Ph.D in Mathematics
The aim of the doctoral program in mathematics is two-fold: 1) to prepare graduates for productive careers in industry, government, or education, and 2) 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 and a thorough understanding of one 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.
Course Requirements/Residency: A total of 72 units are required to complete the doctoral degree. 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. The minimum grade point average is 3.0.
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 Requirements: 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, Financial Engineering) are exempt from the transdisciplinary course requirement.
Qualifying Examination: Following the first year of coursework, students take a qualifying examination to determine mastery of advanced undergraduate mathematics. The exam is given each spring; 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 (analysis and complex variables) and one in the afternoon (probability, linear algebra, differential equations). Students failing the exam on their first attempt must repeat the exam the following year. Failure to pass the exam on the second attempt warrants dismissal from the program. Note that a terminal masters degree can be awarded at the discretion of the faculty to those who are dismissed based on the exam. Qualifying Exam Description and Reading List
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. Students choose their examination areas (subject to approval of their advisor) depending on 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 allotted period, without mitigating circumstances, 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 designated foreign languages (French, German, or Russian). In addition, students are strongly encouraged to obtain good working knowledge of computing, as well as the equivalent of two courses in probability statistics. The selection of appropriate research tools must be approved by the PhD advisor.
Oral Examination of Dissertation / Advancement to Candidacy: After completing the qualifying and preliminary examinations, doctoral students must prepare and pass the dissertation topic oral qualifying examination, an exposition and presentation of the student’s proposed dissertation research. After passing this examination, the student becomes advanced to candidacy for the Ph.D. Students should take the dissertation topic oral qualifying examination within six months of completing the required 72 units of coursework.
Other Formal Requirements: General doctoral degree requirements at CGU may be found in the “Academic Program” section of the Bulletin under “Degree Regulations.” It is the student’s responsibility to be aware of and to meet these requirements.