MATHEMATICS GRADUATE
STUDENT HANDBOOK
UCSD Mathematics

Finding a Faculty Advisor

Aside from passing qualifying exams and completing a dissertation, one of your most important tasks as a PhD student is to find a doctoral advisor. Though there are plenty of steps you can take at the beginning of graduate school to jump-start the process, most of the work involved in securing an advisor usually takes place between the “pass your qualifying exams” and the “advance to candidacy” milestones. This period of time is both challenging and rewarding, as it is the point at which you begin to develop some autonomy as a researcher ⎼ not just a student learning material for assignments or tests. This section of the handbook offers some tips and best practices for navigating this process.

Disclaimer: Some students enter graduate school knowing exactly with whom they would like to work and even possibly on what they would like to work. Other students enter graduate school with only a very vague idea of their interests and need to do lots of exploring before making a decision. Most students enter somewhere in between. As a result, the process of finding an advisor varies widely from student to student. The following tips and best practices correspond roughly to what is “typical” or generally desirable, so don’t worry too much if your timeline is a bit different. When in doubt, reach out to older students, your course advisor, or other familiar faculty for guidance.

Before Passing Your Qualifying Exams

Typical/desirable: Years 1 and 2

Required: before beginning of Year 3

Of course, the first milestone of math graduate school at UCSD is passing your qualifying exams. Before you have done so, it is technically your primary focus and will therefore likely take up most of your time. However, there are many things you can do in your first and second years to help yourself to secure an advisor down the line. Consider, for example, the following.

Attend seminars. You may have heard and tried to implement this advice before, and you may have perceived it as pointless because you had trouble understanding more than the first few minutes of each talk. This is perfectly normal at the beginning of graduate school. Therefore, if you view the primary goal of seminar attendance as “to learn about research going on in [insert relevant discipline],” then it is often correct to say that attending seminars is pointless before you have gained lots of additional experience. However, this is not necessarily the primary reason to attend seminars at the beginning of graduate school. Here are other reasons to keep in mind.

  • You will meet and/or become familiar with the UCSD faculty in the seminar’s discipline.
  • You will meet and/or become familiar with older students in the seminar’s discipline.
  • By listening to more and more talks ⎼ even if you can only appreciate the first few minutes ⎼ you will slowly develop a rough understanding of the basic objects of interest to the seminar’s discipline.
  • Post-seminar lunches (if applicable) are a good way to interact with faculty and older students outside the classroom and official meetings.

So do not worry if you don’t always understand very much from seminars you attend. (Indeed, other audience members may understand even less than you sometimes!) Just the exposure can be helpful. That being said, however, there is also a seminar that is specifically geared toward first and second year graduate students looking for advisors: the Graduate Colloquium (MATH 296). You are strongly encouraged to attend the Graduate Colloquium, as it is a perfect way to get a feel for what research is happening in the department and which professors are actively looking for students.

Read about professors’ research online. Even if most of your time is devoted to your classes and studying for qualifying exams, you can occasionally browse faculty members’ webpages for information about their research. When doing so, try to focus initially on the introductions to papers and to expository material. As with seminars, it is not important that you understand the results of each paper you read; it is more important to get the lay of the land. The following, for example, are good questions to ask yourself when you are browsing a professor’s papers.

  • What sorts of objects are interesting to this professor?
  • What sorts of tools does the professor seem to use frequently?
  • With whom does this professor work? Do you recognize any names?
  • Which books or expository papers does the professor cite frequently?

Figuring out even vague answers to these questions can give you many more directions for your independent reading and learning. This process can be very helpful, for instance, for narrowing down the list of professors with whom you would like to pursue a reading course.

Talk to professors and older students. If you are interested in a professor’s research and would like to learn more, then send them an email or drop by their office hours if there are no students there. If you are nervous or unsure about this, then keep the following in mind.

  • You can ask your course advisor or graduate mentor (if you have one) for advice.
  • You can ask for advice or information from the graduate student Point Person for the research area in which the professor works. (For UCSD’s math research areas and the professors therein, please visit https://math.ucsd.edu/research/.) The Point Person will either know the professor personally or will be able to put you in contact with another student who does know the professor.
  • Your first email to a professor does not need to contain a dissertation proposal. A simple expression of interest and request for a meeting suffices. For example:

“Dear Professor Thought,

“I hope this message finds you well. My name is Jeff, and I am a first year PhD student here at UCSD. I have been looking recently at some of your research ⎼ particularly your proof of the Riemann Hypothesis ⎼ and I am interested in learning more. Would you be willing to meet with me sometime soon?

“Thank you for your time!

