Comprehensive Examinations

The M.A. in Mathematics requires a comprehensive examination in which the student is tested on four graduate mathematics courses that were part of the student's degree program. The student may choose, in consultation with the Director of Graduate Studies, which courses will be covered in the exam. The exam is three hours in length, allowing forty-five minutes for each of the four components. Typically three questions are posed for each course, from which the student must answer two. To pass the examination students must achieve an overall grade of at least B and a grade of at least C on each of the four components. Students may repeat the comprehensive examination at most once.

The comprehensive examination aims to determine whether the student has incorporated the main ideas or skills taught in the selected course. Consequently, a suitable question might relate to one major concept or theorem (e.g. "State the Central Limit Theorem and use it to derive the normal approximation to the binomial distribution."), or it might be a question with several parts that either tests the ability to use certain tools (e.g. moment-generating functions or important theorems) or work with the definitions of basic concepts. Due to the time constraints, the examination cannot sample a wide range of the course subject matter. Thus it cannot literally be "comprehensive". The examination questions should reflect the instructor's opinion why it is important that a student should take the course.

The comprehensive examination will normally be given on the third Wednesday of the Fall and Spring Semesters. The student should arrange to take the comprehensive exam, in consultation with the Director of Graduate Studies, during the preceding semester.