Doctor of Philosophy (PhD) in Pure Mathematics

The program information below was valid for the winter 2023 term (January 1, 2023 - April 30, 2023). This is the archived version; the most up-to-date program information is available through the current Graduate Studies Academic Calendar.

The Graduate Studies Academic Calendar is updated 3 times per year, at the start of each academic term (January 1, May 1, September 1). Graduate Studies Academic Calendars from previous terms can be found in the archives.

• Admit term(s) 
  • Fall
  • Winter
  • Spring
• Delivery mode 
  • On-campus
• Program type 
  • Doctoral
  • Research
• Registration option(s) 
  • Full-time
• Study option(s) 
  • Thesis

• Minimum requirements 
  • A Master's degree (or equivalent) in Mathematics with at least a 78% standing. Exceptions may be made for students with an Honours Bachelor degree who demonstrate a very high level of background preparation and research potential.
• Application materials 
  • Supplementary information form
  • Transcript(s)
• References 
  • Number of references:  3
  • Type of references: 

    at least 2 academic

• English language proficiency (ELP) (if applicable)

Thesis option:

Graduate Academic Integrity Module (Graduate AIM)

Courses 

• The program requires a minimum of 4 graduate courses with an average of at least 70% (with unit weights equal to 0.50) for those entering the PhD program with a Master's degree. At least 3 of the 4 required courses must be PMATH graduate courses numbered in the 800's and 900's. If the 4th course is not a PMATH course it must be approved by the Pure Mathematics Graduate Committee. None of the 4 required courses can be graduate courses numbered in the 600s or reading courses. Up to 3 course credits may be granted by the Graduate Committee for work completed towards the PhD degree at another institution provided that the relevance of the previous work to the student's proposed program is clearly established.
• Students entering the program with a Bachelor's degree normally must also satisfy the course requirements of a Master of Mathematics (MMath) degree in addition to those of the PhD program. The number and nature of such courses shall be specified at the time of admission, or early on in the program.

Link(s) to courses

• Pure Mathematics (PMATH) courses

PhD Lecturing Requirement

• Regular participation in at least 1 departmental seminar is expected and the student must present at least 2 talks in a department seminar.

PhD Qualifying Examination

• Students are required to meet the University-level PhD Qualifying Examination minimum requirements outlined in the “Minimum requirements for the PhD degree” section of the Graduate Studies Academic Calendar (GSAC).
• In addition to the University-level PhD Qualifying Examination minimum requirements, students in the PhD in Pure Mathematics program are also required to meet the following requirements:
• Satisfactory performance in 2 written Qualifying Examinations:
  • 1 in algebra
  • 1 in analysis and topology
• The syllabus is based on the material covered in the University of Waterloo's undergraduate courses, and is posted on the Department webpage. These written exams are offered annually.
• Students must attempt both exams within one year of their registration in the PhD program.

PhD Thesis

• Students must complete a thesis embodying the results of original research. This is the most important requirement! The thesis must be of a standard that warrants publication in the research literature of the field. The thesis must be acceptable to a committee approved by the Graduate Committee consisting of the student's supervisor and four other professors; one of whom must be from another department, and one must be an independent external examiner familiar with the student's research field. The student is required to defend the thesis at an oral examination.