Applying to Graduate School

Contributed by Marco Carone - Honours Representative, SUMS Council (2004-2005)


Having been through the excruciatingly stressful process of choosing graduate schools and completing the steps required to get into these schools, it would be unfair to simply sit back and let fellow students endure much pain without providing a helping hand. The truth is that, in our own time, most of us got help from friends and schoolmates having already completed the admissions process, and so, it is only natural to offer some guidance and advice to prospective graduate students.

It is not an overestimation to say that going to graduate school is one of the most crucial stages in your life. Indeed, it involves, in most cases, moving off to a different province or country for a significant period of time, and the choice and location of school will very often have direct impact on your future domicile and possible career path. The purpose of making a statement underlining the importance of graduate school selection is certainly not to add on to the anxiety you already have regarding the issue, but rather, to stress the fact that it is a process which requires utmost patience and diligence. As any other undertaking, with proper preparation and a good strategy, the process may be completed efficiently and without undue strain. The intent behind the creation of this section was simply to give you some hints towards building a good strategy for graduate applications, and to answer some questions most students have regarding the whole process. Please keep in mind, though, that graduate school is not for everyone: many students carry on to graduate studies as the only logical continuation of their undergraduate education, but in reality do not have the necessary skills and motivation to complete these studies.

Preparing your graduate applications involves many equally important steps. These steps include choosing a specific field of study and program, selecting schools of interest, taking, if needed, the Graduate Record Examination (GRE), identifying different sources of funding, obtaining various letters of recommendation, gathering up-to-date academic transcripts, choosing a means of application submission, completing application forms, and the list goes on. The advice provided in this tutorial will be presented in the form of several pointers, from which we expand as thoroughly as possible. Please note that there may be an inherent inclination of the information below towards applications to American graduate schools, although this fact should not make this tutorial any less useful.


Preparing early.
Facing the GRE.
Choosing a degree
Choosing suitable schools.
Finding sources of funding.
Obtaining letters of recommendation.
Completing and submitting the applications.
Awaiting replies and making the final decision.
Links that should prove useful during the course of your application:

1) Preparing early.

The first component of a good strategy would undoubtedly be to begin preparing the applications early. Most schools grant admission to their graduate programs for the Fall term exclusively, and application deadlines are usually between the 1st of December and the 1st of February of the academic year preceding your first year of projected graduate studies. It is usually deemed optimal to begin thinking about your applications during the summer prior to your last undergraduate year. The challenge of completing graduate applications does not reside solely in the application process itself, but rather in the fact that it needs to be completed while you probably have a full course load to take care of. Hence, summer preparation enables you to advance the status of your application work while you actually have time to do so. It is important to note that most schools do not make application forms available before September of the year preceding that for which students are applying. Nonetheless, these forms do not vary greatly from one year to the next; hence, it is a good bet to prepare according to the indications found on application forms for the previous year, usually readily available online.

2) Facing the GRE.

The Graduate Record Examination is a standardized test which admission boards sometimes require in order to quantitatively compare students from various schools across the globe. If you are considering applying to schools in the United States, you will absolutely need to complete the General GRE test. It consists of three subparts: the quantitative, the verbal and the analytic writing sections. The quantitative section tests mathematical skills acquired during the course of secondary school education and some very basic topics in probability and statistics. The verbal section tests the depth of your vocabulary, your ability at comprehending various texts, and your skills at making cognitive links. Finally, the analytic writing section tests your ability at cogently articulating your position regarding a given topic and at assessing a given argument in a critical manner. For Mathematics students, the quantitative section should not be of any concern, but beware that, for most graduate programs in Mathematics or Statistics, you are expected to get a near perfect score on that particular section and not all questions are completely trivial, as they often incorporate a slight catch which you need to be able to detect. The analytic writing component should also pose no great threat to mathematically-inclined students, so long as they have had proper academic background in writing and are able to present their arguments in proper English. To most, the main challenge of the General GRE is, by far, the Verbal section. In this part, you will be presented with a slew of words you did not even know existed. Preparation is crucial for this section. To get ready for the GRE, it is quite useful to purchase a preparatory booklet such as those sold by Kaplan or The Princeton Review, for example. Such booklets will guide you through key examples, tips and strategies, series of exercises, and practice tests. They will enable you to get used to the style of question presented on the exam, and will especially help you through the Verbal component by providing you with lists of words you should definitely know before tackling the exam. Your preparation for the GRE should be thorough and this exam should certainly not be taken lightly: depending on your background, you should plan anywhere from three to five weeks of serious studying for the exam. In Montreal, the General test is given at Prometric Testing Center, located at walking distance from McGill University, and should cost around $CDN150. Do not wait until the last minute to take a testing appointment, especially in peak periods such as the months of October and November. The test is administered on computer and is adaptive, that is, the difficulty of the questions given to you vary upon your success at answering previous questions. This type of testing enables the test-givers to zero in on your grade in a very precise manner, but know that it also entails that missing some of the first questions in a given section will greatly penalize you. As such, it would be desirable to allot some extra attention to getting the first questions in a section, particularly in the Quantitative component, where you are most prone to making concentration slips. You are allowed to take the GRE more than once, but there is a minimum time interval (around a month) imposed between each sitting. It is important to note however that all GRE results from the past five years will show on the score report sent to the institutions of your choice. At the end of the examination, you will be asked to select a maximum of four institutions to which your results should be sent. To send score reports to more than four schools, you will have to wait two weeks from the date of your examination and use ETS’ (the maker and administrator of the GRE) automated hotline for additional score orders. To use this system, you will need to have the institutional and departmental codes for the departments to which you are applying. Each additional score report should cost you approximately $US15, plus a phone service charge.

