Frequently Asked Questions About Graduate Studies in Pure Mathematics at Waterloo
Question: The University of Waterloo has three separate math departments! [These are Pure Mathematics, Applied Mathematics, and Combinatorics & Optimization.] I have interests that overlap with two or more of these departments. What are my options?
Answer: At the Master’s level, all three departments allow you to take some of your required courses from outside the "host" department. For example, if you were in the Pure Math Master's program, we require 6 courses. Up to 2 of those could come from outside the Pure Math department, as long as they have sufficient mathematical content. Almost any course in Applied Math or C&O would qualify, as would many courses in Statistics, Computer Science, or Physics. We very often have students who take advantage of this option.
It is also possible to have co-supervisors, one from each of two math departments. This happens less frequently but it is allowed. You should look at the rules for each department's Master's programs, and the available courses, and apply to that department from which you anticipate wanting to take the most courses. You can consider co-supervision later, if it indeed seems desirable.
At the PhD level, more specialization is expected and required, so there is less flexibility. When applying to a PhD program, the choice of supervisor (and that person's current research focus) should be the single most important factor in making your decision.
Question: Do I have the necessary background preparation / requirements to apply to the graduate program in Pure Mathematics at Waterloo?
Answer: Whether or not you have the minimum requirements to apply for our graduate program depends on which Pure Mathematics courses you took at the undergraduate and master's levels. In general, we expect to see significant preparation in real analysis, complex analysis, group theory, ring theory, geometry, topology, and noncommutative algebra. In particular, it is not enough to just have taken calculus, linear algebra, and differential equations.
These are the requirements for an undergraduate degree in Pure Math at Waterloo. If you have taken courses very similar to at least two thirds of the 3xx and 4xx courses listed here, then you can apply. If not, your chances are almost nil to get in, unfortunately. If you did already obtain the necessary background as an undergraduate, with a very good average, and if your research interests match up with someone in our department, then you can apply. Admission is very competitive and is not guaranteed by any means.
Question: What is the difference between the MMath (Thesis) and MMath (Research Paper) options?
Answer: The default "option" in our Master of Mathematics program is the Research Paper option. All students who are admitted into the MMath program are admitted into the research paper option. This requires 6 courses and a Research Paper, typically 20 to 35 pages in length. After the first term, for some students we may propose that they transfer to the Thesis option, which requires 4 courses and a thesis, typically 50 to 100 pages in length. Usually, the students who are transferred into the Thesis option are those whose background preparation while they were undergraduates is already very strong, so much so that there are not many courses available that they could still take for credit, and they don’t need as much coursework preparation as others. This allows them much more time to complete a Master’s thesis, which is often significantly longer and mathematically deeper than a Research Paper. Note: Both the MMath (Research Paper) and the MMath (Thesis) programs are one year (3 terms) programs.
Question: What is the difference between the regular MMath and PhD programs and the MMath Quantum Information and PhD Quantum Information programs?
Answer: The Quantum Information (QI) versions of our programs are the same as our corresponding regular Pure Math graduate programs, but with some of the options specified, and with the requirement that the thesis/research project be on the topic of quantum information (and so, supervised by one of our faculty members working in Quantum Information). Students in the QI version will have an affiliation with the Institute for Quantum Computing (IQC), and will be eligible for IQC scholarships/awards. If you are interested in working on a subject that would qualify, you should apply for the QI version of the program. If you would also like to be considered for the regular version of the program, you can indicate that on your Supplemental Information Form in Question 4 or 5. There is no need to apply to both programs.
The standard funding packages for the QI versions of our programs are the same as for the regular version; the difference is that students in the QI version may be eligible for certain IQC scholarships/awards.
Question: Can I apply directly to the PhD program with only an undergraduate degree?
Answer: In general, we do not admit students directly from a Bachelor's program into our PhD program. Direct admission into the PhD program does sometimes happen, but normally only for those coming from a program where an equivalent of an MMath was completed as part of the undergraduate degree.
In case you are from the USA, you may be unaware that the Canadian system is different from the US system. Typically, the normal path in Canadian graduate studies is to first earn a Master's degree (which is only a 1 year program!) and then to continue on to the PhD degree which (usually) only takes 4 years instead of 5, so the total duration is essentially the same as the US system. The first year of most US PhD programs consists of course work at the level of our Master's courses. Moreover, all of our graduate students (including all Master’s students!) receive full financial support from our department. This differs again from the US system, where often Master’s students do not receive any funding.
