The aim of the doctoral program in mathematics is two-fold.

• To prepare graduates for productive careers in industry, government, or education
• To produce capable scholars who excel at communicating their knowledge to their students, fellow mathematicians, and surrounding communities

The program is designed to develop a fundamental understanding of basic fields of mathematics along with expertise in a major field of interest.  Emphasis is placed on the abilities of recognizing significant research problems, of formulating solutions, and of transmitting successful outcomes to others.

Degree Requirements

Course Requirements. A total of 72 units of coursework are required to complete the doctoral degree.  These units must include one transdisciplinary course  per University policy.

Students must fulfill the CGU residency requirement: at least two semesters of full-time study within a two-year period or 48 units within a three-year period.  It is recommended that coursework be completed on a full-time basis; while part-time attendance is an option, degree requirements should be fulfilled within a seven-year time frame.  

Satisfactory Academic Progress.  The University’s policy on satisfactory academic progress  applies.  Students who do not maintain a minimum overall grade point average of 3.0 in Mathematics courses are placed on academic probation.  Students who remain on academic probation after taking and additional 8 units of Mathematics coursework may be excluded from the program.  

Advising. Students are assigned a primary advisor during coursework.  A supervisory committee consisting of at least three faculty members is selected once coursework is complete.

Qualifying Examination. The written qualifying examination is given once per year, at the end of the Spring semester.  Full-time doctoral students usually take the exam immediately following the first year of coursework.  Part-time students take the exam after having completed 16 units of coursework.

The six-hour exam is scheduled in two three-hour sessions: one in the morning and one in the afternoon. Students failing the exam on the first attempt must repeat the exam the following year.  Failure to pass the exam on the second attempt, results in dismissal from the program.

Students dismissed from the doctoral program in Mathematics for failure to pass the exam may, at the discretion of the faculty, qualify for a terminal master’s degree.  Moreover, these students may not transfer to another doctoral program through the Institute of Mathematical Sciences.

Preliminary Examinations.  Upon successful completion of the qualifying examination, students are required to pass two written preliminary examinations, each covering roughly two semesters of advanced graduate coursework.  Subject to advisor approval, students select their examination areas based upon their research interests and relative orientations toward pure or applied mathematics.

Students have two opportunities to pass each exam and must complete these exams within one year of passing the written qualifying exam.  Unless there are mitigating circumstances, failure to complete the exams within the specified period is cause for dismissal from the program.

Research Tools. Two research tools, intended to help prepare students for independent research, are required.  Mathematics students can be examined in scientific computing, specific computing languages, statistical research methods, computer database management, or a designated foreign language such as French, German, or Russian. Selection of research tools is subject to the approval of the advisor.

Advancement to Candidacy. After completing the qualifying and preliminary examinations, doctoral students must prepare a dissertation proposal.  In an oral examination, the student presents an exposition and presentation of the proposed dissertation research.  After passing this examination, the student is advanced to candidacy.  The oral examination must be scheduled within six months of completing the required 72 units of coursework.

Dissertation Defense and Approval.  Policies and procedures are detailed in the Doctoral Degrees  section of the Bulletin and on the registrar’s Completion of Degree webpage.

University Policies.  University policies detailed in the Student Information  section of the Bulletin apply.