While I was a graduate student, no later than my third year of studies, I decided to write an essay of advice to prospective graduate students about choosing a program and mentally preparing themselves for graduate study. I’d been through it myself, of course, and also was closely involved in the prospective student visits at Notre Dame, and felt like I had something to say. I got some positive response from it, so I preserved it through several changes of website, including here. I don’t dare edit it from this far-away perspective, lest it lose any usefulness it may have once had, so here it is in its original form.

Advice to Prospective Graduate Students

So my only expertise lies in the fact that I’ve been through the whole application-visiting-selecting a school process. If you are interested, I still will proffer my opinion.

My advice to you can be summed up as follows: apply to schools based on their programs, attend a school based on its people.

To expand: Make a really big list of schools. Rankings are good for this, as are asking your professors where they went and where decent schools are. If you know or have a good idea of what you want to specialize in, cross out the schools that don’t have it (this is obviously not a problem if your field of interest is algebra, for example). The more particular you are, the more will get crossed out this way. Unless your application is exceedingly strong, you’ll want to include a range of schools, but you can probably cross out ones that are both weak overall and weak in your field in particular. This process ensures that everywhere you apply is academically suited to you.

Next, cross out the schools that are places you wouldn’t possibly want to live – the prospect of living in a big city for six years appalled me, so I crossed out University of Chicago; I’m from Illinois, did undergrad in Virginia, and wanted to be closer to home this time around, so I crossed out everything on both coasts.

Now you have a list of schools with programs that match your interests and that you wouldn’t be unhappy at. Apply to those. If the list is still unmanageably long (I ended up applying to six schools, which I believe is the low end of average, but of course you can apply to as many schools as you have funds and patience for), it’s time to get arbitrary – high application fees and ugly departmental websites are both good criteria for bringing a list of 30 schools down to a reasonable level.

Having pre-weeded for academic interests (though later in the process you may learn things which require more weeding), you can feel comfortable choosing a school from those that accept you on purely personal grounds. Of course, don’t go crazy on it – if you are choosing between MIT and The School of Advanced Math and Potato Processing in Challis, Idaho, unless you feel you will be desperately unhappy at MIT I think the choice is clear. In general, though, don’t sacrifice quality of life for anything less than a perfect program. It isn’t worth it.

Visit the schools that accept you before you make your decision. The counter-intuitive advice I’m going to give on selecting a school is this: go where the people are most like you. If the program is large, look at the group of people who specialize in what you want to specialize in; if the program is small look at everybody. Don’t worry about an excess of homogeneity – this is mathematics grad school, at the least there will be several international students to keep things diverse. What I mean is, go where the attitude is most in line with yours. In undergrad, there are tons of people all the time, potentially a new friend around every corner. In grad school, the pool size is decreased and you will be spending a lot of time with these people. They will be your main human contacts for years, and if most of them rub you the wrong way your life will be very much unhappier than it needs to be. Go where you fit in, and you will be happier and thus more productive. Grad school is difficult and a good support system is not to be undervalued.

Incidentally, if your undergraduate school, like mine, is small with no graduate program, don’t worry. I know I felt completely in the dark, but it’s really just what you would expect. It’s a lot of work, yes, but if you’re of the caliber to be considering it at all, it won’t kill you.