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Ph.D. Degree Programs

The UCSD Mathematics Department admits students into the following Ph.D. programs:

In addition, the department participates in the following Ph.D. programs:

For application information, go to How to Apply (Graduate).
 

Ph.D. in Mathematics

The Ph.D. in Mathematics allows study in pure mathematics, applied mathematics and statistics. The mathematics department has over 60 faculty, approximately 100 Ph.D. students, and approximately 35 Masters students. A list of the UCSD mathematics faculty and their research interests can be found at here. The Ph.D. in Mathematics program produces graduates with a preparation in teaching and a broad knowledge of mathematics. Our students go on to careers as university professors, as well as careers in industry or government.

In the first and second years of study, Ph.D. students take courses in preparation for three written qualifying examinations (quals). One qual must be taken in Algebra or Topology, and another in Real or Complex Analysis. A third qual may be taken in Numerical Analysis or Statistics or one of the remaining topics in the first two groups. All three quals must be passed by the start of the third year. After the qualifying exams are passed, the student is expected to choose an advisor and follow a course of study agreed on by the two of them. At this point, the student chooses a thesis topic, finds a doctoral committee and presents a talk on his or her proposed research topic. If the committee is satisfied with this talk, the student has "Advanced to Candidacy." The student will then pursue their research agenda with their advisor until they have solved an original problem. The student will submit a written dissertation and reconvene his or her committee for a Final Defense. At the Final Defense, the student gives a seminar talk that is very similar to a talk that he or she might give for a job interview.

Nearly every admitted Ph.D. student gets financial support. The financial support is most commonly in the form of a Teaching Assistantship, however, Research Assistantships and other fellowships are also available.

Because of the large faculty to student ratio, graduate students have many opportunities to interact with faculty in courses or smaller research seminars. The graduate students also run their own "Food for Thought" seminar for expository talks as well as a research seminar where they give talks about their research.

UCSD has excellent library facilities with strong collections in mathematics, science, and engineering. Ph.D. students are provided with access to computer facilities and office space.

Full-time students are required to register for a minimum of twelve (12) units every quarter, eight (8) of which must be graduate-level mathematics courses taken for a letter grade only. The remaining four (4) units can be approved upper-division or graduate-level courses in mathematics-related subjects (MATH 500 may not be used to satisfy any part of this requirement). After advancing to candidacy, Ph.D. candidates may take all course work on a Satisfactory/Unsatisfactory basis. Typically, students should not enroll in MATH 299 (Reading and Research) until they have passed at least two Qualifying Examinations at the PhD or Provisional PhD level, or obtained approval of their faculty advisor.
 

Written Qualifying Examinations

Students in the Ph.D. program are required to pass a set of written qualifying exams. Full information on the qualifying exams may be found here. 

 

Master's Transferring to Ph.D.

Any student who wishes to transfer from masters to the Ph.D. program will submit their full admissions file as Ph.D. applicants by the regular closing date for all Ph.D. applicants (end of the fall quarter/beginning of winter quarter). It is the student's responsibility to submit their files in a timely fashion, no later than the closing date for Ph.D. applications at the end of the fall quarter of their second year of masters study, or earlier. The candidate is required to add any relevant materials to their original masters admissions file, such as most recent transcript showing performance in our graduate program. Letters of support from potential faculty advisors are encouraged. The admissions committee will either recommend the candidate for admission to the Ph.D. program, or decline admission. In the event of a positive recommendation, the Qualifying Exam Committee checks the qualifying exam results of candidates to determine whether they meet the appropriate Ph.D. program requirements, at the latest by the fall of the year in which the application is received. For students in the second year of the master's program, it is required that the student has secured a Ph.D. advisor before admission is finalized. An admitted student is supported in the same way as continuing Ph.D. students at the same level of advancement are supported. Transferring from the Master's program may require renewal of an I-20 for international students, and such students should make their financial plans accordingly. To be eligible for TA support, non-native English speakers must pass the English exam administered by the department in conjunction with the Teaching + Learning Commons.
 

Foreign Language Requirement

There is no Foreign Language requirement for the Ph.D. in Mathematics.
 

Advancement to Candidacy

It is expected that by the end of the third year (9 quarters), students should have a field of research chosen and a faculty member willing to direct and guide them. A student will advance to candidacy after successfully passing the oral qualifying examination, which deals primarily with the area of research proposed but may include the project itself. This examination is conducted by the student's appointed doctoral committee. Based on their recommendation, a student advances to candidacy and is awarded the C. Phil. degree.
 

Dissertation and Final Defense

Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the Ph.D. degree is awarded. When the dissertation is substantially completed, copies must be provided to all committee members at least four weeks in advance of the proposed defense date. Two weeks before the scheduled final defense, a copy of the dissertation must be made available in the Department for public inspection.
 

Time Limits

The normative time for the Ph.D. in mathematics is five (5) years. Students must be advanced to candidacy by the end of eleven (11) quarters. Total university support cannot exceed six (6) years. Total registered time at UCSD cannot exceed seven (7) years.
 

Ph.D. Program Time Limits
By Fall of the beginning of the 3rd year Pass Qualifying Exams
By the end of 9 quarters Find thesis advisor
By the end of 12 quarters Advance to Candidacy
By the end of the 5th year Final Defense


It may be useful to describe what the majority of students who have successfully completed their Ph.D. and obtained an academic job have done. In the past some students have waited until the last time limit before completing their qualifying exams, finding an advisor or advancing to candidacy. We strongly discourage this, because experience suggests that such students often do not complete the program. Although these are formal time limits, the general expectation is that students pass two qualifying exams, one at the Ph.D. level and one at the masters level by the beginning of their second year. (About half of our students accomplish this.) In the second year, a student begins taking reading courses so that they become familiar with the process of doing research and familiarize themselves with a number of faculty who may serve as their advisor. In surveying our students, on average, a student takes 4 to 5 reading courses before finding an advisor. Optimally, a student advances to candidacy sometime in their third year. This allows for the fourth and fifth year to concentrate on research and produce a thesis. In contrast to coursework, research is an unpredictable endeavor, so it is in the interest of the student to have as much time as possible to produce a thesis.

A student is also a teaching assistant in a variety of courses to strengthen their resume when they apply for a teaching job. Students who excel in their TA duties and who have advanced to candidacy are selected to teach a course of their own as an Associate Instructor. Because there are a limited number of openings to become an Associate Instructor, we highly recommend that you do an outstanding job of TAing in a large variety of courses and advance to candidacy as soon as possible to optimize your chances of getting an Associate Instructorship.

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