If you believe that you would qualify for direct entrance to the PhD program from an undergraduate program, you should apply to the PhD program. You will automatically be considered for the MMath if your undergraduate experience is judged to have been below the Masters equivalent level.
Question: I already have a Master's degree, but I’m not sure it gives the required background to enter the Pure Math PhD program. Can I apply to the Pure Math MMath?
Answer: You can apply to MMath, but we prioritize students who do not already have a Master's degree. That said, if you apply to our PhD program, but would be willing to do an MMath first, please indicate this at the top of Question 4 of the Supplemental Information Form (SIF) part of your application. If we feel your existing Master's degree is not suitable preparation for our PhD, we may consider you for admission to our MMath program.
Question: Do I have to choose a potential supervisor on my application?
Answer: For PhD applicants, we cannot offer admission unless there is at least one willing supervisor in our department. We will show your file to some potential supervisors to see if they are willing to supervise you. Therefore, you should pick at least one potential supervisor, and up to three if you prefer. If you are offered admission and accept our offer, you are not obligated to work with the faculty member or members that you had listed on your application, as long as you can find another willing supervisor in the department.
For all applicants (both MMath and PhD), when you list names of possible supervisors on your application, these faculty members will be shown your application and be invited to give their opinion to the admissions committee. Note that your research interests should be somewhat represented by the faculty members in our department to be considered. Our areas of research are described here:
Question: Whom should I ask to write letters of recommendation for me?
Answer: In general, you want to choose letter writers who can say more than "this student took my class and got a good grade". Are there any professors with whom you did undergraduate research? They would be excellent choices. You need 3 letters, so if 2 of them are very informative, and the 3rd is generic, you're still okay, but it's far better to have 3 very informative letters. Therefore it is in your best interests to identify all three of your letter writers and start talking to them immediately and frequently. If they know more about you, they can have more to say, which makes it easier for us to make an informed decision on your application.
Question: My average is a bit below the minimum requirement of 78%. Can I still apply?
Answer: The minimum average is a university policy, but there is a bit of leeway. If your application is extremely strong in all other aspects, then we may be able to petition the university for an exemption to the 78% minimum in your case. But you would have to have a very strong application otherwise for this to be possible. Normally, your chances of admission are not high if your average is below 80%.
Question: What is an "unofficial transcript"?
Answer: For some reason this seems to confuse some applicants. An unofficial transcript is issued to you, the applicant, directly by your university’s registrar’s office. In particular, it has the university logo on it. You can scan it in and upload it, or it may be sent to you in PDF format already. What makes it "unofficial" is that your university is not sending it directly to us, it’s getting to us via the applicant as an intermediary. In particular, please do not send us a "home-made" table listing your courses and grades. That is unacceptable.
Question: Do I need to submit GRE scores to apply to graduate studies in Pure Math at Waterloo?
Answer: No, we do not require them. However, if you have taken them and done well, you may submit them, and it may help your application.
Question: Are scholarships available for graduate study in pure mathematics?
Answer: We offer full financial support to all admitted graduate students, and part of the package is made up of scholarships. While many internal awards are considered part of what makes up the standard offer, some students will qualify for various additional internal scholarships, which may reduce their TA load and/or increase their funding level as compared to our standard offer.
Canadians and Permanent Residents please note: Winners of NSERC or OGS awards will have their TA load greatly reduced, as well as receive more funds for the year! Please check the GSPA webpage on External Awards to find out more about how to apply. We strongly encourage all eligible applicants to apply for these prestigious awards!
Question: Does a graduate student at Waterloo have to pay tuition? Why isn’t it just waived?
Answer: Yes, graduate students have to pay tuition. Many universities do indeed waive tuition fees for graduate students. Waterloo is not one of them; our department has no control over that. We do offer full financial support to all admitted graduate students, both at the Master’s and the Doctoral levels. Your tuition fees will be automatically deducted from this amount. Current tuition fees can be found here:
We try to increase the level of financial support as much as we can every year. Tuition fees are much higher for international students, and because of this, we do offer more financial support to international students than to Canadians, to offset the difference in tuition fees on our basic offers. That said, there are often additional scholarships/awards that are only open to Canadian citizens or Permanent Residents. The university has provided an estimate of grad student living costs website here:
More information regarding financial support can be found on our financial information page here:
Question: How much TA work (Teaching Assistant) will I be required to do as a graduate student?
