Finding an Advisor

Finding an advisor can be a lot of work.

Here is what the graduate council has to say about the advisee/advisor relationship: Mentoring Guidelines

In the process of finding this person, it can help to reflect upon what you hope or think the grad school experience should entail, and gauge potential advisors using these things as a guide. This document will talk about finding an advisor in the context of the following ideas:

Grad school should involve working on interesting stuff -- ideally, stuff that is both interesting to you and to other people.
Grad school can serve as preparation for a job doing this interesting stuff.
Finally, none of this is possible unless you retain your sanity throughout grad school.

This last item is a bit tongue-in-cheek, but it is true that grad school can be very trying at times (but not all the time!). It is important to reduce any sources of anxiety that you can -- stress is an unavoidable part of life sometimes; and it is equally important to increase your productivity/overall content as a grad student in any way that you can.

Working on stuff you find interesting

This sounds easy enough; after all, you know what you like and dislike, right? Probably not, if you are at the beginning of grad school. Here are some mines to watch out for:

don't force yourself to try to like something. On the other hand, it's good to be open-minded and reserve judgment. You may very well find something interesting the more you learn about it.
don't confuse what others tell you to find interesting with what you find interesting.
it's easy to leave a professor's office thinking something is cool, but is this enthusiasm momentary or is it something that will last? Make sure that this is something that you are interested enough in to pursue by yourself if you had to.
remember that a subject just has to be interesting enough. Given all the constraints on finding the appropriate advisor, a compromise between your interests and your advisor's may be necessary.

Finding your area of interest

attend seminars on different subjects. (Keep an open mind!)
ask other students what they're working on.
ask professors about their area of research, especially if you've enjoyed their class or think they might do interesting stuff.
another interesting question to ask professors: what sort of grunt work do you do on the way to getting results?
do some independent reading on topics that pique your interest. When you don't know some term or phrase that is used in the paper/book, ask professors and students about it, and use this as a conversation opener to talk about things related to what the paper/book is about.
think about what qualities things you seem interested in have in common; use this as a gauge whenever you come across something new. (But keep an open mind.)

Once you find some areas that you are interested in, you may want to find an advisor who knows something about at least one of those areas. To get to know the faculty, you can:

Read over faculty profiles
Try to take a class (especially a large group reading seminar) with interesting faculty members.
Participate in a small group reading seminar with faculty members you are serious about wanting to work with.
Ask an interesting faculty member for an independent reading seminar or summer project.
Ask an interesting faculty member about working on a small quarter-long project with them.
Talk with other students about what it's like to work with a faculty member you have in mind.

By the way, if a faculty member proposes a project that you try and then don't find interesting, it's okay to tell them. There's a true story of a professor at the University of Oklahoma who turned down four projects from his advisor, until finally the advisor said, "I think you actually want to work with (this other person). " This other person turned out to be a much better match for him, and he ended up being very excited about, and therefore motivated by, his final dissertation project.

Grad school as job preparation

Strictly in terms of job preparation, the ideal advisor

will maximize the probability that you finish your dissertation,
is influential in the area where you want to get a job, and
is willing to use that influence to you get a job.

When considering a faculty member as a potential advisor, find out:

if their work is well-referenced. This is a sign that people care about their work, which means that this faculty member can tell what kind of work is interesting to the mathematical world. To get an academic job, you will need to work on research that other people are interested in. Some advisors give their students projects, whereas others ask students to pick their own project. Either way, your advisor should be able to gauge whether or not your project is something that others will find interesting.
if this faculty member will write you a good letter of recommendation and help you with the job search process. A good way of finding this out is talking to other students, especially former students of the advisor. You can also talk to faculty members from other schools at conferences. Keep in mind that when you apply for jobs requiring a masters/doctoral degree, academic or not, you will need a letter of recommendation from your advisor.
where former students of the faculty member have found jobs.
average length of time for faculty member to graduate doctoral students; on a related note, whether most of the faculty member's students end up graduating. (Or do they drop out, leave math, transfer, or something else?) Remember that sometimes, these cases have more to do with the student than the advisor. If you find that there is a consistent trend of long graduation rates and leaving, though, you may want to try and find out more details before signing on to the faculty member as an advisor.
how experienced as an advisor this person is.

This last criterion is only one indicator, and not necessarily the most important one. There is a true story of a grad student in Davis (not in math) who was choosing between two professors as an advisor. Both were interesting researchers, but the one who seemed nicer and more accessible had never had students before; whereas the other one had been tenured for years and had many students and was an excellent lecturer. This grad student was advised to choose the senior professor by many people, and did. Unfortunately, as excellent of a lecturer as this senior professor was, he was terrible one-on-one, never made time for his students, and didn't care when the grad student told him her results. When the grad student tried to switch labs, he wouldn't let her. Through all this, the junior professor continued to answer questions from the grad student, and helped her with her labwork. The grad student wished that she had talked to other students about what was was really like working at the senior professor's lab before agreeing to be his student. (Disclaimer: there are plenty of tenured professors who are friendly! This story was just included to illustrate the importance of finding out as much as you can about an advisor before signing on.)

