A candidate for the Ph.D. degree in mathematics must fulfill the following degree requirements: 72 points of credit; a written comprehensive examination, an oral preliminary examination, and an oral defense of the dissertation.
Coursework: All students in the Ph.D. program must complete 72 points of coursework. It is possible, with departmental permission, to take courses, relevant to students’ course of study, in other departments at NYU or at other universities. A base minimum of 32 points of credits must be completed at the Department of Mathematics.
The Written Comprehensive Examination: The examination tests the basic knowledge required for any serious mathematical study; it is comprised of three individual examinations in Advanced Calculus, Complex Variables, and Linear Algebra, and is given on three consecutive days, twice a year, in early September (or, sometimes, late August) and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. Students may take the written examination twice; a third and final time requires the permission of the Director of Graduate Studies.
The Oral Preliminary Examination: This examination is usually taken after two years of full-time study. Its purpose is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place twice a year: fall, and late spring. Cooperative preparation of often helpful and is encouraged. Students may take the oral examination twice; a third and final time requires the permission of the Director of Graduate Studies. All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points. It is recommended that students attempt the examinations well before this deadline.
The Dissertation Defense: The oral defense is the final examination on the student’s dissertation. The defense is conducted by a panel of five faculty members (including the student’s advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student’s topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.