The Department of Pure Mathematics is one of five separate and unique departments in the Faculty of Mathematics. The department offers graduate programs leading to the degrees Master's of Mathematics (MMath) and Doctor of Philosophy (PhD).
In the MMath program, we offer two options, either
It is expected that a Master's of Mathematics program will normally be completed within 34 terms. Continued funding is conditional on being in good academic standing and satisfactory performance of teaching assistant duties.
Why Study for a MMath Degree?
Traditionally, students completed a Master's degree in Pure Mathematics and then continued their studies at the PhD level, with the aim of becoming a mathematics professor. While this is still the goal for many graduate students today, others have different intentions. Some obtain a Master's degree in Pure Mathematics because they find the theoretical background useful for their subsequent pursuit of a PhD in a more applied discipline; some to have more background for teaching mathematics at the high school level. Others have found that the strong analytic skills acquired in their graduate degree, and their enjoyment of mathematics, have led them to a career in business or industry, working alongside engineers and other scientists. In recent years, the most common career choices for Pure Mathematics graduates have been in the computer industry, teaching, and business, especially insurance and banking.
By choosing one or two courses from other departments, as part of one's Master's degree in Pure Mathematics, students can learn about a variety of careers which require a strong mathematical background. For example: a student interested in number theory might take a course in cryptography from the Combinatorics and Optimization department; a student interested in Fourier analysis might study signal processing from Electrical Engineering and consider pursuing a career in the communications industry; a student with a strong background in analysis might find a course in finance of interest. These are only a few examples of directions for graduate students who find mathematics exciting and are looking for an intellectually rewarding career. Since each Master's program is individually tailored to the student's interest, background and longterm goals, there are numerous possibilities.
MMath Program Admission Requirements
The minimum requirements for admission to the MMath program normally include:

an Honours Bachelor's degree (or equivalent) in Mathematics with at least a B+ standing (78%);

three letters of reference, we recommend these from academic sources;

proof of competency in English (if applicable). A Test of English as a Foreign Language (TOEFL) (or equivalent) score of at least 580 (paperbased) and 4.0 on the TWE, 237 (computerbased) and 4.0 on the TWE, or 9293 (Internetbased) with a minimum score of at least 24 in the Speaking and Writing sections. (See English Language Proficiency in the Graduate Studies Calendar for other acceptable tests.)
The deadline for applications to the Master's of Mathematics program is February 1st for international students; the deadline is more flexible for Canadian students, however, we begin making offers in February. Please refer to the application section of this website for more information.
Good academic standing:
To be in good academic standing, a student would normally be expected to successfully complete a minimum of three graduatelevel courses, each Fall and Winter, until their course requirements are satisfied and maintain an average of at least 70%. Good academic standing is required for continued funding.
MMath Degree Requirements
Master's of Mathematics (MMath) with Research Paper Option
Course Requirement:
This program requires a minimum of six term graduate course credits (with unit weights equal to .50) with an average of at least 70%. At least four courses must be PMATH courses. At least two of the courses must be PMATH graduate courses numbered in the 800's and 900's. At most two courses can be graduate courses that are jointly held with undergraduate courses. In order for a reading course to count as one of the six required courses, approval must be obtained from the departmental Graduate Committee. A reading course consisting of work done by a student in the immediate preparation for writing the research paper would not normally be counted as one of the 6 required courses. The selection of courses normally requires the approval of the student's graduate advisor.
MMath Research Paper Requirement:
Credit is given when the research paper is completed to the satisfaction of the supervisor and one other reader, normally a faculty member at Waterloo, including adjunct or emeritus, or postdoctoral fellows. Exceptions require approval by the Graduate Officer. The research paper will normally be completed in the Spring term (MayAugust) for students who entered the program in the previous Fall term. A typical research paper is roughly 2530 typed pages. One cerlox bound copy is to be kept in the Pure Math Department.
Students normally take three courses in each of the Fall and Winter terms and complete their research paper in the summer.
Master's of Mathematics (MMath) With Thesis Option
Students desiring to pursue the MMath with thesis option must have the approval of the Graduate Committee. Approval will be given to students who demonstrate their readiness to do specialized graduate work and would normally be granted in the first or second term of graduate studies.
Course Requirement:
Four term graduate course credits with an average of at least 70% (with unit weights equal to .50 each). Students normally take three courses in the Fall term and one in the Winter term. At least two of the courses must be PMATH graduate courses numbered in the 800's and 900's. The other two courses can include at most one graduate course that is jointly held with undergraduate courses and at most one graduate course from outside the Pure Mathematics Department. The selection of courses normally requires the approval of the student’s graduate advisor. In order for a reading course to count as one of the four required courses, approval must be obtained from the departmental Graduate Committee. A reading course consisting of work done by a student in the immediate preparation for writing a thesis would not normally be counted as one of the 4 required courses.
Seminar  Milestone:
Regular participation in a departmental seminar is required.
MMath Thesis Requirement:
The thesis must be acceptable to a committee consisting of the student's supervisor and two other readers. Normally, the two other readers will be faculty members at Waterloo, including adjunct or emeritus professors. At least one of the two other readers must be a member of the Pure Math Department. The committee requires approval by the Graduate Officer. The nature and length of a Master's thesis can vary greatly. However, a typical thesis is roughly 50100 typed pages. The thesis should be a synthesis of some research papers or monographs, and may also contain some original work. The student will give a talk on his or her thesis research.