Math PHD Requirements Starting Fall 2021

Course Requirements – Core and Electives (48 units) (see attached Progress Checklist)

Students must acquire proficiency in mathematics by completing 48 units or passing twelve 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.

  •  Core Courses (24 units)
    • MAT 201AB (Analysis) (4 units each)
    • MAT 250AB (Algebra) (4 units each)
    • MAT 215A (Topology) (4 units)
    • MAT 239 Differential Topology (4 units)
    • Similar courses completed at another institution may substitute for all or part of the Math 201AB, Math 215A, Math 239, and Math 250AB, if the GPC gives its approval.
  • Elective Courses (24 units): All courses at the 200 level (MAT 280 and below) count towards elective units. No more than 6 units of MAT 280 (Topics in Mathematics) may be counted toward the M.A.
  • Research – Students may take research units (299) when doing research with a faculty member. There is no specific requirement for a minimum number.
  • English Language Requirement - Students who have not obtained a previous degree at an approved English-medium institution or demonstrated English- language proficiency through an appropriate exam (e.g. TOEFL) are required to complete appropriate English-language courses, as described in the policy Graduate Student Course Requirements – English as Second Language (GC2018- 02). Courses taken in satisfaction of this requirement do not count towards the units required for graduation
  • Summary - 24 units of core coursework, and 24 units of electives are required for a total of 48 units. Full-time students must enroll for 12 units per quarter including research, academic and seminar units. Courses that fulfill any of the program course requirements may not be taken S/U unless the course is normally graded S/U. Once course unit requirements are completed, students can take additional classes as needed while completing their dissertation, although the 12 units per quarter are generally fulfilled with a research class (299) and perhaps seminars. Per UC regulations students should not ordinarily enroll in more than 12 units of graduate level courses (200) or more than 16 units of combined undergraduate and graduate level (100, 200, 300) courses per quarter.

Teaching Skills

The department has a commitment to develop outstanding teaching skills in its Ph.D. students. All Ph.D. students are required to be teaching assistants for at least one quarter. Exceptions require approval of the Graduate Program Committee. Students beyond their first year are encouraged to apply for positions as Associates In mathematics to develop and improve their lecturing skills. The department makes every effort to give all students exhibiting solid teaching skills the opportunity to serve at least one quarter as an Associate In mathematics.

 Advancement to Candidacy 

Students entering with a BA or BS should advance to candidacy by the end of the ninth quarter. Students entering with a MA or MS or equivalent should advance to candidacy by the beginning of their seventh quarter. Before advancing to candidacy for a doctoral degree, a student must have satisfied all requirements set by the graduate program, must have maintained a minimum GPA of 3.0 in all course work undertaken (except those courses graded S or U), and must have passed a Qualifying Examination before a committee appointed to administer that examination. Normally, students advance by the end of the ninth quarter. The student must file the appropriate paperwork with the Office of Graduate Studies and pay the Candidacy Fee in order to be officially promoted to Ph.D. Candidacy. Refer to the Graduate Council policy on Doctoral Qualifying Examinations (GC2005-02) for further details.

Preliminary Examination, Qualifying Examination and Dissertation requirements

 Preliminary Examination is a written exam, which comprises of graduate material in Analysis, Algebra, and Topology as covered in the following six graduate courses: 201AB, 250AB, 215A and 239. The exam consists of three parts: Analysis (201AB), Algebra (250AB), and Topology (215A, 239). The exam is written and administered by the GPC. The exam is offered twice yearly, normally at the beginning of the Fall and Spring quarters. Students in the Ph.D. program may take any or all three parts, during a given offering of the exam. Students in the Ph.D. program must pass two of the three parts of the Preliminary Exam by the beginning of the student’s 7th quarter. Passing two of the three parts is considered fulfilling the Preliminary Examination requirement.

Qualifying Examination (QE) must be passed by the end of the student’s 9 quarter. This is the final requirement for the advancement to candidacy, all other requirements must be completed, and a Dissertation Advisor selected, before a student can petition for this examination.

  • General Information - The purpose of this examination is to determine if the student is capable of independent research. In consultation with the Dissertation Advisor, the student proposes to the GPC a date for this exam, the material to be included, and a committee of four examiners. Normally three of the members are members of the Department of Mathematics. Per Graduate Council guidelines, at least one member must be external to the Department. The Dissertation Advisor can be a member of the committee but cannot be chair.

  • Written Portion of the Exam –Dissertation Prospectus-Thedissertation 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 proposal must be submitted to GPC for their approval at least 6 weeks before the proposed date of the exam. After approving the proposal, the GPC will recommend the appointment of the QE Committee to Graduate Studies. Example QE Proposal here

  •  Oral Portion of the Exam - Normally the QE is given in the form of a seminar talk on the candidate’s proposed research topic, in which the committee members have the opportunity to ask in-depth background questions and evaluate the breadth of the candidate’s knowledge. The talk should last no longer than 45 minutes, but, the entire QE could last up to three hours.

  • Outcome of the exam - The committee will reach a decision on the student’s performance immediately after the oral exam. The committee, having reached a unanimous decision, shall inform the student of its decision to:
    • “Pass” (no conditions may be appended to this decision)
    •  “Not Pass” (the Chair’s report must be submitted to Graduate Studies within 72 hours and specify whether the student is required to retake all or part of the examination, list any additional requirements, and state the exact timeline for completion of requirements to achieve a “Pass”), or
    • "Fail"
    • If the committee is unable to reach a unanimous decision, the QE Report must be submitted to Graduate Studies within 72 hours and specify the opinions of the majority and minority of the committee.
    • If a unanimous decision takes the form of “Not Pass” or “Fail,” the Chair of the QE committee must include in its report a specific statement, agreed to by all members of the committee, explaining its decision and must inform the student of its decision. If a student does not pass the QE on the first attempt, then, at the recommendation of the QE Committee, and subject to the approval of Graduate Studies, the student may repeat the exam once, within six months of the first attempt. Failure to pass on the second attempt disqualifies the student from continuing in the Ph.D. program.

​​​​​Dissertation Requirements: Ph.D. candidates will complete a written dissertation that represents an original and significant contribution to the scientific body of knowledge. The dissertation committee will evaluate when this dissertation requirement has been met. We do not have any program-specific requirements, such as length or presentation format. The Thesis Advisor provides information about appropriate length and formatting guidelines as expectations vary within subfields of mathematics.

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 BA or BS should accomplish their PhD by the end of their fifth year. Students entering with a MA or MS should accomplish their PhD by the end of their fourth year.