2013-2014 Bulletin 
    
    Mar 29, 2024  
2013-2014 Bulletin [ARCHIVED BULLETIN]

Mathematics, PhD


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The aim of the doctoral program in mathematics is two-fold–to prepare graduates for productive careers in industry, government, or education; and 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

Basic Requirements. A total of 72 units are required to complete the doctoral degree.  In addition, students must meet the standard University requirements below, which are detailed more fully in the Registration and Degree Information  section of the Bulletin.

  • CGU residency requirement of at least two semesters of full-time study within a two-year period or 48 units within a three-year period.
  • Time to degree is limited to seven years.
  • A minimum grade point average of 3.0 must be maintained, in compliance with satisfactory academic progress requirements.

It is recommended that coursework be completed on a full-time basis.  While part-time attendance is an option, students must, nevertheless, keep in mind the seven year time to degree standard.

Advising. Students are assigned a primary advisor during coursework.  A supervisory committee consisting of three faculty members is selected once preliminary examinations have been completed.

Transdisciplinary Course Requirement. All students entering the doctoral program are required to complete one transdisciplinary course during their second year of course work.  For details on this requirement, refer to the “Doctor of Philosophy Degree ” section of the Bulletin.  Note that joint doctoral students (Computational Sciences, Computational & Systems Biology, Engineering & Industrial Applied Mathematics, and Financial Engineering) are exempt from the transdisciplinary course requirement.

Qualifying Examination. The qualifying examination is given once per year, at the end of the Spring semester.  Full-time students in the Mathematics PhD program normally 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.  The exam determines mastery of the advanced undergraduate mathematics areas of analysis, complex variables, differential equations, linear algebra, and probability. Students failing the exam on the first attempt must repeat the exam the following year.  Failure to pass the exam on the second attempt, however, warrants dismissal from the program.  For students dismissed from the doctoral program for failure to pass the exam may, at the discretion of the faculty, qualify for a terminal master’s degree.

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 orientation toward pure and applied mathematics.  Students have two opportunities to pass each exam and must complete these exams prior to the completion of 48 units of coursework.  Failure to complete the exams within the specified period may result in 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.  In addition, students are strongly encouraged to develop a good working knowledge of computing and complete the equivalent of two courses in probability statistics.  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 qualifying 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 qualifying examination should be scheduled within six months of completing the required 72 units of coursework.

Dissertation Defense and Approval.  Policies and procedures are detailed in the Registration and Degree Information  section of the Bulletin.

University Policies.  University policies detailed in the Registration and Degree Information  section of the Bulletin apply.

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