The general aim of the doctoral program in mathematics is to prepare qualified graduate students to become productive workers in industry or government, or academic research scholars capable of communicating their knowledge to students and to the mathematical community. The program is planned to develop in the student a fundamental understanding of certain basic fields of mathematics, a deep understanding of a major field of interest, the ability to formulate and recognize significant research problems, and the ability to analyze problems, reach solutions, and transmit ideas to others.

Each student is assigned an advisor upon arrival. A supervisory committee consisting of three faculty members is appointed when preliminary examinations have been completed.

DEGREE REQUIREMENTS

Course Requirements. A total of 72 units are required. Students must complete at least two semesters of full-time study in residence (both semesters must be in the same academic year or in consecutive years).Whenever possible, it is strongly recommended that all of the graduate work be done in full-time resident study. A student who is very well prepared might expect to complete the Ph.D. program in three years of full-time study or the equivalent, but most students will find it necessary to take longer than this.

Upon arrival, students are given a more detailed description of the regulations and procedures governing the administration of the graduate program in mathematics. Students are strongly encouraged to obtain good working knowledge of computing, as well as knowledge at least equivalent to a year’s course in applied analysis and a year’s course in probability statistics.

Transdisciplinary Course Requirements. All students who enter the doctoral program after the fall 2004 semester are required to complete the transdisciplinary course requirement within the first two years of their program. For details on the requirement, see the “Doctor of Philosophy Degree ” section in this Bulletin. Please note: joint doctoral students (with California State University, Long Beach or San Diego State University, and students in the Ph.D. in Computational and Systems Biology) are exempt from the transdisciplinary course requirement.

Qualifying Examination. All math Ph.D. students must take, at the end of their first year of study, a qualifying examination covering areas of advanced undergraduate mathematics that all prospective Ph.D. students in math should have mastered: undergraduate analysis, complex variables, probability, linear algebra, and differential equations. The exam is given each spring (late May or early June). Part-time students take this exam at the end of the academic year in which they first complete 16 units. This six-hour exam is split into two three-hour sessions, one in the morning (analysis and complex variables), and one in the afternoon (probability, linear algebra, differential equations). Students are given two chances to pass the examination, and upon failing it for the second time, are dropped from the Ph.D. program, but allowed to complete a master’s degree at the discretion of the examining faculty. Students failing the exam a first time MUST repeat the exam the next time it is given.

Preliminary Examinations. After passing the qualifying examination, Ph.D. students are required to pass two written preliminary examinations, each covering roughly two semesters of advanced graduate work in appropriate areas of graduate level pure or applied mathematics. Students can choose their examination areas (subject to approval by their graduate advisors) in pure or applied mathematics, depending on their research interests and relative orientation toward pure and applied mathematics. Students who take both preliminary examinations in areas of applied mathematics are automatically placed into the applied mathematics concentration. Students are given two chances at passing each exam, and must complete these exams before the completion of 48 units of coursework toward the degree. Failure to complete the exams within this period, without mitigating circumstances, will be cause for dismissal from the Ph.D. program.

Research Tools. Two research tools are required as described in the “Registration and Degree Information ” section of this Bulletin. Students will be allowed to be examined in scientific computing, specific computing languages, statistical research methods, computer database management, or the foreign languages of German, French, or Russian.

Dissertation Topic Oral Examination / Advance to Candidacy. After completing the qualifying and preliminary examinations, Ph.D. students must prepare and pass the Dissertation Topic Oral Qualifying Examination, which amounts to 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 must take the Dissertation Topic Oral Qualifying Examination within six months of completing the required 72 units of coursework toward the Ph.D.

Other Formal Requirements. General Ph.D. requirements at Claremont Graduate University may be found in the “Academic Program ” section of this Bulletin under “Degree Regulations.” It is the student’s responsibility to be aware of these requirements and to meet them.