The advisor you choose will have a lasting effect on your career. We'd like to suggest some issues to consider and questions to ask to help you think through this decision.
The most important question you need to answer is this: ``Can I work with this person on a regular basis over the course of three to five years and get the guidance I need to develop a research project?'' There are also pragmatic questions to ask.
Does the prospective faculty member currently advise other graduate students? You'll want to talk to them. If there are no senior students, you should find out when the professor last had a student. A faculty member who advises graduate students or a secretary might help you get in touch with previous students. You'll want to find out if the prospective advisor has ever had students who didn't finish or took an inordinately long time to get their degree.
Past students will likely be happy to talk to you about their experience under this advisor. Their doctoral theses will be in the library, so you can see what sort of work they did under this advisor and perhaps learn if and where their thesis work was published. You can also find out how helpful the advisor was to them in getting a job.
Does the prospective advisor attend conferences or meetings regularly? Does he or she present papers? An advisor who tends not to go to meetings may not be well-connected with other researchers and may not be keeping up with the latest developments. An advisor who actively attends and presents their work at conferences is more likely to help you find a good topic of interest to other researchers. He or she is in a better position to introduce you to other researchers in his/her field and to help you know where to apply for jobs.
Getting to Know the Professor
You probably first get to know a prospective advisor by taking one of their classes. If you think you want to work with this faculty member for your thesis, meet to talk with them. Ask about their research. You'll learn a lot about their style by the way they describe their work and how much enthusiasm they show for it. Find out if you can sign up for a reading course. That will give you the opportunity for close interaction without entering into a student-advisor relationship.
Does your advisor have grant money? even research support for a graduate student? Although you may be able to support yourself as a Teaching Assistant, having research support can give you more time to focus on research problems. If your advisor does have money for research support, you'll want to find out if being a research assistant for this advisor means getting to work on your thesis problem or if it requires work on a different project.
You may well not have an idea of the kind of mathematics you want to pursue, and that's fine. But you should try to find out whether your prospective advisor is in a large or small specialty and whether this specialty is an active and growing area. Looking at conference proceedings or finding web pages of people in this specialty are reasonable ways to judge this. Small areas may have at best special sessions at the Joint Meetings. Large areas will have their own conferences that may even publish their own refereed proceedings. Working in a very active area makes it easier for people to appreciate your work, helps you publish in better journals, gives you better opportunities to meet other researchers, and can help you find a job. On the other hand, a small area may have less competition on topics and make it easier to meet the experts in the field.
A Famous Advisor
If your advisor is well-known and has a lot of students, you'll have less close contact with him/her. On the other hand, a famous advisor may point you to better problems and will be well-connected in the community.
An Advisor in Poor Health
Grads do indeed get stranded by advisors who die or suffer health problems serious enough to sap their energy from research. If you want to work with a professor who is in poor health, find out if there are other faculty members with closely related research interests who can help you in case your advisor becomes disabled.
The Student-Advisor Relationship
The majority of graduate students have at least mild frustrations with their advisor. This is not surprising given the imbalance of power in the relationship. So keep social expectations in a student-advisor relationship to a minimum. If you're fortunate, you'll find more than just an advisor: you'll find a mentor who may later become a friend and colleague.
Prepared by the editorial board of the Young Mathematicians Network.
Last revised 13 September 1997.
The YMN Board:
Charles Yeomans <firstname.lastname@example.org>
Nancy Wilson <email@example.com>
Emil Volcheck <firstname.lastname@example.org>
Frank Sottile <email@example.com>
Jonathan Rubin <firstname.lastname@example.org>
Michael Prophet <email@example.com>
Franklin Mendivil <firstname.lastname@example.org>
Leigh Lunsford <email@example.com>
Kevin Knudson <firstname.lastname@example.org>
Matt Hudelson <email@example.com>
Birk Huber <firstname.lastname@example.org>
Philip Gustafson <email@example.com>
Greg Dresden <firstname.lastname@example.org>
Kevin Charlwood <email@example.com>
Frank Arlinghaus <firstname.lastname@example.org>