Graduate School Application and Information


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Ph.D. Program

Program of Study

The normal first year of study consists of MATH 131a and b, 141a and b, and 151a and b. With the permission of the Graduate Advising Head, a student with superior preparation may omit one or more of these courses and elect higher-level courses instead. In this case the student must take an examination in the equivalent material during the first two weeks of the course. The second year's work will normally consist of MATH 140a and higher-level courses in addition to preparation for the qualifying examinations described below and participation in the Second Year Seminar. Upon completion of the qualifying examinations, the student will choose a dissertation adviser and begin work on a thesis. This should be accompanied by advanced courses and seminars.

Teaching Requirements

An important part of the doctoral program is participation, as a teaching fellow, in a structured program of undergraduate teaching. During the spring semester of the first year, every student takes part in our teaching apprenticeship program to learn basic classroom teaching skills. All graduate students are then expected to teach a section of calculus or precalculus for at least four semesters, usually beginning in the second year of study. Teaching fellows must also enroll every fall semester in the Teaching Practicum, in which their teaching is evaluated and discussed.

Residence Requirement

The minimum academic residence requirement is three years.

Language Requirement

Proficiency in reading one of French, German or Russian, determined with the consent of the adviser.

Qualifying Examination

The qualifying examination consists of two parts: a major examination and a minor examination. Both are normally completed by the end of the third year. For the major examination, the student will choose an advanced topic in a specific area of mathematics (e.g., low-dimensional topology, gauge theory, complex geometry, dynamics, geometric group theory, combinatorics, random matrix theory, representation theory, or number theory) and a major examiner from among the faculty. Together they will plan a program of study and a subsequent examination in that material. The aim of this study is to prepare the student for research toward the Ph.D. The minor examination will be more limited in scope and less advanced in content. Its subject matter should be significantly different from that of the major examination.

Dissertation and Defense

The doctoral degree will be awarded only after the submission and acceptance of an approved dissertation and the successful defense of that dissertation.