April 30, 2005
A student who does not elect the thesis option will take the Department Comprehensive Examination. The Examination will consist of an oral portion and a written portion.
The oral portion
The goal of this presentation is to have the student
prepare and explain a topic which is a natural extension of a course or courses
in the student's program. For example, a mathematics student might learn about
and present a talk on polynomial rings, if that topic was not covered in
his/her Algebra course; or, a suitable topic might be the characterization of
all univalent mappings of the unit disk, if that topic was not covered in
his/her Complex Analysis course. A statistics student might present a design
that was not covered in his/her Design of Experiments course; or, a suitable
topic might be the application of a nonparametric method that was not covered
in a previous course. The topic will be chosen in conjunction with a Department
faculty member who will supervise the work; however, it is expected that the
work be done by the student. This activity is intended to be a demonstration of
the student's ability to learn independently and the ability to compose and
deliver an oral presentation. This is not intended to be a
"mini-thesis". The presentation will take place at a Department
seminar to be scheduled during the second year of the student's program.
The written portion
There will be one five-hour comprehensive examination
for each of the two program tracks. The student may split the exam into the two
parts outlined below (part A and part B) and take each part on two consecutive days.
The student will answer a total of five questions from examinations structured as follows.
Mathematics track
Part A:
Four questions from Advanced Linear Algebra; the student will choose two
of the questions to answer.
Part B: The student will first
choose three courses from among Numerical Analysis, Probability, and his/her
mathematics electives. There will be two questions prepared from each of these
courses. The student will choose one
question from each of the three courses.
Statistics track
Part A:
Four questions from Mathematical Statistics I; the student will choose two
of the questions to answer.
Part B: The student will first
choose three courses from among Statistical Methods I, Probability, and his/her
statistics electives. There will be two questions prepared from each of these
courses. The student will choose one
question from each of the three courses.
The Graduate Coordinator will set up a Committee of Examiners. This committee will construct and grade the examination and will forward its recommendation of pass or fail to the Graduate Coordinator. In case of disagreement, the Graduate Coordinator shall refer the matter to the Graduate Committee for resolution. In case of student failure, the Committee of Examiners will recommend a remedy of repeating all or portion of the examination (with possibly different questions). The proposed remedy must be approved by the Graduate Committee. In case the whole examination must be repeated, the student must wait for at least one semester before attempting the examination again. In case of failure on the second attempt, the student must appeal to the Graduate Committee for another change to take the examination.