To enter the Ph.D. program a student should hold at least a Bachelor's degree in mathematics. The academic record of a student applying to the Ph.D. program should contain substantial evidence that the student will succeed in the doctoral program. In reviewing an applicant's folder, the Graduate Committee gives substantial weight to the applicant's transcripts and letters of recommendation.
The Ph.D. degree has no rigid course requirement beyond the residency requirement (however, breadth and depth of knowledge are strongly encouraged).
It does require:
- 1. Passing written and oral qualifying examinations.
- 2. Writing a dissertation embodying the results of original research which is acceptable to the student's dissertation committee.
- 3. A final oral defense of the dissertation. A student's progress towards the Ph.D. degree is initially supervised by a three person committee, increasing to four or five members following the written qualifying exams. The student's faculty advisor chooses this committee, and is its chair.
The Ph.D. Qualifying Examination System consists of two parts. The first part consists of four Written Qualifying Exams and the second consists of an Oral Qualifying Exam.
Written Qualifying Exams are offered every year in August before the start of Fall semester classes and in January before the start of Spring semester classes. Study guides and copies of previous qualifying exams are available on the Graduate Program website for students to use in preparing for their Written Qualifying Exams.
Written qualifying exams are offered in algebra, complex analysis, numerical analysis, probability, real analysis and topology.
There are three possible grades on each exam: pass, master's pass or fail. Each PhD candidate is required to either: (i) attain pass grades on three written qualifying exams or (ii) attain pass grades on two written qualifying exams and master's pass grades on two written qualifying exams.
The choice of which three or four exams to apply to meet these requirements from the six available exams must be approved by the student's Preliminary Advisory Committee.
The Oral Qualifying Exam is based on the student's anticipated area of specialization. In it, the student is expected to present material from a research paper and to answer general questions about his or her area of specialization. It is typical for students to take their oral exam within 1 year of their passing the Written Qual requirements. (Students who passes Written Quals early will sometimes take additional time to pass the Oral Qual.) To begin preparing for the Oral Qual, a committee of four or five is chosen (including the student's thesis advisor). The student prepares by reading research papers in the area, and the student, advisor, and committee agree upon a body of material for which the student will be responsible. The exam consists of a presentation on the prepared research papers, followed by a question period covering the presentation and the agreed upon body of material.