This examination is usually (but not invariably) taken after two years of full-time Ph.D. study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation.
The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information.
What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.
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 three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents.
The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.
All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.
Upcoming Oral Exam Dates
|Examination||Examination Dates||Application Deadline|
|October 2017 Orals||Tuesday, 10/24/17
|February 2018 Orals||Tuesday, 2/6/18
|April 2018 Orals*||Tuesday, 4/10/18
Students should submit an electronic application (insert link here) to take the oral examinations, including their special exam outline, to Graduate Mathematics at email@example.com.