Mathematics Assessment of Comprehensive Knowledge

The comprehensive examination in the Ph.D. degree program majoring in Theoretical and Computational Science with a concentration in Applied Mathematics or Pure Mathematics consists of two separate 3-hour written comprehensive examinations from the following two areas: Analysis and Algebra. In addition, there is an oral component to the comprehensive examination which will take place after a student has passed the written components.

The written portion of the graduate comprehensive examination for students with a concentration in Applied Mathematics or Pure Mathematics will test material that might normally be taught in the following two courses: Analysis 5505/7505 and Algebra 5405/7405 (combined with material taught in our undergraduate offerings). A list of approximately 100 problems in Analysis and a list of approximately 100 problems in Algebra is maintained by the graduate education committee and may be revised from time to time as the committee deems necessary. The Chair of the Department Graduate Education Committee shall ensure students have access to these lists. Problems on the comprehensive examinations will be substantively similar to problems on these lists.

The comprehensive examination committee comprises the supervisory committee and a chair. The Chair of the Department Graduate Education Committee shall be the chair of all Comprehensive Examination Committees unless they are a member of the supervisory committee in which case they shall designate an alternate chair.

For each written exam, with the advice of the Chair of the Department Graduate Education Committee, the comprehensive examination committee shall nominate an examiner or examiners. Where multiple students are expected to write the same component of the comprehensive around the same time, and where possible, the same examiner(s) should be chosen for all students. The examiner may be a member of the supervisory committee, but may not be a supervisor. In consultation with the comprehensive examination committee(s) the examiner(s) shall set an exam consisting of questions substantially similar to those on the corresponding problem list. The examiner(s) will grade the exam and submit their grade recommendation to the comprehensive examination committee for approval. If a student obtains over 60% on a component they shall pass that component, if a student obtains less than 50% on a component they shall fail that component. For any other outcome the comprehensive examination committee will review the student's exam and make a decision as to whether the student has passed or failed. Each component a student fails must be rewritten within 4 months. A maximum of two attempts on each component of the written comprehensive examination is allowed. For clarity, a different examiner may be selected for each attempt of each component.

A student would normally complete the written portion of the comprehensive exam within 12 months of entering the Ph.D. program. This portion of the exam must be satisfactorily completed within 17 months of entering the program.

The oral component of the comprehensive examination will be on the student's research topic for their thesis. It will consist of a 30-minute presentation by the student, followed by questions from the committee. The maximum length of the oral exam is two hours, not including the presentation. The student's comprehensive exam committee will decide upon the material to be covered in the presentation and the questions. This material could include, for example, chapters from a textbook or articles relevant to the proposed research project. The committee shall provide the student a list of this material. The oral component of the comprehensive exam would normally be completed within 16 months of entering the program and must be completed within 24 months of entering the program. The oral component of the exam would not usually be planned until after the student has completed their thesis proposal, including the thesis proposal defence, which should be completed within 12 months of entering the program. The student has two attempts to pass the oral exam.

The deadline for the written and oral comprehensive exams may be waived by the Department Graduate Education Committee in exceptional circumstances.

The thesis proposal will usually inform the choice of topics for the oral component of the comprehensive examination and so would usually be completed before the oral component of the comprehensive examination is scheduled. The deadlines and policies for the thesis proposal are specified by the School of Graduate Studies.

Please review the Comprehensive Examination Policy in the Graduate Studies Calendar and Graduate Studies Policies and Procedures document for additional details.

Approved by Graduate Council on April 11, 2024.