Answer: MMath students without an external award should expect to have 2 TA units each term. PhD students without an external award should expect to have 5 TA units each year (no more than 2 per term). One TA unit is 80 hours per term (~ 5 hours per week, but not evenly distributed because of midterm/exam grading). There are three terms in the year [Sep-Dec, Jan-Apr, and May-Aug]. The first 12 weeks of the term are lecture period, and the last 4 weeks are exam period. Therefore most graduate students in our department are expected to work about 10 hours per week as a TA, for most of the time. The amount you are paid as a TA is included in the total financial support offered.
Graduate students holding NSERC or OGS have their TA load adjusted to just 2 TAs for the year! Sometimes additional TA jobs (for additional money) are available to these students if they want them.
Your actual TA duties depend on the particular assignment. You can be assigned a variety of different types of TA units. Here are some possibilities:
[a] If you are a TA for a 100-level or 200-level "MATH" course (usually some flavour of calculus or linear algebra) then you would probably be expected to help "mark" (the Canadian way of saying "grade") mid-terms and exams, proctor the mid-terms and exams for this course and possibly other related courses, distribute the weekly assignments to the undergraduate assignment markers (graders), collect the assignments from the markers, and record the marks. You wouldn't mark assignments. We have undergraduates doing that. These types of TA positions may occasionally also involve giving a weekly tutorial, where you would solve homework problems in front of the students. Such courses can have 100 to 200 students.
[b] If you are a TA for a 300-level or 400-level "PURE MATH" course, then that usually involves marking the assignments, and sometimes writing solutions or holding occasional office hours. These courses can have anywhere from 20 to 60 students.
[c] You can be assigned as a TA in the "Tutorial Centre" which is basically a drop-in centre where you're expected to help the students for a certain number of hours per week in various 1st and 2nd year MATH courses.
Question: I am an international applicant. Do I need to write the TOEFL?
Answer: There are a variety of examinations that University of Waterloo Graduate Studies accepts as proof of English language proficiency. There are also exemptions from submitting English language proficiency examination scores in many situations, such as if you have completed three or more years of post-secondary education or completed a graduate degree at a Canadian university. Please see the GSPA page on English language proficiency for the complete list of exemptions, and for the table of accepted examinations and required scores.
Question: My TOEFL (or other acceptable English language test requirement) is too low. Can I still apply?
Answer: The University of Waterloo has certain absolute minimum requirements in English proficiency for considering an application for graduate studies from international students. These minimum requirements can be found here:
In particular, for the internet-based TOEFL test, the minimum requirement is a total score of 90 and at least 25 in each of writing and speaking. The departmental requirements can be found here:
In particular, we require a total overall score of at least 90 on the TOEFL exam, including the same 25/25 minimums on writing/speaking.
If an applicant is just short one or two points in these two categories (that is, has a scores of 24/25, 25/24, 24/24, 23/25, or 25/23) and has an overall total of more than 94, then exceptions can sometimes be made if the overall quality of the applicant's file is very strong. Because such an exemption requires the department to make a formal request from the University, such requests are only made for very strong applicants. Applicants who score lower than this on their TOEFL exams cannot be considered.
Question: Are there any local (in Waterloo) options to increase my English language proficiency?
Answer: Renison University (which is affiliated with the University of Waterloo) does offer intensive English language proficiency courses specifically designed to help you meet the minimum English language requirements for admission to the University of Waterloo’s degree programs. Information about these courses can be found here:
Please note that this is only a realistic option for you if you are already in the Waterloo area or can legally come to the Waterloo area. The Department of Pure Mathematics cannot give any authorization that would qualify you for a student permit to take such English language courses, as we cannot guarantee admission to the Pure Math graduate programs until after we see the results. Moreover, no financial support for these English language courses is available from the Pure Math department at Waterloo.
Question: As a graduate student, would I be covered by medical/dental insurance?
Answer: Yes, all graduate students at the University of Waterloo are covered by medical and dental insurance through the Graduate Student Association. The precise details can be found here:
Question: What do graduate students do in the summer?
Answer: The academic year at Waterloo for graduate studies is twelve months. We have three terms: Fall (September to December), Winter (January to April) and "Spring" (May to August). Graduate students are expected to be present in the department and engaged in their research even during periods when courses are not being offered. Of course, reasonable vacation time is allowed, by agreement with your supervisor and the Associate Chair of Graduate Studies.
Question: I missed the Dec 1/Jan 1 application deadline for Fall, can I still apply?
Answer: It will be too late to catch the first round of offers, however, if you submit an application for Winter term before April 1, then you would be considered for any remaining spots depending on the acceptance rate of our first round Fall offers. If you prefer to start in the Fall, you can make a note of this on your application, and if you receive an offer from us, we can switch it to a Fall start. Note that the second round offers will not be going out until early May.