Aside from the General Subject test, ETS also offers Subject GRE tests, such as the Mathematics Subject test. If you are applying to programs in Pure Mathematics and Applied Mathematics, you will most likely be asked to write the Mathematics Subject test. It consists of 66 multiple-choice questions, half of which involve basic to advanced calculus (including differential equations), a quarter of which involve algebra (linear and abstract), and the remainder can comprise any other topics you are expected to have seen during the course of your undergraduate degree (discrete mathematics, real and complex analysis, topology, geometry, numerical analysis, and probability and statistics). This test requires a great deal of preparation as it will assume you have freshly seen the topics involved. You can either study from your own class notes, from texts, or better yet, get a concise preparatory booklet for the Mathematics Subject test from one of the publishers listed previously.

3) Choosing a degree

It is safe to assume that you have, by now, an idea of what branch of mathematics you would like to enter graduate school in. Else, you will need to concentrate on determining which branch has generated much enthusiasm from your part, in which you feel you have certain abilities and in which you are ready to work in for a good period of time. Your professors would be very helpful in assisting your graduate school orientation.

Once you have determined a particular branch, you will need to choose whether to apply to a Master’s or a Ph.D. program. If you are applying to Canadian schools, then you will most likely have no choice: Canadian universities usually require students to complete a Master’s degree before entering a doctoral program. On the other hand, it is pretty standard to apply directly into a Ph.D. program in the United States with at hand only an undergraduate degree. The idea behind this particularity is that if you know you eventually want to get a doctoral degree in your field, then the administrative burden which the transition from the Master’s program to the Ph.D. program could be avoided by placing you directly in the Ph.D. program. Note, however, that you will not save any time by going to the Unites States and bypassing the Master’s program: indeed, the doctoral program you will get admitted to from your undergraduate training will require four or five years to complete, the equivalent of a Master’s and a Ph.D. completed successively. Nonetheless, the Master’s program is often considered a dead end in the US, and so, applying to it might indicate to the admission boards your intent not to pursue further studies subsequent to the Master’s. In short, if your ultimate goal is to obtain a doctoral program, then it is, in the case of most American schools, recommended to apply to the Ph.D. directly. If during the course of your doctoral program, you feel that you are not suited for the doctoral program or you simply do not want to continue with the program, then provided you have completed the requirements of the Master’s program, administrators will enable you to leave the school with a Master’s degree in hand.

4) Choosing suitable schools.

One of the great decisions to be made during the application process is surely that regarding the selection of schools to which you will actually apply. On one hand, you would like to apply to as many schools as possible to increase the probability of being accepted somewhere, whereas, on the other hand, you do not want to impose on yourself an unnecessary load of application work and a Visa bill driving you to bankruptcy. Depending on the strength of your dossier, you should be aiming at applying to anywhere from 6 to 12 different schools. Faculty members involved in your intended field of study will be in the best position to help you make a good roster of graduate schools. In this process, you will need to be very honest to yourself about your chances of admission. Note however that even with a flawless dossier, you are not guaranteed admission to all schools in the world, as competition is fierce and available positions are usually incredibly limited. Similarly, if you feel your dossier has significant flaws, do not get prematurely discouraged: outstanding strengths in other components of your file may possibly counterbalance any other poor component. Further, keep in mind that the best schools in a particular field are not necessarily the schools with high name recognition.

5) Finding sources of funding.