If you want a job outside of academia, you might ask around to see if the faculty member has landed students such jobs/is supportive of students finding jobs outside academia.

Retaining your sanity

Your advisor is someone that you will need to talk to, and therefore someone that you can be honest with. As a corollary, your advisor should be someone you aren't scared of. Here are some examples of things that you might want to be honest with your advisor about:

what you do and don't know mathematically,
whether you find a project interesting
what your career goals are
crises/events in your life that may affect your work (wedding, break-ups with a long term partner, death in the family, etc.).
what you can and can't handle (though do try first)

Your advisor should serve as your advocate to the department. If you are ever caught in a situation where it becomes necessary for someone to stand up for you -- for example, TA issues, department political issues -- your advisor should be someone who can do that.

Finally, every advisor has a different working style with their students. For example, some advisors meet with their students every week; others once a month; others once every two months. What is the style that suits you best? Some advisors like to give their students projects and reading; other advisors would rather have students find their own projects, and make a point of not suggesting problems early on. Some advisors prefer their students to work independently, others will expect their students to collaborate. When considering advisor choices, keep the following in mind:

Pick someone who will be available to answer your questions and talk to you about your work.
Pick someone you think you can work with.
Is this someone you can be honest with about what you do and don't know, etc. ?
Ask if former students were happy with their relationship with the advisor.
Is this someone you can communicate with? (Do you understand when they try to explain something to you; do they understand what you ask when you have a question?)

What if I can't find the perfect person?

It may or may not be possible to find a person that matches every criterion you have for the perfect advisor. You should prioritize your criteria: is finding a job the most important thing? Or do you need a supportive advisor who can get you through grad school in the first place? Is your candidate advisor good at placing students in academia and/or industry?

How do I propose to them to be my advisor?

Once you've found a good match, ask that person to be your advisor. One way to do this: during an appointment, ask "I was wondering if you could be my thesis advisor" -- yes, it can be that simple! Be aware of possible constraints like sabbatical timing.

A final note on retaining one's sanity

Have you ever torn yourself to bits wondering why a friend hasn't returned your phone call for two weeks, imagining all sorts of scenarios where you might have slighted this friend or otherwise ired this friend, only to find out that your friend had gone on a vacation and in the last minute rush of packing forgotten to tell you about this?

Remember that your advisor is human too, and moreover that they have duties other than being your advisor: classes to teach, other students to advise, committees to serve on, committees to chair, perhaps a family to parent. Just because they don't answer your emails, or seem a little out-of-it or moody during a meeting doesn't mean they've suddenly decided you aren't worth their time. It may mean that they have lots of stuff to think about. Your relationship with your advisor, just like your relationship with many other people, isn't a life-or-death situation -- you are both human. On the same token, if you haven't been able to see them for a long time, and they haven't answered your emails, it may be worth finding out why (instead of imagining grand hypotheses on why you are a bad student...) and seeing if other students are experiencing the same thing.

It is okay, and even encouraged, to seek out other faculty members! Sometimes your advisor is the best person to talk to. Sometimes your advisor isn't. A former student once said that she liked to talk to a particular set of four professors: "one for the weird explanation", "one for the standard explanation", "one for the quick explanation", and "one for the clear explanation." The first one described her advisor.

What do I do in advisor meeting?

This probably depends on your advisor.

Some advisors will assign reading and ask their students to present a coherent summary of it to them when they meet; others might be surprised if you try this. (If this is something that you know you will benefit from, you should go ahead and do it, and then they won't be surprised the next time.) Some advisors will quiz you on that reading.

Some advisors won't assign reading, and expect you to find reading material for yourself. You could choose to summarize what you've read to them, or tell them what you are reading and ask for related references and problems.

If you've written some sort of program or think you've proven something, you should let your advisor know.

What might be expected from you, in the advisor/advisee relationship

The best way of finding out what an advisor expects of their students is to ask them. They should be more than happy to tell you.

Here are some things that were taken from the UC Davis Graduate Council Mentoring Guidelines (a great document!)

As partners in the mentoring relationship, graduate students have responsibilities. As mentees, students should:

Be aware of their own mentoring needs and how they change through their graduate tenure. Graduate students should discuss these changing needs with their mentors.
Recognize that one faculty member may not be able to satisfy all of a student's mentoring needs. Seek assistance from multiple individuals/organizations to fulfill the mentoring roles (described in the Mentoring Guidelines ) .
Recognized that their mentoring needs must respect their mentor's other responsibilities and time commitments.
Maintain and seek regular communication with their mentors, especially their major professor.