“Best wishes,

“Jeff”

  • Along similar lines, you do not have to come to your first meeting with a professor prepared with a dissertation proposal. The following will suffice:
    • a concise description of your background,
    • a clear and honest description of your interests (if you are not sure about your interests, then that’s ok ⎼ give your most genuine description), and
    • a question or two to help guide the meeting (e.g., Would you be willing to give a beginner-friendly explanation of your research interests? Are you open to taking students in the near future? Which courses do you recommend I take before considering the possibility of a reading course?).

Finally, do not forget to use older students as a resource. They recently went through this process and have valuable “insider info.”

 

After Passing (Most) Qualifying Exams, before Advancing to Candidacy

Typical/desirable: Years 2 and 3

Required: before end of Year 4

Take reading courses. Reading courses (MATH 299) are the best tools for “advisor shopping” at UCSD. These can certainly be done before passing all of your qualifying exams, but it is often helpful or necessary to have one or two ⎼ or at least a couple of quarters of qualifying exam course material ⎼ under your belt before you begin. Once you’ve gotten some fundamentals out of the way, however, you should start asking professors in whose work you are interested if they would be willing to supervise a reading course with you. Deciding on a topic may seem like a daunting task, but do not worry; there are plenty of ways reading courses naturally occur.

  • There may be some topic necessary to understand a professor’s research about which there is no UCSD course.
  • There may be a group of students already planning a reading course in which you are interested.
  •  You may have come across a topic in one of your courses that you wish to pursue further.
  • A professor may have some projects in mind for graduate students, in which case the professor may have a plan and resources to ease a new student into work.
  • Your background and interests may leave you ready to work on a problem straight away, in which case this would be the purpose of the reading course.

If none of these apply to your situation, then seek some advice about your next steps from your graduate student mentor (if you have one), your course advisor, or other familiar faculty.

Start working on research. Often research projects will emerge somewhat naturally from reading courses. Other times, reading courses will serve as background in order to prepare you to work on certain problems a professor might have in mind. Whatever the case, you will slowly transition from “learning” in a traditional, linear way to “doing research” in a more independent, nonlinear, uncertain way. This transition can be difficult. Here are some things that may help you smooth it out.

  • Identify blocks of time to work on research during which you free yourself of distractions. (Turn off your phone, for instance.) Research is not assignment-driven, so it is difficult to measure progress in terms of tasks. But making sure you devote a specific amount of time to your research each week can go a long way in keeping you on track.
  • Document your work. If you learn or figure out something, then write it down, even if you are not sure it is relevant. This is not only a good way to track progress, but it also allows you to see that even when you get stuck, you are still doing research and making progress. Finally, writing things down forces you to articulate your ideas well; this can identify potential issues in your arguments before they become a big problem.
  • Jot down questions ⎼ for your advisor or for your future self ⎼ as they arise. These are easy to forget, and it can be very frustrating to leave a meeting with your advisor and then shortly after remember an important question you meant to ask.
  • Spend plenty of time not doing math. Exercise. Sleep enough. Have fun with your friends. Eat healthily. As cliché as it may sound, these things will make you more productive ⎼ not hold you back ⎼ in your research.
  • Discuss the struggles you face with your friends and mentors. All graduate students get stuck and tired, and it can be very helpful to share these feelings with people who understand.

Consider personalities and work habits. Though your interest in your research topic is of significant importance, it can be argued that “chemistry” with your potential advisor is of utmost importance. Suppose you are considering Professor Thought as your advisor. Then you should consider the following questions before making the final decision.

  • Is Professor Thought’s advising style compatible with your working habits? More specifically, is Professor Thought too hands-off or hands-on? Do you feel like you need more guidance or access? Do you feel pushed too hard?
  • Is the experience of working or discussing ideas with Professor Thought positive? Do you feel respected by Professor Thought? Do you learn from Professor Thought? Have you felt yourself grow as a mathematician while working with Professor Thought?
  • Does Professor Thought communicate in a timely manner with you? Is Professor Thought available for meetings when you need to discuss something? Does Professor Thought complete necessary administrative tasks in a timely and professional manner?

If these questions raise red flags in your mind, then consider having a discussion with Professor Thought about your concerns. For help strategizing about these matters, talk to your graduate mentor (if you have one) or older graduate student friends of yours; these can be tricky situations, so it is helpful to have lots of different perspectives.

Note on changing advisors/areas: If you begin to work with a faculty member and decide the advising relationship is not the right fit, or you become more interested in another area of research, then it is perfectly acceptable to switch as long as you adhere to the required timeline for advancement to candidacy. For this reason, if you are not initially sure who your advisor will be, then it is a good idea to do reading courses with multiple professors. When the time comes to decide (or you change your mind), be upfront with your plans and expectations. Though this may seem scary, remember that professors want you to do what is best for you.