Graduate school can either be a costly experience or quite a profitable one. If you are thinking of moving out to anywhere outside your domiciling city, you will need to cover a huge set of expenses during the course of your program. Luckily, admission to graduate programs in mathematics or statistics is usually granted with a waiver of tuition fees and a substantial annual stipend of anywhere from $US10,000 to $US25,000, depending on your school of choice, the department to which you are applying, available funds and obviously, the strength of your dossier. In rare cases, these stipends are awarded without any obligation from your part, but in most cases, they will come in the form of an assistantship, either for research or teaching. These stipends will usually be plenty to cover room and board, and other living expenses. Apart from the package awarded to you by the school, it is possible to obtain some additional funding. For Canadians, the National Science and Engineering Research Council (NSERC) offers a series of scholarships tenable during the course of your graduate studies. These scholarships, called either the Post-Graduate Scholarships and the Canada Scholarships, are approximately valued at slightly more than $CDN15,000 per annum. The main difference between the two is that location of tenure is not an issue for the PG Scholarships (although you must provide strong argumentation and a faculty member’s support for wanting to attend an out-of-Canada institution), while it is for the Canada Scholarships, which are to be held only in Canada. The PG Scholarships are much more difficult to obtain than the Canada Scholarships, and motivation for out-of-Canada study is actually quite a stringent condition. For Quebec residents, there exists yet another form of scholarship possibility provided by the Fonds de Recherche sur la Nature et les Technologies (FQRNT). These scholarships do not have any restriction on location of tenure and are also valued at about $CDN15,000. Note that when applying to these scholarships, regardless of the fact that you may be applying to a doctoral program, since you have at hand only an undergraduate degree, you will need to indicate that you are pursuing a Master’s degree in your projected studies. Note also that although you may apply for both NSERC and FQRNT scholarships, you can ultimately accept only one out of the two. If you receive one of these scholarships, the schools which accept you might decide that they will deduct the scholarship’s value from the stipend they have offered you, but other schools let you add on the revenue from these scholarships to their original stipend, in which case you will likely end up making a profit out of your graduate studies!

Application for the NSERC and FQRNT scholarships are, to say the least, as tedious as that of most graduate schools. You will be required to write a few essay responses to various questions, and will be expected to describe in reasonable detail the nature of your projected graduate thesis. Obviously, you are not expected to know exactly what you will be doing, and you will certainly not be held liable if you deviate from what you provide in the application forms. Nonetheless, you will need to do a bit of research or consult with some faculty members to outline a viable project you may be interested in working on. Although filling out these scholarship applications will be somewhat of a strain, the reward will be immense: indeed, since the deadlines for these scholarships precede graduate school deadlines by at least a month, you will have gathered much of the information required by graduate school and as a result, the completion of graduate school applications will be to some extent facilitated. Regardless, the amounts offered by these scholarships are substantial and this fact alone motivates the pain involved in completing the applications.

6) Obtaining letters of recommendation.

For the fellowship/scholarship applications, you will normally be required to provide two letters of recommendation, while for graduate school applications you will have to present three such letters. As are your GRE results and your GPA, solid letters of recommendation constitute a necessary ingredient to a positive response from graduate schools. From the words of an admissions representative from the Harvard School of Public Health, “you are required to get not only a good letter of recommendation, but a great letter of recommendation.” Unlike what most students think, it is a better strategy to get as recommender a relatively unknown professor who knows you well and will eagerly write about you rather than soliciting a renowned professor who either does not know you very well, is not very impressed with your work or will not take the time to write something considerable about you. In choosing your recommenders, you should also try, as much as possible, to have representation from all domains relevant to your projected field of study. For example, if you are interested in performing graduate studies in statistics, it is necessary to have at least one recommender from the field of statistics. For the remaining two, it may be a good idea to get faculty members from fields such as analysis or numerical analysis, both subjects bearing great importance in graduate-level statistics. Note that you may have people from outside the academic realm writing for you, but they should be truly relevant to your intended field of study, so be very careful in doing so.

Once you have selected three recommenders, you should ensure that you make the process as effortless for them as possible. It is customary to prepare for each recommender a package containing a recent copy of your undergraduate transcript, a copy of your Curriculum Vitae, pre-addressed and stamped envelopes for each school to which you would like them to write, and a paper giving clear and precise instructions for each school, with a listing of school deadlines and of your own target deadline. It is also a good idea to include a draft of the statement of purpose you will be presenting to the admissions boards: this document will allow your recommenders to better understand your motivation in pursuing graduate studies. Your target deadline should be at least two weeks away from the day you hand these packages to your recommenders, although most recommenders complete their task within a week. Remember that once you receive notification of the admission decision from the various schools to which you have applied, it is a nice gesture to send a little note to your recommenders to give them the news and thank them once more for their time.

7) Completing and submitting the applications.

Once you have selected schools, departments and programs to which you will apply, you need to determine how you will go about submitting the application. These days, the most efficient means of filling out admission applications is to complete the online forms the schools post on the web. Further, the application costs are often lower for online applications, ranging in general from $US45 to $US100. For a given university, simply go to the graduate school’s webpage and follow instructions regarding applications. You will be required to create an online account with the school. Make sure you write down your username and password for future access to your application, as remembering the username/password combination for each school you apply to may prove to be quite a challenge. Information regarding GRE requirements, deadlines and other essentials regarding your application should be available either on the website of the graduate school in question, or on the website of the department to which you are applying. Gathering all the necessary details should prove to be the most difficult part of your application. Nonetheless, the online forms should be simple enough to complete.

