Part B

Students can choose between two possible format options for the Part B Examination:

Option 1: An oral examination based on existing literature covering two advanced topics of Mathematics or Statistics that provide background for the intended area of specialization.

Option 2: An oral examination based on a written literature review of, and research proposal on, a single advanced topic of Mathematics or Statistics.

This examination has strict deadlines. Only students who have successfully passed the Part B examination prior to the completion of their Ph.D. 3 year will be permitted to register at the Ph.D. 4 level. Only in exceptional circumstances will the deadline be relaxed, with a formal letter to this effect from the Graduate Program Director acting in consultation with the Chair of the Department and the Progress Tracking Committee (or at least the advisor(s)) of the student.

The Progress Tracking Committee, in consultation with the student, will determine the choice of the format option, the examiners, the allowed material during the examination, and, in the case where Option 1 is chosen, the examination topics. This information should be sent to the Graduate Program Coordinator no later than the beginning of the student’s second semester at the Ph.D. 3 level. In case of disagreement with their Progress Tracking Committee, the student can appeal this decision by writing to the Graduate Program Director.

A Standing Committee on the Part B Examination shall be set up by the Graduate Affairs Committee and shall consist of a Chair and two other members. This subcommittee will be chaired by the Graduate Program Director or their delegate and responsible for approving the choices made by the student’s Progress Tracking Committee, for deciding on any appeal from the student on these choices and for arranging the place, date and time of the examination. The Part B Subcommittee will assume total responsibility for informing students of deadlines both impending and expired concerning the Part B Examination. 

Option 1

The Progress Tracking Committee, in consultation with the student, will determine the choice of two topics, the material that will be allowed during the examination, a principal examiner for each topic and two additional examiners. Each topic should be at the level of a one-semester 600 or 700 level course, or on similarly advanced material defined by a book, a designated part of a book or a collection of research papers. A reasonably detailed description of each topic, countersigned by its prospective principal examiner, will be submitted in writing to the Part B Subcommittee. This should be done no later than the beginning of the student's second semester at the Ph.D.3 level.

The Part B Subcommittee will inform the student in writing of its approval of the proposals. Later, with at least 6 weeks of advance notice, the student proposes a range of dates for the examination to take place. The examination should be scheduled at least 3 months before the beginning of the first semester of Ph.D. 4. The Part B Subcommittee will then set up an Examining Committee consisting of the 2 principal examiners, two additional examiners, and a member of the Part B Subcommittee who will act as Chair of the Examining Committee. The members of the Progress Tracking Committee will usually serve on the Part B Examining Committee. Principal and additional examiners need not be from the department and can include post-doctoral fellows. The examination will be scheduled in consultation with the participants and with the help of the Graduate Program Coordinator.

Option 2

The Progress Tracking Committee, in consultation with the student, will determine the choice of the material that will be allowed during the examination, in addition to the student’s written research proposal, as well as the choice of two additional examiners, in addition to the advisor(s), to compose the Examining Committee. This should be done no later than the beginning of the student's second semester at the Ph.D.3 level.

The Part B Subcommittee will inform the student in writing of its approval of the proposals. Later, with at least 6 weeks of advance notice, the student proposes a range of dates for the examination to take place. The examination should be scheduled at least 3 months before the beginning of the first semester of Ph.D. 4. The Part B Subcommittee will then set up an Examining Committee consisting of the student’s advisor(s), two additional examiners, and a member of the Part B Subcommittee who will act as Chair of the Examining Committee. The members of the Progress Tracking Committee will usually serve on the Examining Committee. Examiners need not be from the department and can include post-doctoral fellows. The examination will be scheduled in consultation with the participants and with the help of the Graduate Program Coordinator.

Next, with at least 2 weeks of advance notice, the student sends to the Graduate Program Coordinator a written thesis proposal (10-20 pages plus references) consisting of                                              

• at least 9 pages of literature survey on a research topic
• at least 1 page about their research intentions, identifying open problems they wish to address and the approach they plan to take to the solution. 

Option1

The oral exam will be open to members of the Department but not to students other than the candidate. The exam will be conducted mainly by the principal examiners, each in turn taking between 20 to 40 minutes to examine the student. The other examiners may seek clarifications. Questions will largely deal with the specifics of the assigned topic (e.g. statements, ideas of proofs) but may also relate to the broader context (e.g. examples, counterexamples, elementary results). In this second respect, questions may be asked whose answers do not specifically lie in the assigned material but are nevertheless considered fundamental by the examiners for a good understanding of that material. After the principal examiners have finished their questioning, the other members of the Examining Committee may pose further questions. The Examining Committee will then meet privately to determine by a majority vote whether or not the student has passed the examination. The Chair of the Examining Committee will record the decision by sending an e-mail to the Graduate Program Coordinator in copy to the student and the Examining Committee. The principal examiners will meet with the candidate to provide constructive feedback soon after the examination has taken place.

Option 2

The oral exam will be open to members of the Department but not to students other than the candidate. The exam will consist of a 30-minute presentation of the thesis proposal followed by a 40 to 60-minute oral exam on the proposal and related material. Questions will largely deal with the specifics of the proposal (e.g., expected results, methods) but may also relate to the broader context (e.g., examples, counterexamples, elementary results). In this second respect, questions may be asked whose answers do not specifically lie in the material of the proposal but are nevertheless considered fundamental by the examiners for a good understanding of that material. The Examining Committee will then meet privately to determine by a majority vote whether or not the student has passed the examination. The Chair of the Examining Committee will record the decision by sending an e-mail to the Graduate Program Coordinator in copy to the student and the Examining Committee. The advisor(s) will meet with the candidate to provide constructive feedback soon after the examination has taken place.

Option 1

In the case that a student fails the examination in one or both topics presented, they may repeat the examination once with the same Examining Committee (or one diverging from the original committee by as few members as possible), and this within the following four months, at a time to be approved by the Part B Subcommittee. Students who fail at the second attempt will be asked to withdraw from the program.

Option 2

In the case that a student fails the examination, they may repeat the examination once with the same Examining Committee (or one diverging from the original committee by as few members as possible), and this within the following four months, at a time to be approved by the Part B Subcommittee. A failure will require a new written submission addressing the concerns raised by the examiners. This may or may not require a repeat oral presentation, depending on the examiners’ judgment. Students who fail at the second attempt will be asked to withdraw from the program.