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by Kyle Kneisl, Ph.D., 2002, UNC Mathematics
Applying to graduate school for higher degrees in mathematics can be a hectic and complex process. This document seeks to demystify some of its intricacies. The statements made are the reflections of just one recent successful applicant to graduate school, and as such there can be no guarantee as to their validity or applicability for your situation. The information presented below is not intended to reflect the procedures or policies at any particular school; rather, its purpose is to discuss the aspects of the process common to most of the graduate schools to which you might apply.
Nothing in this document reflects any official policy or advice of this Department's faculty.
OVERVIEW
Graduate school in mathematics is the next step in acquiring the advanced degrees in mathematics which are essential for many professions. A person who is completing an undergraduate degree in mathematics and has aspirations to be a professor of mathematics or a mathematical research scientist must go through graduate school. Remember that graduate school is a very challenging experience for even the most gifted student. Attrition in graduate programs is generally high. Make your decision carefully.
We will separately address the application process, what to do after you've been accepted, and some things you may need to know about secondary issues such as financial considerations.
THE APPLICATION SUBMISSION PROCESS
Regardless of where you are applying, the same basic elements will be considered in an admission decision. Each of these will be discussed below. You will need to submit complete and official undergraduate transcripts, GRE general test results (and usually GRE subject test results), letters of recommendation, and a completed application form. You will almost always be given a chance to make a "statement of purpose", and some schools may require this of you.
For fall admission, most graduate schools will require that you submit all materials by January or February at the very latest, and will recommend that they be submitted far earlier than that. Make sure you understand the deadlines at any school to which you might apply. It is best to have your materials submitted by December, or even earlier, if they are ready. Applications submitted later in the process will generally be at some disadvantage compared to earlier applications. Following receipt of all of your materials by the graduate school, you may be surprised at the promptness with which a decision to admit you will be communicated.
THE GENERAL GRADUATE RECORD EXAMINATION (GENERAL GRE)
This is a crucial part of your application. Every graduate school you apply to will require that you submit scores from this examination. It is best to take this examination before the end of your junior undergraduate year.
The exam consists of 3 parts: Verbal, Quantitative, and Analytic, each of which is scored out of 800 points, reminiscent of the SAT examination you likely took for undergraduate admission. The "verbal" is comparable to, but much more difficult than, the SAT verbal examination. The quantitative part of the exam consists of questions which assess basic mathematical thinking. Many students applying to graduate school in mathematics will get a perfect, or nearly perfect, score on this section. The analytic section ostensibly tests logical thinking, presenting you with logic games and analysis of short written passages. Naturally, most successful applicants to graduate school in mathematics will do quite well on this section as well. As a result, the verbal portion of the examination will play an important role, as this is likely the area of the examination with the highest variance among mathematics applicants. It may surprise you to know that it is a somewhat widely held belief that your verbal GRE score may be one of the primary statistical indicators of your potential success in graduate school for mathematics. Take all parts of the examination seriously.
Read all of the helpful materials that the Educational Testing Service will provide to you regarding the General GRE examination. The exam is given at least twice per year in hundreds of venues across the world. Several study materials are available; those that you can purchase directly from ETS are quite useful.
Again, you should certainly have attempted this exam at least once before the end of your junior year, if not earlier. Your success on this exam will not likely be improved by waiting overly long to take it.
You may view the GRE examination website, which includes sample questions, by CLICKING HERE.
THE SUBJECT GRADUATE RECORD EXAMINATION IN MATHEMATICS (SUBJECT GRE)
The nation's better graduate schools will often "strongly recommend" or require that you submit scores on this much more detailed examination, generally taken by mathematics undergraduates. The Educational Testing Service offers advanced exams in several popular undergraduate subject areas, such as Biology, Physics, Computer Science, Education, Mathematics, and so forth. Obviously, you will need to take the 'Mathematics' examination. This examination is scored out of 990 points and is quite thorough and reasonably challenging. There is an exhaustive grilling on all aspects of the undergraduate calculus sequence, as well as a healthy dose of questions on such topics as linear algebra, topology, abstract algebra, complex analysis, and combinatorics. The purpose of the examination is to get some objective idea of the breadth and depth of your undergraduate exposure to mathematics.
Some material on this examination will reflect the topics covered in upper level undergraduate mathematics courses. As a result, the Subject GRE in Mathematics is often not first attempted until the beginning of the senior year. It is wise, however, to take it as early as possible. By taking all GRE exams (general and subject) as early as possible, you assure that your GRE scores are promptly available to graduate schools so that your application will receive immediate consideration.
Tip: Even if a school does not require the exam, take it and submit the scores. You're not fooling anyone by taking the exam and not submitting the scores until you have seen that you have "good" scores. Competitive schools will immediately note that you have not submitted subject test scores, and it may count against you.
If you have software capable of reading .pdf format files, you may actually download some free documents from the GRE site regarding their subject tests by CLICKING HERE.
THE TEST OF ENGLISH AS A FOREIGN LANGUAGE (TOEFL)
If English is not your native language, you will need to take the TOEFL examination. Different schools have widely differing standards for TOEFL scores. If applicable, you should contact the schools to which you are applying for further information.
