Admission Requirements
To be considered for admission into the Doctor of Philosophy (PhD) program in Pure Mathematics, applicants normally require a Master's degree in Mathematics with a minimum B+ (78%) average. Exceptions may be made for students with an Honours Bachelor degree who demonstrate a very high level of background preparation and research potential.
Specific Admission Requirements are as follows:
- a Master's degree (or equivalent) with at least a B+ standing (78%);
- three letters of reference, at least two of which must be from academic sources;
- proof of competency in English (if applicable). A score of at least 580 (paper based), 237 (computer based), or 92-92 (Internet based) is required in the Test of English as a Foreign Language (TOEFL) and 4.0 on the TWE. See the English Language Proficiency page for other acceptable tests of English;
- a one-page personal statement.
Degree Requirements
PhD Course Requirement
This program requires a minimum of four term graduate courses with an average of at least 70% (with unit weight equal to .50) for those entering the PhD program with a Master's Degree. Three of the required courses must be PMATH graduate courses numbered in the 800's and 900's. None of the four required courses can be graduate courses that are jointly held with undergraduate courses or reading courses. Up to three 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.
Those entering the PhD program with a Bachelor's degree normally must also satisfy the course requirements of an 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.
PhD Thesis Requirement
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.
PhD Comprehensive Examination 1
Satisfactory performance in two written comprehensive examinations is required:
- one in algebra
- one 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 in the spring of each year. 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.
PhD Comprehensive Examination 2
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 his or her 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 Graduate Committee.
PhD Lecturing Requirement
Regular participation in at least two departmental seminars is expected and the candidate must present at least two talks in a department seminar.