PhD Degree Requirements

There are three principal stages for every student in the doctoral degree program, including:

Pre-PhD Program

This is the stage for students intending to enter the program who have yet not completed the qualifying procedure.

PhD Program

This is the stage for students who qualified for the PhD, and are completing the language requirement and preparing for the oral preliminary examination.


Students are advanced to candidacy after satisfying the language requirement and passing the preliminary exam. At this stage, students are working primarily on research and their dissertations.

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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 are offered in:

  • Algebra (500-level)
  • Analysis (500-level)
  • Topology/Geometry (500-level)
  • Real Analysis (600-level)
  • Algebraic topology (600-level)
  • Algebra (600-level)
  • Applied math (600-level, every other year)
  • Differential geometry (600-level, every other year)
  • Probability (600-level, every other year)

You must take sequences in three areas and pass two qualifying examinations. To be eligible to take a 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.

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PhD Program

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. You should choose a PhD advisor by the end of the academic year in which you pass the qualifying exams. Browse our list of faculty research interests to find an advisor who aligns with your course of study.

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.

Read and refer to the math department Graduate Handbook, as well as the Graduate School’s policies. Please note that in literature from the Graduate School, “thesis” is associated with the master’s degree and “dissertation” with the doctoral degree. Follow the instructions for the dissertation.

Be sure to communicate regularly with your adviser for advice and support.

The process for uploading the dissertation is time consuming. Make sure to visit the Graduate School’s page on Electronic Thesis or Dissertation (ETD) Submission. This page is essential and you should review it well in advance of submitting your dissertation. It includes a link to the step-by-step ETD Submission using ProQuest, which can be printed and reviewed in advance.

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