Applied Ph.D. Program Requirements (Fall 2024)

This plan requires a total of 60 units. 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 requirements set by the graduate program, maintained a minimum GPA of 3.0 in all course work undertaken (except those courses graded S or U), passed the PhD Preliminary Examination, and passed the Qualifying Examination. A dissertation and an exit seminar are required.

Course Requirements

1. Core Courses - 20 units total
   • Area A (12 units in one of the series) :
   1. Analysis Series MAT 201AB/MAT 201C/MAT 205/MAT206 (Analysis) or
   2. Methods of Applied Mathematics MAT 207ABC.
       
   • Area B (8 units in one of the series):
   1. Data Science series: Numerical Optimization (MAT 258A), Discrete and Mixed-Integer Optimization (MAT258B), Mathematics of Data Science (MAT 270); or
   2. Numerical Methods series: Numerical Methods: Fundamentals (MAT 226A), Numerical Methods: Large-Scale Matrix Computations (MAT 226B), Numerical Methods: Ordinary Differential Equations (MAT226C), Numerical Solutions of Differential Equations A, B and C (MAT 228ABC); or
   3. Probability series: Probability Theory A and B (MAT235AB), Mathematical Statistics III (STA231C); or
   4. Theoretical Computer Science series: Theoretical Computer Science (ECS220), Design and Analysis of Algorithms (ECS222); or
   5. Courses in the analysis series if Methods in Applied Mathematics is chosen in Area A or Methods in Applied Mathematics if Analysis is chosen in Area A.
       
2. Electives - 40 units total
   • Graduate Advanced Mathematics: 12 units of 200-level Mathematics courses whose course numbers are 279 or less. These include courses from areas A or B not selected as core courses. One mathematics-oriented graduate course outside of Mathematics, could be substituted but only with prior approval by GGAM Chair.
      
   • Field of Specialization (FOS): Minimum of 15 units in a field of specialization, such as, any courses in Area A or B not taken to satisfy the core requirements, optimization, and control, differential equations, probability and statistics, discrete mathematics, mathematical physics, mathematical biology, harmonic analysis and signal processing, etc. Out of this minimum of 15 units, at least one course of 3 or more units must be outside of Mathematics. Courses outside of the mathematics department have to be approved by the Chair of the graduate group. For a list of preapproved courses, see the GGAM webpage and consult with the potential thesis advisor. An updated list of courses can be found in https://appliedmath.ucdavis.edu/graduate/sample-depth-courses
      
   • Advanced Mathematics: Maximum of 12 units, in three 100 level (i.e.upper division) math courses.
      
   • GGAM miniconference: Attendance at the annual GGAM mini-conference, which takes place during winter quarter graduate welcome and consists of faculty talks and a student poster session showcasing the research being done at GGAM, is required in the first or second year, for which 1 unit of 290 will be given in order to document compliance.
      
   • MAT 290 seminars
      
   • MAT 390 and Teaching: Each student who accepts a TAship in the Department of Mathematics is required to complete MAT390, which is 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). All PhD students are required to be teaching assistants for at least one quarter. Exceptions require approval of the GGAMEXEC. Students beyond their first year are encouraged to apply for positions as Associate-Instructors to develop and improve their lecturing skills.
      
   • Research Units: Students can register for research units but these units cannot substitute course requirements unless previously reviewed and approved by the chair of the graduate group.

Ph.D. Preliminary Examination

The Ph.D. Preliminary Examination is a written examination covering materials from the student’s chosen tracks Area A (MAT 201AB or MAT 207ABC) and Area B: Data Science: (MAT 168, MAT170); Numerical Methods (MAT128ABC); Probability (MAT 135AB); Theoretical Computer Science (ECS220, ECS222), Analysis (MAT201AB) or Methods in Applied Mathematics (MAT 207ABC) not overlapping with Area A. The exam is offered in June and September every year. Ph.D. students are required to pass this examination before the end of their second year.  They may take the examination multiple times; what matters is when they pass, not how many attempts.

Qualifying Examination

Students must complete the course requirements before taking their Qualifying Examination (QE). The QE will consist of a written research proposal, a syllabus of materials relevant to the research proposal covered in the chosen tracks in Areas A and B, and oral examination. Approximately six weeks before the date of the proposed QE, the research proposal, along with the QE Application, is submitted to GGAMEXEC for approval. Once approved and required signatures obtained, the QE Application will be forwarded to the Office of Graduate Studies for final approval. The QE should be taken by the sixth quarter and no later than the end of the ninth quarter after admission to the Ph.D. program. Passing the QE makes the student eligible for advancement to candidacy.

Dissertation

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 Advisor. 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 applied 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.

Exit Seminar

Ph.D. students are required to give a 60-minute seminar presentation, open to the public, on their dissertation subject.

Optional Final Oral Examination
(at the discretion of the Dissertation Committee)

After the exit seminar, the student’s dissertation committee may meet privately with the student to discuss the contents of the dissertation and ask additional questions. Satisfaction of this requirement must be verified by the Dissertation Committee Chair.