## Prerequisites:

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, letters of recommendation, and GRE scores.

## Requirements:

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 in Algebra, Real Analysis, Complex Analysis, Topology, Numerical Analysis and Probability. The 8000-level sequences in each area are designed to prepare the student for Qualifying Exams. Written Qualifying Exams are offered every year in August and in January, during the week before the start of classes. Syllabi, and copies of old Exams, are available from the department office for students to use in studying for Exams or can be found on-line from the section for current graduate students.

Each Ph.D. candidate is required to pass four Qualifying Exams, including both Real and Complex Analysis, and either Topology or Algebra.

**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 to be taken within 1 year of the time the student passes his or her last Written Qual. (A student who passes Written Quals early will be allowed 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.

See the Graduate Guidebook for full details.