Guidelines on master’s comprehensive examination

A student in the MS in Mathematics degree program, regardless of concentration, is required to take, and perform satisfactorily on, a comprehensive examination. Although the catalog says that the examination could be either written or oral for the General Mathematics and Applied Mathematics concentration, it has been the department’s long practice that the examination is oral. The deadline for the comprehensive examination is the last day of the semester in which you intend to graduate.

For an oral examination, this is typically what you need to do:

  1. Form the Comprehensive Examination Committee (CEC): At the beginning of the last semester (or at least the first half of the semester), you talk to professors in the program from whom you have taken classes and choose three of the professors to serve in your CEC. After the CEC is formed, you need to inform the Graduate Coordinator who needs to approve it. There is NO paperwork though.
  2. Prepare the examination: Although in general the CEC will not provide you any formal syllabi, you can talk to the three professors in your CEC and ask them for lists of topics they may test you on in the oral examination. They may provide you such kinds of lists, either orally or in writing.
  3. Schedule the examination: When you are ready for the examination, communicate with your CEC to set up a date/time for your examination. You should reserve at least one hour for the examination. After the date/time is set, you need to ask the front desk to help you reserve a room for your examination. Typically we use Fretwell 315 or the Math Conference Room (Fretwell 379), if either is available.
  4. Inform the Graduate Coordinator of the schedule: Once the date/time/room is set, you MUST inform the Graduate Coordinator of the schedule AT LEAST one week prior to the examination. Your examination is open to all graduate faculty in the department so it has to be announced. Unannounced examinations will not be counted.
  5. Take the examination: Each professor in your committee will ask you several questions. While you are not expected to answer every question correctly, you are expected to demonstrate a consistently high level of understanding of the material and ability to participate at a substantial level of constructive mathematical thinking. Roughly speaking, being able to attain proficiency level with the lines of questioning 70% of the time or higher is a pass.
  6. Complete the Exam Report form: At the end of the examination, ask the CEC to fill out and sign the Exam Report of Comprehensive Examination form currently available at
  7. Turn in the form to the Graduate Coordinator.

Several Remarks:

  1. A student who fails the examination on his/her first attempt is allowed a second chance, usually within one semester from his/her first attempt. The student, as he/she wishes, can retake the exam in the same semester as the first attempt, as long as time allows.
  2. The comprehensive examination can be waived for those MS students who are also in our doctoral program and have passed at least one part of the doctoral qualifying examination. But some paperwork has to be done.
  3. For those students who also need to defend their MS projects, it is quite common that they choose the same three professors in his/her CEC for project defense and actually do the project defense and the comprehensive examination on the same day. In this case, a student needs to reserve at least 2 hours for the defense and the examination.