This exam, like the GRE, is administered by the Education Testing Service. You may access the TOEFL information page by CLICKING HERE.
YOUR UNDERGRADUATE TRANSCRIPT
It should not be a surprise to you that potentially the most important part of your application is your undergraduate transcript. The most successful applicants will show a high GPA from a reasonably well-respected undergraduate school, in addition to a full exposure to courses offered in your mathematics department. That is to say, your grades, the quality of your school, and the breadth and depth of your exposure to mathematics (insofar as is reflected on your transcript) will be of paramount importance. Certainly, having outstanding grades in a number of upper level mathematics courses will prove important.
You will need to send official transcripts to all potential graduate schools, as well as send some indication of the courses currently in progress that are not yet reported on your transcript. Transcripts can take some time to acquire. If you anticipate a delay in getting official transcripts submitted, no one will fault you for enclosing an unofficial transcript (usually available immediately) with your application until the official ones arrive.
LETTERS OF RECOMMENDATION
Most schools will require approximately three letters of support written by your professors, attesting to your skills and suitability for graduate school. Different schools place widely varying emphasis on letters of recommendation; in any case, they are taken seriously.
To request letters of recommendation, you should keep the following points in mind. Professors who have had the maximum amount of in- class and out-of-class exposure to you are excellent choices for recommendations, as they can comfortably say the most about you as a student of mathematics. Professors whom you have impressed in some way are also candidates for letters. Remember, graduate school admissions committees have read thousands of letters. Your letters, if possible, should reflect the special interactions you have had as a student.
Make a careful decision as to whom is to be solicited. Prepare a copy of your transcript and vita for each potential letter writer. Professors who know you very well may not need this data, but it should be offered nonetheless. Visit or phone (do not email) the professor and ask if he or she would "feel comfortable writing a positive recommendation on your behalf for graduate school". He or she will usually be quite candid in response. If agreeable, provide them with the necessary materials.
You are usually asked on the application if you waive your right to see the letters submitted on your behalf. As far as I know, most students elect to waive this right. Some professors will not write a recommendation unless you waive this right. Furthermore, one assumes that graduate schools will have greater assurance that your letters are candid and thorough if the letter writer is assured that his comments will be kept in confidence.
What if you don't know three professors particularly well? In this case, if you did well in an advanced course and/or a course taught by a well-known research professor, simply show up at their door with your materials. If you are not well known to the professor, you should certainly have a comprehensive transcript and/or vita available for that professor's review. This will help him or her in writing as complete a letter as possible. Part of the professor's job is to furnish such letters of recommendation to qualified students, and they will make the time if you have done well in their courses.
TO HOW MANY SCHOOLS SHOULD I APPLY, AND WHERE SHOULD I APPLY?
This is a personal decision with no obvious correct answer. You should assemble as much advice as you can from trusted professors in your department. For example, one bit of advice which is commonly given is to choose a school to which you expect to be easily admitted, and then choose one which may be more competitive and to which you feel you are far less likely to be admitted. Having defined the strongest and weakest schools to which you will apply, now chose a smattering of schools which fall in between. To determine these limits, your best recourse is to speak with several knowledgeable faculty members who are in a position to assess your chances at various types of schools. You should get several opinions.
The aforementioned represents just one of several strategies that may prove useful to you. Again, ask for advice from as many faculty as possible.
It is now the case that most mathematics departments maintain a website. You will certainly find much useful information there. For example, you will usually be able to read a listing of the faculty and their research interests.
How many should you apply to? If you have the time, money, and inclination to do so, feel free to apply to as many as you wish. Most students apply to at least four schools.
THE APPLICATION ITSELF
You should call or write for an application for all schools in which you are interested. Address your inquiry to "Graduate Secretary", care of the Mathematics Department. Indicate that you would like an application for graduate school sent to you. It may also be possible to use the internet to request an application be sent.
Once you receive it, you should promptly fill out the application and assemble your supporting materials. You should probably type the application. Send the application to the University, and include all necessary supporting documents. You may wish to send your application certified with return receipt. This will give you a record of mailing date, as well as written confirmation and date of receipt by the University. Certified mail with return receipt is inexpensive.
Many schools now offer an on-line internet application. One can assume that finding this on the University's web site should not prove to be too difficult.
You can expect to pay from $15 to $50 for your application fee. If you need GRE test scores sent above and beyond the three or four which (if you specify them at test time) are free-of-charge, that will also entail an additional fee. Remember that official transcripts also cost money. These items can quickly add up to be several hundred dollars.
WHAT HAPPENS AFTER YOUR APPLICATION IS SUBMITTED
Obviously, any graduate school will extend their first offers of admission to their strongest candidates, and fill in remaining spaces with qualified, but somewhat weaker, candidates. However, it is reasonable to assume that a graduate school would not accept and fully support any student that they did not feel could succeed in their program. You should not be dismayed if quite some time passes before an offer is extended to you. Even if you are not at the top of the list an acceptance is, after all, an acceptance.
