Ph.D in Mathematics

** New Examination Policy for Ph.D. in Mathematics, effective Fall 2005

Overview		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.
Requirements		A total of 72 units are required. Students must complete at least two semesters of full-time study in residents (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 some 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 computer programming, and knowledge at least equivalent to a year's course in applied analysis and a year's course in probability and statistics.
Preliminary Examination		All doctoral students in mathematics are required to pass preliminary written examinations or to qualify for exemption from such examinations by the end of their second year of graduate work. The examinations are in four of the five core areas of real analysis, complex analysis, algebra, applied mathematics, and topology. With the department's approval, two of the four examinations may be in distinct areas of applied mathematics.
Qualifying Examination		In preparation for this examination, the student is expected to spend at least one semester in advanced graduate or directed reading courses where exposure to research material is emphasized, and the student is expected to gain some facility in the appropriate research techniques. The student, in consultation with the student's qualifying examination committee and with the approval of the faculty, must prepare a written dissertation proposal containing an outline of the research to be undertaken, references to relevant source materials, and a list of mathematical support areas appropriate to the research topic. The qualifying examination will test the student's knowledge and understanding of the basic mathematics and the research approaches, and will assess the soundness of the dissertation proposal. Before taking the qualifying examination, the student must have completed satisfactorily all parts of the preliminary examination, passed language examinations, and completed two years of full-time graduate study or the equivalent (at least one year at CGU). The student may take the qualifying examination at any time thereafter, when prepared to demonstrate breadth of knowledge at an advanced level and some acquaintance with an area of research. The qualifying examination is usually a three-hour oral examination. The qualifying examination may not be attempted more than twice without the approval of the faculty.
Research Tools		Doctoral students must demonstrate adequate proficiency in two of three languages (French, German, or Russian), or in one of these languages and computer programming.
Other Requirements		General Ph.D. requirements at CGU may be found in the Bulletin under "Degree Regulations."