FAQ

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.

Pure Mathematics undergraduate requirements

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 Essay) options?

Answer: The default "option" in our Master of Mathematics program is the Research Essay option. All students who are admitted into the MMath program are admitted into the research essay option. This requires 6 courses and a Research Essay, 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 Essay. Note: Both the MMath (Research Essay) and the MMath (Thesis) programs are one year (3 terms) programs.


Question: Can I apply directly to the PhD program with only an undergraduate degree?

Answer: In general, we usually do not admit students directly from a Bachelor's program into our PhD program, unless they are extremely well qualified. Direct admission into the PhD program does sometimes happen, but it is quite rare. Officially, the university requires "advanced research ability" for admission to a PhD program, so if you don’t have a Master’s degree then you absolutely need to have evidence of significant research experience as an undergraduate. Exceptionally strong background preparation would also be required for direct placement in the PhD program.

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 do 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, because of an extremely high level of preparation, you can send an email to the Associate Chair of Graduate Studies with a list of the courses that you will have completed when you graduate and any information about undergraduate student research experiences you might have had. The Associate Chair will then give you an opinion about whether or not direct application is possible.


Question: If I complete the Master of Mathematics (MMath) program, is admission to the PhD program guaranteed?

Answer: Admission is not guaranteed, but if you do sufficiently well in your courses, and have a willing thesis supervisor, then you can expect to be admitted. It is the same application process for everyone, but our own MMath students have an advantage that we know them better and are more able to make an informed judgement on their ability to succeed in our PhD program. Not all our MMath students choose to pursue a PhD program, and even those who do, don’t always apply to Waterloo. In addition, every year there are one or two of our own MMath students who apply to our PhD program and are turned down. But invariably, those are students who did not work hard enough in the MMath program and didn’t take it seriously enough. It’s up to you to demonstrate your ability and performance to us.


Question: Why do I have to choose a potential supervisor on my PhD application?

Answer: For PhD applicants, we cannot offer admission unless there is at least one willing supervisor in our department. If your application is strong, we show your file to some potential supervisors to see if they are willing to supervise you. Therefore, you should always 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. Most incoming PhD students are fairly certain about who they want to work with from the start.


Question: Do I need to submit GRE scores to apply to graduate studies in Pure Math at Waterloo?

Answer: It's up to you. We don't require them. If you have done very well on them, it certainly would help for us to see the scores. But the most important component of your application, by far, is the letters of recommendation.


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: It depends. The minimum average is a university policy. If your application is extremely strong in all other aspects [in particular, the letters of recommendation], 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. Such an exception hasn't happened in recent years. In fact, 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: 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. I don’t know why. 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:

Tuition fee schedules

We try to increase the level of financial support as much as we can every year. Tuition fees are much higher for international students. Because of this, we do offer more financial support to international students than to Canadians, but the difference is not enough to offset the difference in tuition fees. However, all of the foreign graduate students that I talked to in our department tell me that they manage to get by with their level of support. The "minimum living costs" indicated on the university's website here:

Minimum living costs

are actually greatly inflated. I don’t know why they would publish such numbers, when the official university policy says that the minimum support we are required to provide graduate students is $21,225 for PhD and $0 (!) for Masters. We are definitely well over both of those minima.


Question: Should I contact faculty members who might be potential thesis supervisors?

Answer: For an MMath (Master of Mathematics) application, this is not necessary but it certainly doesn't hurt. However, for PhD applications, this is strongly encouraged! We do not even consider applications for the PhD program unless there is at least one willing thesis supervisor. The best way to find this out is to contact faculty members by email. When you list names of possible supervisors on your application, these faculty members will be shown your application and give their opinion to the graduate 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:

Areas of research


Question: How much TA work (Teaching Assistant) will I be required to do as a graduate student?

Answer: All graduate students, whether Master’s or PhD, unless they hold major scholarships, will usually do 2 TA units per term. There are three terms in the year [Sep-Dec, Jan-Apr, and May-Aug]. Each "TA unit" is supposed to be about 5 hours per week for the duration of a 16 week term. The first 12 weeks of the term are lecture period, and the last 4 weeks are exam period. Some more senior PhD students get a break of 1 TA unit in the Spring term, so they will do 5 TA’s in the year instead of 6. 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 with major external scholarships usually do 2 TA’s per year, one in the Fall term and one in the Winter term. 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: 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:

English language proficiency requirements

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 department of Pure Mathematics has set higher internal requirements for admission. The departmental requirements can be found here:

Application procedures

In particular, we require a total overall score of at least 92 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:

English Language Institute (Renison University College)

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:

GSA health and dental insurance


Question: Are scholarships available for graduate study in pure mathematics?

Answer: There are some scholarships. Most, but not all, are restricted to Canadians, just like most scholarships in the USA are restricted to American citizens. Moreover for the majority of the internal university scholarships, their use is to replace TA funds. So scholarship recipients don't necessarily end up with more money, but they do have less TA time commitments and thus more time for research. We are working on creating more merit-based scholarships for international students.

Canadian applicants should apply for NSERC graduate scholarships. Information on these can be found here:

NSERC website


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.