While by no means required, you are also encouraged to visit all candidate schools, both for your sake and theirs. You should probably do this in the months following your submission of an application. A visit should help you know what you are getting into. Any school to which you apply will make arrangements for you to visit the campus and department as a prospective student. Stronger candidates may be able to secure remuneration for their travel and lodging expenses, but you will probably have to (tactfully) ask. Make a careful note of any faculty or graduate students who spend a quantity of time with you, as you may wish to thank them and/or contact them with additional questions.
WHAT TO DO AFTER YOU HAVE BEEN INFORMED OF DECISIONS
Once a school has accepted you, that offer of admission is pending your decision until a certain date, usually sometime in the spring of the year in which candidates are admitted to the fall. There is a national agreement amongst graduate schools to allow you until the date of April 15 to make your final selection. The purpose of this agreement is to alleviate the pressure of accepting a given offer of admission until all schools have had a chance to act on your application. However, many students have made their decision well before this date.
After you have heard from everyone who you wish to hear from, it's time to make a decision. Tips on making a decision will follow in a subsequent part of this document. Please consider observing the following courtesies:
For schools which have accepted you, but you will not attend
Mail, email, or FAX your decision, as promptly as possible. This will free up space for them to admit other "waitlisted" candidates. Thank them for their offer of admission, but advise them you must regrettably decline. You might also advise them of the school which you have decided to attend. Additionally, you may wish to advise them of the reasons for your decision. This will be helpful to the department's future admissions strategies. For schools which have treated you well, a lengthy discourse on your reasons for rejecting them may be important to them, and you should provide it if you are so inclined. You may also wish to specifically thank any graduate students or faculty who met with you on any campus visit in this letter, or separate ones.
For the school you have decided to attend
Mail and/or FAX your decision, care of the department's Director of Graduate Studies and/or Chairman. Thank them for their offer of admission. You may also wish to thank anyone who met with you on any campus visit.
For schools which have not acted on your application
Advise them immediately that your final choice has been made, and that you respectfully withdraw your application for admission to their program. This will open up space for other candidates.
TIPS FOR MAKING YOUR FINAL CHOICE
The reasons for choosing a particular graduate school over another are much different than choosing a particular undergraduate school over another. For this section, more than any other, you should always keep in mind that you are simply reading my opinion on this matter, which amounts to a distillation of the advice given to me by faculty when I was in your shoes. You must exercise your own best judgment for this as it is one of the most important decisions of your life.
You may want to primarily consider only the following criteria: Professional opinion of the prospective University, and financial package. Considerations such as location, cultural environment, politics of the area, and so forth have much less (if truly any) importance. Remember, ostensibly you will someday be a professional research mathematician. The first position you get upon receiving your advanced degree will be influenced predominately by your choice of University and advisor. You don't want to undermine your ability to get the best jobs because you wanted to be "somewhere with a beach" or "somewhere without snow".
Let us now separately address these two important criteria:
Professional opinion of your graduate school's degree is crucial. A number of ratings of various schools are published. You should seek out this data. While fine distinctions are certainly not important, there will be a dramatic difference in schools of widely different rankings when it comes to professional opportunity. You should strongly consider the most recent ratings of every graduate school to which you apply as an almost decisive criterion.
Financial package is also worth considering, but to a much reduced extent. Because of the difficulty in achieving higher degrees in mathematics, it is only rarely possible (and never recommended) for a student to fund his or her graduate degree through outside work. Furthermore, graduate students, particularly in mathematics, are a crucial piece of the labor pool at the University. Mathematics departments play an integral role in all undergraduate education. Departments at large universities in particular usually offer numerous low level "service" math courses, and only a fraction of the needed teaching pool can be found among the math faculty. As such, all graduate students admitted (at least the ones expected to be able to survive the program) will generally be offered, at the minimum, the opportunity to work for the department teaching courses or researching for a "reasonable" stipend. These stipends will vary. Be sure to inquire about the amount of teaching you will be expected to do during your graduate career. The teaching load varies according to how far along you are in your own program of study, sometimes increasing significantly after your first year and possibly decreasing again toward the end of your thesis preparation.
Some good programs, but significantly weaker than the best place that would admit you, may attempt to entice you by offering comparatively substantial stipends. Thus there will likely be an appreciable discrepancy between the financial offers that are given to you. You should try to resist the impulse to be driven by high stipends; you will get by, and you are better off in the strongest place.
Additionally, a third criterion may apply to some students. If you are a strong candidate for graduate school and have your heart set on a certain mathematical discipline or faculty member, this will obviously change the landscape of which schools will appear "strong" for you. However, restricting your choices on this basis should be done with the greatest caution.
Note that in the event that you are admitted without an offer of a financial package, you probably should not go to that University. This advice applies 99% of the time. Such offers are tantamount to rejections, and you must realize this. You should only choose from schools which offer you full financial packages.
Conclusion? Take all schools that do not offer you comprehensive financial support and remove them from any consideration. Of what remains, arrange them roughly in order of their respective ratings. Now, choose from among the best one or two schools in your pile. It's that simple. Do not allow yourself to be swayed by peripheral considerations, unless the schools compare almost identically in terms of ratings. After making your decision, promptly advise all schools which have accepted you (or are still considering your application), as outlined in a previous section. |
