By Diana Davis

Now is the time when college seniors across the country are receiving their graduate school application decisions: accepted or rejected? Or perhaps wait-listed? And after you’ve received those coveted acceptances, you have to decide between them. How to choose? If you have been accepted to four schools, simply roll a tetrahedron; if you’ve been accepted to two, simply flip a coin. The problem emerges if you have been accepted to three schools…

Just kidding! Here are some important considerations when choosing a graduate school. I encourage others to write comments about which considerations are important to you, or tell about how you made your decision about which school to attend.

**Mathematical considerations:**

*Are there people in my area of mathematics?* If you’re not sure what you want to study, make sure you choose a school with a wide range of areas represented. If you know what you want to study, consider choosing a school with several professors and graduate students in that area, so that you will have several advisers to choose from, and grad student colleagues to talk with. If you are interested in an area of math that is not present at every grad school, such as logic or combinatorics, that may narrow your choices.

*Is there a professor I would like to work with?* Look at the faculty listing on the department’s web site, and research the mathematicians in your area of interest. Are they taking students, and have they had students recently? Glance at their recent publications. Do the topics seem interesting to you? What topics have their students worked on recently?

*Do most matriculated students earn a PhD? If not, why not?* At some schools, almost everyone who enters the PhD program graduates with a PhD. At other schools, the number could be considerably lower, even under 50%. Some schools fail a lot of students on the qualifying exams, and if that happens to you, you will leave grad school after two years with a master’s degree and no PhD. Such schools will likely have a different culture than schools where almost everyone graduates. Make sure that you ask current graduate students about this. Also, do most students graduate in four, five or six years?

*What sort of jobs do students get after graduation?* Ask current graduate students what sort of jobs graduates have gotten in the past few years. Do they tend to get tenure-track academic jobs, or post-docs, or do they go into industry, or what?

**Non-mathematical considerations:**

*Are the graduate students happy?* Make sure to think about whether you could spend four to six years in the city where the school is located, and in the department you visit. Can you see yourself there? Do the grad students seem to have the kind of social life (or lack thereof) that appeals to you? If things like ethnic restaurants, parks and recreation areas, or night life are important to you, ask your graduate student host to show you these things during your visit (or if you can’t visit, research them online or ask current students via e-mail).

*Where do graduate students live?* Your living situation can make a big difference in your quality of life, if you have a terrible roommate or live far away from the department. Ask where the graduate students live, what they pay for rent, and if they have roommates. Also ask whether it is necessary to have a car.

*How is the stipend?* Your acceptance letter will likely tell you what your graduate student stipend will be. Make sure to check whether all of the tuition, health insurance and fees are covered by the graduate school, and if not, how much you would be expected to pay out of your stipend each semester. Additionally, the stipend may only cover the academic year, and the department may give you additional money for summer support, or extra support from your adviser’s grant. Check with current grad students to see if this is the case. Also, ask them if the stipend is sufficient for their needs — $18,000 may be more than enough in one part of the country, but may be insufficient in another area where the costs of living are much higher, so don’t just compare the raw dollar amounts of the stipends.

What do you think — what other considerations are important, and how did you choose your graduate school?

Teaching responsibilities are another thing to consider. These responsibilities can vary from serving as the primary instructor for a course to no teaching at all. Some students jump at the opportunity to be a course instructor, while some would prefer to just grade homework. Ask current students what teaching is required of you and what teaching is available to you.

Yes, excellent point. At some schools, you may start lecturing immediately in your first semester, while at others (such as Brown) you might have no teaching responsibilities the first year, then give TA sessions the second year, and finally prepare your own lectures the third year. Ask about this, and how many semesters off of teaching you are likely to have.

Brian also makes a good point to investigate what teaching is available. If you are fortunate enough to never have to teach and to be able to devote all your time to research, you may find yourself on the job market five years later with no teaching experience, so see if you could offer to teach even if you don’t have to. Also see if grad students usually teach just calculus, or if they also teach higher-level undergraduate classes.