You will be required to provide a statement of purpose in the course of your application. Although all schools have different means of describing what the statement of purpose should contain, an efficient way of dealing with the various letters you will have to write is to compose a draft satisfying the subject criteria of all schools at once. Then, for each school, you may slightly tailor this draft by adjusting for length regulations imposed by the school in question, and by adding some school-specific details. It is a good idea to do a little research on the schools to which you are applying, that is, to gather some information on the school’s prominent research areas and its faculty members: indeed, to ensure proper fit of the student within the department, boards of admissions increasingly seek students displaying knowledge about the department to which they are applying. You should be able to find ample information about a department on the web. When tweaking your statement of purpose, note that if you plan on applying to different fields (say, for example, statistics at one school and biostatistics at another), then you should modify your statement of purpose as to reflect the different orientation of these fields. The importance of the statement of purpose is debatable: in fact, some affirm that it has very little weight in the admissions process, while others assert that it is essential to your dossier, especially in the case of an admissions board hesitating between your application and another. Regardless, it is important that a well-written and concise statement of purpose be presented. In writing the statement, remember that admissions officers will be faced with a huge number of applications, so it is important to be right to the point in your statement and to avoid writing a uselessly long text. Further, do not use cliché statements in your text: although this advice seems trivial, it is surprising to see how many people do this.

Once you have written all necessary essays and completed the application forms, you will be close to the end. In fact, you will most likely be able to submit the online part of your application, if that is the method of application you chose earlier on. Then, to complete the whole process, you will have to send a package to each school with your supporting documents. This package almost surely will consist of official copies of your transcripts and sealed letters of recommendation, as most likely requested by the school, although some universities do ask the recommenders to mail their support letter directly, or in other cases, to submit their letter online. Further, it is a good idea to add to your package a copy of your personal GRE score sheet: even though it cannot be counted as official, it can be helpful if a delay in the submission of GRE scores from ETS to your schools of choice occurs. In addition, the schools will sometimes ask for other documents in your package, such as your statement of purpose or a copy of your Curriculum Vitae. In general, it is not necessary to add in a cover letter to your package, as the packages are most often received, opened and sorted by secretarial staff knowledgeable about what to expect in your package. Once your package is completed, it is highly recommended that you have it sent to its intended school using a courier service in order to ensure it actually gets there in timely fashion. One of the cheapest ways of doing this is using the Xpresspost service from Canada Post: they will charge you around $CAN15, give you a tracking number and ensure your package gets there within three to five business days. It goes without saying that you should not wait until the last minute to submit the applications and send the supporting packages. Actually, even if schools will usually deny this, many faculty members insist that there is a clear advantage to submitting your application as early as possible (especially in obtaining assistantships and scholarships). It certainly cannot hurt to do so, and besides, if you leave the applications to the last minute, you will be caught, in early December, juggling with both application deadlines and your own final examinations.

8) Awaiting replies and making the final decision.

At this point, you are done with the labor-intensive part of the whole process: your application is submitted and your package, sent. You may now give yourself a pat on your back for having survived. The applications will usually begin being reviewed after the Holiday break, that is, at least for schools having deadlines preceding the 1st of January. In exceptional cases, some schools will begin giving out decisions as early as mid-January, but most replies from American universities should come between the 1st of February and the 30th of April. In the case of positive replies, schools will indicate the support package they are willing to give you. You will then have until the 15th of April approximately to make a final decision. Often, schools will invite you to visit them and meet with faculty members to get a feel for the school. You should definitely do so if given the opportunity: your choice of school will affect the next five years of your life, crucial years to your academic development and to your career, and so, a campus visit will give you a better sense of whether or not the school is suited for you (or you are suited for the school). Regardless of your intent to visit the school or not, do not restrain yourself from asking any question you have, be it regarding the curriculum, research possibilities, lodging and food services, living expenses, campus location, means of transportation, insurance plans needed, etc. Your decision should be as informed as possible. After your investigation into each school which has given you a positive reply, you will then be faced with making the final cut. Surprisingly, this choice might end up being the most stressful part of your application process. Good luck!

9) Links that should prove useful during the course of your application:

Extensive graduate school information by
Extensive graduate school information by The Princeton Review:
Official GRE website by ETS:
Official Thompson Prometric web portal:
GRE Mathematics Subject test information and practice examination by ETS:
Online set of practice exercises for the GRE and other standardized tests:
Official Kaplan Test Preparation and Admissions web portal:
Official NSERC web portal:
Official FQRNT web portal:
Canada Post Xpresspost USA Service web site:


Last edited by on Mon, 05/16/2011 - 08:51