The choice of advisor is probably the most important one that a graduate student faces, yet it is often done haphazardly.
The ideal advisor might have the following traits:
Work is easier when both you and your advisor find the research area fun.
Someday you will finish your degree work and be looking for a job. Your advisor's reputation and professional colleagues could be key in opening opportunities for you.
More immediately, your advisor will be leading your research, at least at the beginning, and it is important that the advisor knows how do do quality research.
If you are working your way through school as a teaching or research assistant, you may well want to be supported as a research assistant by your advisor. Even if you have fellowship support or an outside job, grant support is a sign of your advisor's skill as a researcher, although in a few areas of mathematics and computer science, research assistantships may be rare.
You are new at research; it helps if your advisor has some experience in dealing with graduate students.
You don't want to work with an advisor who never shares credit for ideas, who expects every student to spend 7 years as a research assistant, or who doesn't know how to motivate and encourage students.
If your advisor moves to another university before you finish your degree, while you are trying to finish your work, you will have a severe handicap. You may need to consider moving with your advisor or changing advisors--a difficult situation at best. Even if the advisor goes travelling for a year on sabbatical, communication can be temporarily difficult.
You will be working closely with this person until your graduation, and the relationship will not end even then. The more comfortable the two of you are with the relationship, the fewer distractions from the research at hand.
You can learn a tremendous amount from more advanced students, and the opportunity to work in a group of motivated researchers working on similar topics is quite stimulating. Be aware, though, that if the group is too big, you will have little time with your advisor; you may be directed by a post-doctoral student or a more advanced graduate student.
Before you came to your university, you might have made sure that some faculty members were active researchers in areas of interest to you. Now is the time to consider each of those candidates as a potential advisor, measuring them up against the criteria in the previous section.
Use homepages, GoogleScholar, Science Citation Index, Math Reviews, or other electronic resources to find recent publications by each candidate. Read a few of these publications, and try to understand them enough to be able to ask intelligent questions and to see directions for further work.
Get to know potential advisors by taking courses from them, attending seminar talks given by them, and seeing them in their offices (by appointment or during office hours) to talk about their research interests. Ask for relevant papers to read.
Talk to other students about various candidate advisors.
Get advice from faculty members that you respect or from the graduate office of your department.
If your potential advisor is untenured, try to find out the prospects for promotion and tenure. Perhaps some other graduate students can help. Otherwise, good indicators are strong publications in major journals, some grant support, and a good teaching record.
Once you have a good candidate advisor, ask that person to be your advisor. Don't be discouraged by a ``no''--try a different advisor. Good advisors are much in demand, and they don't remain good if they stretch themselves too thin.
The best analogy for the relationship between an advisor and a student is probably that between a parent and a child.
At the beginning, the child has little independence, and almost every action is directed by the parent. Initially, most students need close supervision, being told what papers to read and what tasks to accomplish.
As the child grows, independence develops. A student begins to ask interesting research questions with minimal prompting and can set the direction of the next week's work. The advisor still plays a crucial role as catalyst and evaluator of ideas.
As adolescence sets in, conflicts arise. The student realizes that all too soon, school days will end, and it will be essential to be able to function on one's own. A student eventually may feel that research would be more easily finished without the advisor's ``interference,'' even though the student may lack the detachment necessary to evaluate the work. Independence is frightening, but dependence is resented, and frustration can run high.
In adulthood, parent and child redefine the relationship. The process of graduate school should transform the advisor's student into the advisor's colleague. The two may or may not continue to collaborate after the student graduates, but future contact is ideally built on mutual respect, gratitude from the student to the advisor for the professional formation, and pride of the advisor in the student's accomplishments.
It is important that the advisor and advisee develop a compatible working style. Some people thrive on regular weekly meetings between the two that force the student to synthesize the week's accomplishments (or to explain the reasons for the lack of progress). Others rely on chance encounters in the hall. Some advisors have weekly group meetings at which each student discusses progress and everyone can comment. Some advisors expect students to attend seminars or journal clubs in order to keep up with recent research results.
If you feel that you are floundering (as every student sometimes does), ask your advisor for extra meetings, send frequent email messages asking for pointers, or discuss your work with another trusted faculty member or student.
As in any relationship, conflicts should be faced and discussed. Cultural and generational differences can lead to misunderstandings that are easily resolved once they are recognized. Sometimes a fellow faculty member or graduate student can lend some insight.
In rare cases, the relationship just does not work. In such cases, the student should seek another advisor, leaving the first with as little ill-will as possible.