This program requires a total of 60 units, with students enrolling in 12 units per quarter, including research, academic coursework, and seminar sessions. To advance to Candidacy for a doctoral degree, students must meet all graduate program requirements, maintain a minimum GPA of 3.0 in all coursework (excluding courses graded S or U), pass both the Ph.D. Preliminary Examinations and the Qualifying Examination. Additionally, completion of a dissertation and an exit seminar is required. Please refer to the General Catalog for course names and descriptions.
Course Requirements
Core Courses (20 units total)
Students must complete 12 units in Area A, selecting one of the following series:
- Analysis Series: MAT 201AB + one of MAT 201C, MAT 205, or MAT 206
- Methods in Applied Mathematics Series: MAT 207ABC
Additionally, students complete 8 units in Area B, selecting one of the following series:
- Any unused Area A courses
- Data Science: MAT 258A, MAT 258B, MAT 270
- Numerical Methods: MAT 226A, MAT 226B, MAT 226C, MAT 228ABC
- Probability: MAT 235AB, STA 231C
- Theoretical Computer Science: ECS 220, ECS 222
If a required course is unavailable for two consecutive years, students may substitute a MAT 200-level course with prior approval from the Chair of the graduate group.
Electives (40 units total)
- Graduate Advanced Mathematics (12 units): MAT 200-level courses (279 or below). One non-Math graduate course may be substituted with prior approval.
- Field of Specialization (15 units minimum): Topics include optimization, probability, mathematical biology, signal processing, etc. At least one course (3+ units) must be outside Mathematics. See GGAM’s approved courses list.
- Advanced Mathematics (Maximum 12 units): Up to three 100-level math courses.
- GGAM Mini-Conference (1 unit): Required in the first or second year. Takes place in Winter quarter during the Graduate Student Visitation Event and includes faculty talks and student poster presentations.
- MAT 290 Seminars
Research Units
Students may register for research units, but these do not replace required coursework unless approved by the Chair of the graduate group.
English Language Requirement
Students without prior degrees from an English-language institution or proof of proficiency (e.g., TOEFL) must complete required English courses. These do not count toward graduation units.
Special Requirements – Teaching Skills
The program is committed to developing outstanding teaching skills in Ph.D. students.
- 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 approval from the GGAM Executive Committee.
- Students beyond their first year are encouraged to apply for positions as Associate-Instructors to improve their lecturing skills.
- The program strives to offer all students demonstrating strong teaching ability the opportunity to serve at least one quarter as an Associate-Instructor.
Summary
- Total Units Required: 60
- Enrollment per Quarter: 12 units (including research, academic, and seminar units)
- Minimum GPA: 3.0 overall
- Academic Probation: If GPA falls below 3.0, students are placed on probation. If probation extends beyond three quarters, disqualification may occur upon recommendation of GGAM Chair to the Dean of Graduate Studies.
Ph.D. Preliminary Examination
The Ph.D. Preliminary Examination is a written test covering material from the student’s selected tracks: Area A (MAT 201AB or MAT 207ABC) and Area B, which may include Data Science (MAT 168, MAT 170), Numerical Methods (MAT 128ABC), Probability (MAT 135AB), Theoretical Computer Science (ECS 220, ECS 222), Analysis (MAT 201AB), or Methods in Applied Mathematics (MAT 207ABC), provided there is no overlap with Area A. The exam is administered annually in June and September. Ph.D. students must pass this examination before the beginning of their third year. They may attempt the exam multiple times, with the focus placed on when they pass rather than the number of attempts.
Qualifying Examination
Students must complete all course requirements before taking their Qualifying Examination (QE). The QE consists of a written research proposal, a syllabus of materials relevant to the research proposal covered in the selected tracks from Areas A and B, and an oral examination. Approximately six weeks before the proposed QE date, students must submit the QE Application in GradSphere and research proposal to the GGAM Executive Committee for approval. The QE must be taken by the sixth quarter and no later than the end of the ninth quarter after admission to the Ph.D. program. Successfully passing the QE qualifies the student for advancement to candidacy.
Dissertation
The doctoral dissertation is a fundamental component of the Ph.D. program. Under the guidance of a Dissertation Advisor, students will select a research topic and are encouraged to begin their research as early as possible. The dissertation must present an original, publishable contribution to the field of applied mathematics. Its acceptance by the dissertation committee must adhere to the Graduate Studies guidelines (Plan B). The program does not impose specific requirements regarding length or presentation format. Detailed instructions for preparing the dissertation and the schedule of filing deadlines are available through Graduate Studies.
Exit Seminar
Ph.D. students must deliver a 60-minute public seminar presentation on their dissertation topic.
Optional Final Oral Examination
(at the discretion of the Dissertation Committee)
Following the exit seminar, the student’s dissertation committee may hold a private meeting with the student to review the dissertation and ask further questions. Completion of this requirement must be confirmed by the Dissertation Committee Chair.