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Candidacy exams

Doctoral students in the Department of Mathematics and Statistics are required to pass a candidacy examination within their first two years (24 months) of study. This examination consists of taking written examinations in three different areas from the following list of subjects:

  • Algebra
  • Applied statistics
  • Combinatorics
  • Foundations of optimization
  • Graph theory
  • Numerical analysis
  • Ordinary differential equations and dynamical systems
  • Partial differential equations
  • Probability and stochastic processes
  • Real analysis
  • Statistical inference
  • Topology

The subjects to be taken for examination should be agreed between you and your supervisors. More information can be found in the department's  policy on candidacy examinations.  To request an examination please fill out the candidacy exam request form.

Dissertation preparatory examinations

If your supervisor agrees, you may substitute a "dissertation preparatory examination" for one of the three standard written qualifying examinations. This examination is based upon a written paper and presentation.

A date for the presentation should be selected and agreed upon by you and your supervisory committees. The written paper should be submitted to the committee at least 10 working days before the date of the presentation. At the presentation you will make a brief presentation (about half an hour) of the written paper and then answer questions from the committees. The written paper should demonstrate the your mastery of a body of mathematics chosen by agreement between you and your supervisors. It will generally consist of a study of material needed in preparation for your dissertation work. Some possibilities for the content of the paper are:

  • A new presentation or derivation of a body of work already existing in the literature.
  • A careful literature survey setting out prior knowledge in an area and presenting it in a unified and thoughtful way.
  • A presentation of a new result (this typically would be an initial step in your dissertation research).
  • A research plan for a dissertation, setting out methodology and background work, putting it in context with related work, etc.

This list is not meant to be exhaustive, but to suggest the scope of the comprehensive examination. In order to pass the examination, you'll need to demonstrate to your committee, through the written paper, the presentation and the answers to the committee's questions, that you are prepared to start work on your dissertation.

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