program are required to demonstrate a knowledge of French, German or Russian sufficient to read the mathematical literature in the language. A foreign language examination may be administered by any member of the Mathematics faulty. The examination can be either oral or written. The foreign language requirement must be satisfied before advancement to candidacy for the Ph.D. degree.

Qualifying Examinations For Advancement To Candidacy

All graduate students in the Ph.D. program are required to take an oral examination, called the Oral Qualifying Examination, for advancement to candidacy for the PhD. Degree. Students typically complete this examination between their seventh and twelfth quarter in residence and have an idea of their Ph.D. thesis problem. Any student who has not passed their oral exam by the end of the fourth year will not be permitted to re-enroll. The examining committee consists of the student’s faculty advisor, at least two other faculty member from Mathematics, and at least one faculty member from another discipline. The committee is selected by the student, the student’s faculty advisor, and the Graduate Vice chair. The chair of the committee must be someone other than the student’s faculty advisor. The committee must be approved by the Graduate Division. The committee decides on the topics for the examination, which should be broad enough to encompass a substantial body of knowledge in the area of the student’s interest. The written list of topics to be included in the examination, along with a short bibliography, is prepared by the student. A copy is given to each committee member, and a copy is put into the student’s permanent records. If the student fails the examination, a re-examination can be given within the next three months. Usually, the membership of the examining committee remains fixed.

Dissertation For The Ph.D. Degree

Each graduate student in the Ph.D. program is required to write a Ph.D. dissertation or thesis on a research topic in mathematics. The student, in consultation with the Graduate Vice Chair, is responsible for selecting a dissertation committee. The committee consists of the student’s advisor and at least two other members of the mathematics faculty. In special circumstances, a committee member may be chosen from another department and/or from another institution. The student’s advisor is the chair of the committee. All members of the committee must read and approve the dissertation. After the dissertation has been approved, the student is required to make a public oral presentation of the mathematical results contained in the dissertation. This oral presentation is called the thesis defense. Finally, a recommendation by the dissertation committee will be made to the Mathematics Department and to the Graduate Council on the granting of the Ph.D. degree.

DEGREE TIMETABLES

Students enrolled in the M.A. program are expected to meet the requirements of the degree within two years. Enrollment beyond this time requires the approval of the Graduate Vice Chair. Students enrolled in the M.A. program who wish to transfer to the Ph.D. program will be allowed to do so provided they have passed the preliminary examinations in accordance with the Ph.D. examination requirements. Students in the Ph.D. program customarily receive an M.A. degree in the course of their studies.

Students enrolled in the Ph.D. program are expected to meet the timetable below, which leads to a Ph.D. in four to five years. Enrollment in the Ph.D. program beyond five years requires the approval of the Graduate Vice Chair, while enrollment beyind the university’s normative time of six years may require the approval of the Dean of Graduate Studies and Research.

For both M.A. and Ph.D. students, progress is assessed regularly through student meetings with mentors and advisors. In spring quarter, all students will be scheduled for an annual progress review with the Graduate Vice Chair and the Graduate Program Coordinator. At the end of spring quarter, a progress letter for each graduate student is issued which reflects both target and completion dates for the degree. At this time each student is determined to be making either satisfactory or unsatisfactory progress.

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