The Ph.D. program in Mathematics requires 48 units of graduate coursework, comprising:
- 24 units of core courses
- 24 units of electives
Students may substitute up to three courses outside of mathematics if they are relevant to their area of specialization.
To advance to candidacy, students must:
- Fulfill all graduate program requirements
- Maintain a minimum GPA of 3.0 in all coursework (excluding S/U-graded courses)
- Pass both the Preliminary Examinations and the Qualifying Examination
- Complete a dissertation and deliver an exit seminar
An official copy of the degree requirements, approved by the Graduate Council, is available on the Graduate Studies program webpage.
For course names and descriptions, refer to the General Catalog.
General course syllabi are available HERE.
Course Requirements
Core Courses (24 units)
Students must complete the following six core courses:
- Analysis: MAT 201A, MAT 201B
- Algebra: MAT 250A, MAT 250B
- Topology: MAT 215A, MAT 239
Note: Courses taken at other institutions may substitute for Math 201AB, 215A, 239, or 250AB, pending approval from the Graduate Program Chair.
Electives (24 units)
- Any 200-level courses not listed above count toward elective units.
- Maximum of 6 units from MAT 280 (Topics in Mathematics) may be counted toward the M.A.
Research Units
- Students may take MAT 299 units for research with faculty.
- No minimum number of research units is required.
English Language Requirement
Students must complete English-language coursework if they:
- Did not earn a prior degree from an approved English-medium institution.
- Have not demonstrated proficiency via an exam (e.g. TOEFL).
Courses taken to satisfy this requirement do not count toward the 48-unit graduation requirement.
Teaching Requirement
- MAT 390 (Teaching Assistantship Training) is required for Teaching Assistantship positions in the Department of Mathematics but does not count toward degree units.
- All Ph.D. students must serve as a Teaching Assistant (TA) for at least one quarter. Exceptions require Graduate Program Chair approval.
- Students beyond their first year are encouraged to apply as Associates In Mathematics to further develop lecturing skills.
Enrollment & Grading Policies
- Full-time students must enroll in 12 units per quarter, including coursework, research, and seminars.
- Courses used to fulfill program requirements must be letter graded, unless listed as S/U-only.
- UC regulations limit enrollment to:
- 12 graduate-level units (200-level) per quarter
- 16 combined units (100, 200, 300-level) per quarter
Preliminary Examinations
The Preliminary Examinations are written assessments designed to evaluate Ph.D. students’ proficiency in graduate-level Analysis, Algebra, and Topology. It covers material from the following core courses: MAT 201AB, MAT 250AB, MAT 215A, and MAT 239. The exam is administered annually in June and September. Ph.D. students must pass two of the three parts before the beginning of their seventh academic quarter. They may attempt the exam multiple times, with the focus placed on when they pass rather than the number of attempts.
Qualifying Examination
The Doctoral Qualifying Examination (QE) is a pivotal milestone in a student's academic journey. It is a moment when faculty must thoughtfully assess the student’s overall qualifications for a future role as an educator or leader, as well as their preparedness within a specialized area of study.
The intended outcome of the examination is a unanimous decision by the committee, based on:
- Relevant portions of the student’s academic record
- Performance on designated sections of the examination
- A comprehensive evaluation of the student’s potential for scholarly research as demonstrated during the exam
The Qualifying Exam should be completed by the sixth quarter and no later than the end of the ninth quarter after admission to the Ph.D. program.
Dissertation Requirements
Ph.D. candidates must complete a written dissertation that demonstrates an original and significant contribution to the field of mathematics. The dissertation committee is responsible for evaluating whether this requirement has been satisfied. While the program does not impose specific guidelines regarding length or format, the Dissertation Advisor provides direction on expectations, which may vary depending on the student’s subfield.
Exit Seminar
Ph.D. students are required to give a 50-minute seminar presentation, open to the public, on their dissertation subject. After the seminar, the student’s dissertation committee may meet privately with the student to discuss the contents of the dissertation. Satisfaction of this requirement must be verified by the Dissertation Committee Chair.
Normative Time to Degree
Students entering with a B.A. or B.S. should accomplish their Ph.D. by the end of their fifth year. Students entering with a M.A. or M.S. should accomplish their Ph.D. by the end of their fourth year.
Approved by Graduate Council on June 14, 2024