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Degree Program Overview

The following information is provided as an outline of the doctoral degree program. For more details, including instructions on the various steps in the program, please refer to the Handbook.

Pre-PhD Program

Prior to the start of your first term, you will meet with an advisor to determine which courses are appropriate for you.

Course sequences at the 500 level are offered in:

  • Algebra
  • Analysis
  • Topology/Geometry.

Course sequences at the 600 level are offered in:

  • Real Analysis
  • Algebraic topology
  • Algebra
  • Applied math (every other year)
  • Differential geometry (every other year)
  • Probability (every other year).

You must take sequences in three areas and pass two qualifying examinations. To be eligible to a take qualifying exam in a particular subject, you must complete the relevant 600-level course sequence. Depending upon when you take and complete your 600-level sequences, you may take the exams at the same time or in different years. The qualifying examination subject areas are:

  • Algebra
  • Analysis or probability
  • Applied math
  • Geometry or topology.

After you complete sequences in three areas and pass two qualifying examinations, you will formally progress into the PhD Program.

PhD Program

Finding a PhD Advisor

After entering the PhD Program, you will take more advanced seminar courses and reading courses as you begin the process of finding a PhD advisor. A list of faculty research interests can be found here. You should choose a PhD advisor by the end of the academic year in which you pass the qualifying exams.

Advancement to Candidacy

To advance to doctoral candidacy and begin serious work on your dissertation, you must complete your language requirement and pass your comprehensive oral examination. To meet the language requirement you must demonstrate the ability to read mathematical material in either French, German or Russian. The oral exam will be based on a syllabus that you have written in consultation with your advisor, covering the basic material in your general area of interest. You must take this exam within two years of passing the qualifying exam.


Once you pass the oral exam, you will dedicate your time to completing your dissertation. You will earn your PhD when you successfully defend your dissertation to your PhD committee.