Doctor of Philosophy (PhD) in Pure Mathematics

The program information below was valid for the winter 2017 term (January 1, 2017 - April 30, 2017). 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
  • Part-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.
  • A one-page personal statement.
• 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 that are jointly held with undergraduate courses 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 Comprehensive Examination I and PhD Comprehensive Examination II

• Satisfactory performance in 2 written comprehensive examinations is required:
  • 1 in algebra
  • 1 in analysis and topology
• The syllabus is based on the material covered in the University of Waterloo's third and fourth year undergraduate courses. The Graduate Committee offers these written exams annually. Normally students must attempt both exams within one year of their registration in the PhD program, and both exams must be successfully completed within two years.
• Satisfactory performance in the oral comprehensive examination is required. The oral comprehensive examination demonstrates an in-depth knowledge in an area chosen by the candidate and their supervisor, usually the general area in which the thesis will be written. It should be completed within two years of registration in the PhD program. At most two attempts are permitted. There must be at least two examiners, including the supervisor and another expert in the area of the exam. The Examining Committee and the area to be examined must be approved by the Associate Chair, Graduate Studies.

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.