Students are required to pass twelve graduate courses (MAT 280 and below). Included in this total are the six required core courses: MAT 201ABC, MAT 250AB, and MAT 205A. Three of the twelve required courses may be taken outside of Mathematics if they are related to the student's area of specialization. Students will enroll for 12 units per quarter including research, academic, and seminar units. Before advancing to candidacy for a doctoral degree, a student must have satisfied all course requirements set by the graduate program, maintained a minimum GPA of 3.0 in all course work undertaken (excluding courses graded S or U), passed the Ph.D. Preliminary Examination, and passed the Qualifying Examination. A dissertation is required.
- Core Courses (6 courses total)
MAT 201 (Analysis), A, B, C, (4 units each) - 12 units total
MAT 250 (Algebra), A, B (4 units each) - 8 units total
MAT 205A (Complex Analysis) - 4 units total
- Electives (6 courses total)
Students must pass six graduate courses (MAT 280 and below). Three of these may be taken outside of mathematics if they are related to the student's area of specialization.
- Teaching Skills
All Ph.D. students are required to be a teaching assistant for at least one quarter. Exceptions require approval by the Graduate Program Committee (GPC). Students beyond their first year are encouraged to apply for positions as Associate Instructors to develop and improve their lecturing skills.
- Methods of Teaching Mathematics - MAT390
Each student who accepts a TAship in the Department of Mathematics is required to complete MAT390, taught every Fall quarter. Most students take this in their first year, even if they are supported by a fellowship. MAT 390 does not count toward degree units, but does count for the 12-unit minimum required for registration each quarter.
- Ph.D. Preliminary Exam
The Preliminary Examination is a written examination covering MAT 201ABC and MAT 250AB. The exam is offered at the beginning of Fall and Spring quarters every year. Ph.D. students are required to pass this examination by the beginning of their 7th quarter (4th quarter if entered with an MA or MS equivalent).
- Ph.D. Qualifying Examination (QE)
Students must complete the course requirements, pass the PhD Preliminary Examination, and select a research topic and Dissertation Adviser, before petitioning to take their QE. The QE should be passed by the beginning of the 9th quarter (7th quarter if entered with an MA or MS equivalent). Passing the QE makes the student eligible for advancement to candidacy. The QE will consist of a written research proposal (which should be reviewed and approved by the thesis adviser) and oral examination. Approximately six weeks before the date of the proposed QE, the research proposal, along with the QE Application, is submitted to GPC for approval. NOTE: Staff are instructed to request email confirmation from the thesis adviser that he/she has read and approved the document, prior to submitting to GPC approval. Once approved and required signatures obtained, the QE Application will be forwarded to the Office of Graduate Studies for final approval.
The dissertation proposal should be between one and three pages in length and should contain an outline of the general context of the thesis research, a description of the specific problem(s) to be addressed, and an indication of the methods and techniques to be used. The oral examination consists of a seminar talk on the candidate's proposed research topic, followed by a separate question-and-answer session on independent breadth topics. Ideally, the talk should be no more than 45 minutes, or one hour including questions from the committee. The separate question-and-answer period could be up to two hours.
The doctoral dissertation is an essential part of the Ph.D. program. A topic will be selected by the student, under the guidance of the Dissertation Adviser. Students are encouraged to begin their research activity as early as possible. The dissertation must contain an original contribution of publishable quality to the knowledge of mathematics. Acceptance of the dissertation by the dissertation committee must follow Graduate Studies guidelines (Plan B). The program does not have any program-specific requirements, such as length or presentation format. Instructions on preparation of the dissertation and a schedule of dates for filing the thesis in final form are available from Graduate Studies; the dates are also printed in the UC Davis General Catalog.
Approved by Grad Studies Fall 2007.