Some mathematics doctoral students come to UC San Diego with the desire to work under a certain professor, and they end up doing exactly that. Most other students merely have an idea of what area of mathematics they want to emphasize and with whom they would like to work.
One new graduate student was sure that he wanted to pursue probability. After learning about the research areas of faculty members in the Department of Mathematics, he narrowed his list of preferred advisors down to two people. When he wanted to take a reading course, though, one of those two professors was away on sabbatical. When he read with the only remaining professor, he found the material interesting. The next quarter, he asked that faculty member to be his advisor.
Another graduate student came to the Department thinking that he wanted to focus on numerical analysis. During his first year, he took “Applied Statistics” (MATH 282 sequence) on a whim, and found that he had an intuition for it. The instructor noticed this as well, and suggested that the student take a reading course with him the following fall quarter. By winter quarter of his second year, he had a faculty advisor.
The choice of faculty advisor should be made carefully after getting to know the professor(s) whose research interests are a good match for yours.
Current graduate students encourage new students to take reading courses early and in subjects that they might not have considered before. You may be surprised to find that you are intrigued with an area of mathematics that you otherwise would have dismissed. Even if you feel confident about the area that you would like to pursue, take reading courses with as many faculty members who work in that area as possible to see which personalities you get along with and which you do not.
Be aware that just because you took reading courses with a faculty member does not in itself make that person your advisor. You still need to complete the necessary paperwork. One student thought he had an advisor because he had taken three reading courses with a certain professor. When it came time to fill out the paperwork, the student was stunned to learn that the professor did not want to be his advisor.
Below is a rough timeline for how your search for a faculty advisor should progress.
International Ph.D. students need to advance to candidacy before the beginning of their third year because they will NOT be establishing California residency after their first year in the program. International students will be charged non-residential supplemental tuition until they advance to candidacy.
Think of each professor you meet as a potential advisor. Probably you will be busy taking qualifying examinations in your first year, but it is important to remember that qualifying examinations are not your last hurdle in earning a Ph.D. The reason you are in the program is to write a thesis, and that requires having a faculty advisor. Looking for an advisor in your first year will make life easier later. Consider taking a seminar or two in an area of interest in addition to preparatory coursework for the qualifying examinations. You need something to fill the third course in your schedule each quarter anyway (since full-time students must take 12 units of coursework per quarter), and seminars will prepare you for reading courses.
There is no penalty for asking a faculty member for a problem or for direction in a field during your first year. A professor may be impressed with your zeal and hand you a paper, problem, or book. You should not expect most faculty to pay attention to you until you have passed a few qualifying examinations, but students who have shown some initiative may be directed into research or further study during the summer.
You need not solve the first problem that you are handed, and do not be afraid to ask for another one if you are having a lot of trouble with it. The main purpose of this is to get some experience approaching problems in a particular area of mathematics and learning tools to attack specific problems. This will direct your career at UC San Diego in a way that aimlessly taking courses does not. If at all possible, involve yourself in the summer activities of the Department such as seminars, reading groups, or talks.
Most of your qualifying examination work should be done by this time. That is, you should have completed two of your three qualifying examinations. (If you had to spend your summer studying for an examination rather than working with a faculty member, that is ok.) Provided you are only taking one qualifying examination in your second year, you should be actively looking for an advisor. If you are not careful, that one sequence of qualifying courses (to prepare you for the examination) can consume your time; you need to schedule time to do other things as well. In fall quarter, it is a good idea to take seminars with the goal of a reading course in the winter or spring quarters. A good idea is to sign up for three or four seminars that seem even remotely interesting during fall quarter, and keep the one or two that you like best.
Do a reading course with a faculty member in an area of interest to you. That person will not necessarily end up as your advisor, which is why it is important to start early. If you are interested in an area that does not have a qualifying examination, it is possible that professor will suggest that you take a course (or sequence thereof) when you ask for a reading course. If that is the case, try to start a reading course as soon afterwards as possible.
If you have found an area and a potential advisor, ask if you can do a reading course over the summer with the advisor. The professor may even have some money to help you with funding during the summer.
By your third year, you should be reading seriously with someone. The Department encourages students to advance to candidacy at the end of third year; the middle of the fourth year is the absolute latest, but it is not recommended, since it leaves you only one year to write your thesis. By advancing early, you also give yourself more opportunities for being an Associate Instructor.
The following advice is from a previous Department of Mathematics graduate vice chair, Ron Evans:
We single out the act of finding a thesis advisor, because this is one of the critical transition points where students often drop out of the grad program. This happens mainly due to lack of correct information about graduate studies. Most students think of grad studies as a continuation of undergrad studies, but there is a distinct difference. The difference is that as a grad student you get to have one on one time with a professor who will guide you to work on research problems that are not known to very many people in the world. The privilege to work one on one with a faculty member is why we limit the number of students we can admit into the PhD program.
At UCSD, the main way to find a thesis advisor is to take reading courses with several of the math professors. On average, students take 4-5 reading courses before finding a compatible thesis advisor. Usually, the student has taken the basic graduate courses so that he or she has enough background to look at advanced material. Then he or she meets with a faculty person and requests an opportunity to take a reading course. Reading courses are ways to spend time with the faculty person. They can take on several forms- you may read a book or research paper and meet with the professor where the professor goes over the material you have read. Or you may give talks in a seminar and meet with the professor to help you prepare the talk. Or the professor may give you talks on subjects that do not appear anywhere in the literature.
The professor attempts to match your research interests with the topics of the reading course. You need to be thinking about several issues- Are the topics covered in the reading course of interest to you? Could you perhaps find a problem worthy of a thesis by working on these problems? How well do you work with the professor? The professor is also thinking about how compatible he or she would be with you. If the professor were to accept you as a student there is a commitment to meet with you fairly frequently. The professor is looking to see if you are a self starter or if you need lots of assistance to get you working The professor is also gauging your interest in the problems suggested because you need to demonstrate some drive to be able to solve these problems.
It might be useful to describe how some students drop out of the PhD program due to not finding a thesis advisor. Sometimes students think you just pick an advisor and that person is automatically your thesis advisor. Several students have taken a couple reading courses with a professor and then assumed that person was the student’s thesis advisor. There actually has to be an agreement between professor and student that you are their student. The professor then sends an email to the Graduate Program Coordinator, or to the Graduate Vice Chair, Ron Evans, confirming this.
Some students take one reading course and then decide that since they are not compatible with that professor, they drop out of the program. In reality, you need to get to know at least 3 professors, ideally through reading courses. These 3 faculty will be part of your dissertation committee and eventually will write letters of recommendation for your job. Most faculty here at UCSD are eager to help work with you in reading courses. Actually at many other universities, many professors are unwilling to accept many students.
Another way to find a thesis advisor is to attend the seminars. There are numerous seminars going on that you can attend. I encourage you to begin talking to grad student who are also attending the seminars. They are often the students who have already found thesis advisors and they can give you some useful information about what it is like to work with some of the professors in this field. If you have already decided on a field of interest, you might talk to me as I am aware of which faculty have PhD students and which faculty might be looking to take on students.