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 scientists who excel at communicating their knowledge to their students, fellow mathematicians, and surrounding communities

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

Degree Requirements

General doctoral degree requirements at CGU may be found in the Doctoral Degrees section of the Bulletin. It is the student’s responsibility to be aware of and to meet these 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.

Residency. 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 an additional 8 units of Mathematics courses may be excluded from the program.

Advising. Students are assigned an academic advisor upon entering the program. As they reach the advanced stages of coursework, they select a research advisor, who assumes primary advising responsibilities. In order to advance to candidacy (see below), students must select a PhD committee consisting of at least three Mathematics faculty members from within the Claremont Colleges, chaired by the research advisor.

Qualifying Examination. The written qualifying examination is given once per year, at the end of the Spring semester. Full-time students in the Mathematics PhD program take the exam immediately following the first year of coursework. Part-time students may wait until they have completed 16 units of CGU 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. However, they may not transfer to another doctoral program offered 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 orientation toward pure or applied mathematics.

Preliminary exams should be finished within two years of passing the written qualifying exam, but no later than 3 months after the completion of 72 units of coursework. Unless there are mitigating circumstances, failure to complete the exams within the specified period is cause for dismissal from the program.

Students have two opportunities to pass each exam. If a student fails or forfeits his/her second attempt at a preliminary exam, he/she may submit a petition to the IMS Director, asking for permission to change the preliminary exam subject to a new one. The petition should provide a valid reason for allowing such a change. Before deciding on the petition, the IMS Director will consult the student's academic and/or research advisors, the professor who administered the current preliminary exam and, in the case of students in joint, inter-field or dual-degree programs, the corresponding Program Director(s). Students may be granted such a permission at most once while in the PhD program.

Research Tools. The following two research tools, intended to help prepare students for independent research, are required.

Research seminar requirement. Over a period of at least two semesters, each student must attend a mathematics research seminar regularly. This may be a CCMS research seminar, mathematics colloquium, faculty-organized topical seminar, or student-organized journal club. The student must submit to his or her advisor a list of seminar talks attended, as well as written summaries of three seminar talks. Each summary, of about 1-2 pages in length, should outline the basic problem, the methods used, and the results. Completion of this research tool is required within one year of passing the written qualifying exam.

Proficiency requirement. Each student must demonstrate proficiency in one of the following two categories, by means of a satisfactorily completed course, project or exam. Completion of this research tool is required before advancing to candidacy.

Computational. A computer programming language, statistical research method, or other computational research tool approved by the advisor. OR

Foreign language. French, German, or Russian.

Advancement to Candidacy. After completing the qualifying and preliminary examinations, doctoral students must prepare a written dissertation proposal. In the advancement to candidacy examination, the student presents the proposed dissertation research. The examination should be scheduled within one year of completing the required 72 units of coursework.

Dissertation Completion and Final Oral Examination. The dissertation must be completed within seven years from the semester in which the student was admitted. The dissertation defense may not occur earlier than six months after advancement to candidacy. The defense is a public event announced to the University’s academic community by the registrar’s office. Full policies and procedures are detailed in the Doctoral Degrees section of the Bulletin and on the registrar’s Completion of Degree webpage.