Second Exam Learning Goals
Second Exam Assessment, 2011
Ph.D. Program in Mathematics
In order to be eligible to take the Second Exam, a student must be at Level II, and in particular must have passed the Qualifying Examinations, and have accumulated at least 45 credits of course work.
The Second Exam is an oral examination, taken before a committee of three faculty members, and is ordinarily chaired by the student’s advisor. In format, the examination consists of a formal presentation, generally one to two hours in length, of a part of mathematics of contemporary relevance. Additionally the topic should generally be one whose mastery will facilitate the student’s work towards an eventual Ph.D. degree. Specifically, the subject should be one in which the student has demonstrated aptitude and interest, and has secured the guidance of a member of the faculty who is both knowledgeable in the area and interested in taking on a Ph.D. level advisement role with the student. Passage of the exam requires that the student be capable of putting together and delivering a clear and coherent exposition of a high-level topic in mathematics, and be able, when necessary, to clarify various points, and to answer pertinent questions from a knowledgeable audience. The student’s preparation for the exam is ordinarily formed from a combination of relevant prior course and seminar work, individual reading and study, and consultations with appropriate members of the faculty, as well as with other students.
The student’s performance on the exam is evaluated by the exam committee immediately following the exam, and the results communicated to the student and the Executive Officer, as soon as a determination has been made. Whether the student passes or fails (the only two possible outcomes) is based on the level of knowledge displayed by the student, as well as the quality of the presentation, and the evidence it presents for the student’s suitability to move to the level of working on the Ph.D.
As noted above, the student receives very quick notification, usually just after the exam, about whether they passed or failed. Historically, failures are quite unusual, since if a student is not going to do well, this has usually become apparent well before a Second Exam is reached, and the advisor would have ordinarily made it clear to the student that they are not, in the advisor’s opinion, prepared to pass a Second Exam in the selected field. If, under such circumstances, or after an actual failure of a Second Exam, an advisor feels unable to work successfully with a student towards a Ph.D., the student would be directed to have a conference with the Executive Officer, in order to explore various alternative options, both as regards suitable fields of study and/or advisement, or rarely, the suitability of continuation in the Program. If the student continues in the Program and successfully changes fields, they would be permitted to take another Second Exam in their new field. Under exceptional and quite rare circumstances, a student may be permitted to attempt to retake and pass a Second Exam in the previous field.