So you've decided to go to graduate school and study dynamical systems—Great! Now you need to apply. In this essay, I'll try to share some of my experiences as Director of Graduate Admissions in the Math & Stats Department at Boston University over the past three years along with some tips that may help you present yourself to the graduate committee in the best possible light. Let me start with a disclaimer though—although our graduate application process is similar to that of many other research universities, my experience is limited to BU. So make sure that you check for specific details and procedures of the departments you are applying to.

Even if your application probably won't be due until sometime next January (and many places may not even accept your application for a couple of months), it's definitely not too soon to begin gathering the materials you'll need to apply. In particular, it would be a good idea to talk with the people whom you plan to ask for letters of recommendation just to check and make sure that they are willing to write on your behalf. Although different universities have slightly different requirements for their applications, in almost all cases your application will include at least the following four items:

• an official transcript,
• letters of recommendation,
• a statement of purpose or personal statement,
• GRE scores.

The first of these is perhaps the easiest and most straightforward to obtain—you will presumably just need to go to your college or university registrar with a list of the universities to which you are applying, and they will send out the transcripts to the places you request. While a few schools might accept photocopies of your transcript, most will require an official document from the registrar—at my own university, for example, the graduate school won't even permit us to reject an applicant without an official transcript! If you're already a senior, what's on your transcript is pretty much fixed by now, though you'll certainly want to make sure that the grades in your fall semester courses are as good as possible. If you're getting a jump on this process and are a junior, then you still have a chance to think about which courses would prepare you best for graduate school. One thing that the admissions committee will be looking for are courses that demonstrate that you have a broad undergraduate background in mathematics and the ability to do graduate-level course work. Courses in real and complex analysis and abstract algebra are definitely recommended. If you're sure that you want to study dynamical systems in graduate school (or topology, or number theory, or …), and your undergraduate institution offers a course or courses in that area, by all means take that too, but for most graduate schools, a good foundation in the basics is probably preferable to excessive specialization.

The next items in your application are your letters of recommendation. The best letters of recommendation are those that tell the admissions committee things about you that they can't infer from the rest of your application. If you had the opportunity to work on a summer research project with a professor, for example, he or she might be able to convey to the committee information about your readiness for graduate research that wouldn't be apparent from your classwork alone. Another example might be a professor whom you had for several classes over a period of years who could write about your development as a student. The committee will be trying to get as complete an image of you as possible from your application, and letter-writers that have specific comments about your undergraduate work can really help fill in that picture. As a final note, make sure that you ask your recommenders if they will write for you far in advance, so that they're not stuck trying to cobble together a letter at the last instant—and, most important of all, remember to say "Thanks"—writing a good letter takes time and effort, and it's nice to know that it's appreciated.

The personal statement is the next part of your application, and it's the part where you can make your case most directly to the admissions committee. As with the letters of recommendation, tell the committee something that they can't learn from the rest of your application. While you needn't write a different essay for each place you apply, you should, especially for the programs you are most interested in, do some sort of personalization. What is it that makes you especially interested in this department? Is there a group of faculty members there whose research you became familiar with in the course of an REU? Did you hear a lecture, or read a book, by a professor from this university that sparked your interest in some topic? Recent years have seen a dramatic upsurge in the number of applications received for graduate study—last year, my own university received over 500 applications for our graduate program in mathematics and statistics. This is due in part, I think, to more students applying to more places. As the committee reads your application, they may wonder, "Is this student really interested in our department, or are we just their 'safety' school?" Convince them that their program is one of your top choices and that your interests align well with the strengths of their faculty, and you'll definitely improve your chances of ending up in the "yes" pile.

Finally, most programs will require you to take the GRE exam, and often the GRE Math Subject test. If programs ask you to take these exams, they will probably take the scores seriously and so should you. A low score will not necessarily sink your application, particularly if there are extenuating circumstances (which you should explain in your personal statement), but there are review books available to help you prepare for these exams and you should use them. Many of the questions on the test may concern course material from classes you had three or four semesters ago—it's not surprising if those ideas no longer are fresh in your mind, so work some (actually, make that lots!) of examples from the review books to refresh your familiarity with these topics. In contrast to your transcript, where your course selections have been made, and most of your grades are already determined, you still have the chance to improve your test score—make the most of it!

That probably completes all the material you'll need for most applications, but double-check each school's website to see if they have any special requirements, and make sure you get everything submitted on time. If you don't receive confirmation from the school that your application is complete, it's perfectly OK to send an e-mail and ask if everything has arrived. After your application is in, then comes perhaps the hardest part of the application process—waiting. Given the increasing number of applications that graduate schools are receiving, it will be a while before you hear anything, but hopefully by the end of February or the beginning of March you will start to get responses to your applications. Some may be yes, and some may be no, and since most schools receive applications from many more qualified candidates than they have positions for, some may tell you that you're on their wait list—more on this possibility below. The schools where you are accepted should also tell you that you have until April 15 to make a decision—most top research universities have agreed not to require students to make a decision about their acceptance until that date. You should use that time to decide which of the schools that have accepted you is right for you. If possible, try to visit your top choices. Talk to the faculty whose research interests are closest to your own, and perhaps even more importantly, talk to the current graduate students. You'll be spending LOTS of time with them over the next five years so ask yourself if this is an intellectual and social community that you can imagine yourself being a part of. While you should take the time you need to be sure that you've chosen the correct program, try to be considerate both of the schools who have accepted you and of the other students who are waiting to hear. If you've been accepted to three schools and you know one of these three is not your top choice, let them know as soon as possible that you're not going to be accepting their offer. If you've been put on the waiting list at some schools, you can bet that other students are on the waiting list at that school and the sooner you tell them that you're not coming, the sooner they can offer that position to someone on their waiting list.

Graduate school is a wonderful experience. You'll have four or five years to do something exciting that you love with a focus and intensity that may never be repeated. Getting there can be a difficult and nerve-wracking experience, but it's worth it—Good Luck!

Eugene Wayne