Really nice advice, Diana. There is one thing I would like to add – it’s easy to forget to check at what speed you are expected/allowed to move through the program. I know that I wanted to take all the intro-level graduate courses, and you might want a program that allows/encourages that. You might on the other hand, want a program that encourages you to start research quicker (and perhaps expect more background coming in?). In my opinion, it would be ideal if the program was flexible in the sense that it allowed you to do either – hopefully, it isn’t too stringent on preliminary requirements, so you can move through the program quickly if you want, but it also shouldn’t push you into research before you think you are ready. That may not be your idea of what’s right, but it’s just something to look out for that can easily be overlooked.

I’d like to add that often the advisor has a lot to do with the mathematical considerations above. Some advisors are happy graduate a student in 4 years, while others believe that even if you have enough to graduate in 4 or 5, you should stay the extra year and improve your c.v.. Also, the advisor will have a great deal of say as to how soon the “research” begins. So, if the student has an idea of which professors they might like to work with, they should particularly focus on the current and past students of those particular professors.

I now have a question. Where can one find data on the average time to graduate with a PhD in mathematics?

I’m in this position myself.

One thing I’m wondering about: some schools’ class requirements are very broad (algebra, analysis, and geometry) and some are very specialized (a “probability track” might have no courses in common with a “numerical analysis track.”) I know I should be thinking about this but I don’t know what’s preferable.

I want to do analysis, and I’m really poised between pure and applied right now. If you asked me to get super-specific, I’d say I wanted to do harmonic analysis with applications to large data sets/machine learning, because that’s what I’ve done for research as an undergrad and I liked it — but I can’t realistically be sure that I’ll be doing that forever. I know only very basic algebra, and some geometry/topology, but most of my classes have been in analysis.

Pros and cons to broad vs. specialized? Is it better to bone up on subjects you haven’t studied much before, or speed ahead to advanced courses in areas where you have more background?

Steve — excellent point about the advisor. Also see a previous post on this blog about the importance of the advisor. As for your question, I don’t know; the US News rankings of universities and colleges rank the percentage to graduate in 6 years, so they may have something similar for graduate schools. I have never seen such statistics.

Sarah — I haven’t heard of these specialized tracks. I would say talk to grad students at schools with both systems and see which one appeals to you. It is probably unreasonable to assume that your graduate research will mirror your undergraduate research very closely, because you may find you like the next thing you study, too. If you are sure you know what you want to do, then by all means put yourself on a narrow track, but if you are open to many areas of research, it’s probably better to get yourself a broad education at the beginning of graduate school.

Steve – While I don’t know where you might find such statistics, individual programs usually list a nominal time to complete a doctorate in their handbooks. Sometimes they even have a note about how long students take on average to graduate. For example, my program has a nominal time of 6 years but on average students complete the program in around 5 and a half years.

@Sarah — Even if you know what you want to specialize in, I’d suggest that you allow yourself to have a broad education. Note that this is somewhat independent of what the preliminary exams you have to take are. The main reason I say this is the fields aren’t distinct. When I went into analysis the first thing I did was learn some category theory. When an office mate went into algebra the first thing he needed to do was refresh his complex analysis. My advice is to learn as many of the basic topics while it is easiest, when you have a professor and classmates helping you through rather than spending the time to learn on your own.

Good luck on your grad school hunt!

hi,

Right now i am doing Bacheolorate chemical engineering.I am in my 2nd year and it will take 2 more years to graduate.I am interested in doing masters in mathematics(i dont have any option) in a US university preferably.Though i dont have any formal background in math except

multivariable calculus(B grade),Linear algebra and complex analysis(B),Differential equations(B) i have informal background in tensor analysis,abstract algebra,topology,and i’ll be learning analysis and differential geometry soon.But I have extremely low overall GPA-5.75/10 .Will i be having any chance to get in to a grad school for PhD mathematics?? or atleast MS?? I have geniune interest in maths and i’ll be no more into chemical engineering(i was forced to sit here) so the GPA will be increased to a maximum of 6.5/10 by the time i apply(Fall of my fourth year).I think i can get a good GRE score in maths.Will i have any hope to get into grad school?