### Overview of Requirements

The Ph.D. program is open to students who have a broad mathematical background and who have demonstrated ability and evidence of special aptitude for research in mathematics in their prior work. Students with B.S. or B.A. degrees can apply directly to the Ph.D. program.

To graduate with a Ph.D. in Mathematics, a student must satisfy all of the following requirements:

- Course Credits: 45 credits are required (including 15 doctoral dissertation research credits/GRAD 6950) or if you get a master’s degree in mathematics at UConn then 30 credits are required (including 15 doctoral dissertation research credits) beyond the master’s degree.
- Pass four preliminary exams. These exams are officially referred to as “the written part of the qualifying exam”.
- Pass an oral exam. This exam is the “oral part of the qualifying exam”, and is meant to further the student’s education, scholarship and professional development. It should cover material in the broad area in which the student intends to write a dissertation, but should not focus on the actual thesis research. The student is expected to present the material he/she has studied, and to answer questions about that material. The exam is prepared by the student’s advisory committee, and is normally taken at the end of the third year or beginning of the fourth year.
- Satisfy the language requirement.
- Write a dissertation under the direction of a member of the Graduate Faculty. The Gradaute School has required specifications for the dissertation.
- Thesis templates (for LaTex) are available on our Thesis Formatting page.

### Preliminary Examination

#### General information

Mathematics Ph.D. students may choose one of the options below as the set of courses on which they are to be examined:

- Pure Mathematics: Math 5111, 5120, 5210 and 5310.
- Applied Mathematics: Math 5111, 5120, 5410 and 5510.

Students may mix these options or request a substitution of one other graduate mathematics course for one of the above courses. The philosophy of these options is that the Department wants its students to be knowledgeable in the basic mathematical subjects in the student’s area of study. Therefore, substitution of a course will only be permitted if that course is critical to the student’s plan of study. The substitution must be approved by the Graduate Program Committee and the student’s advisor.

#### Timeframe and Progress Requirements

Students will be expected to take the exams according to the following schedule:

- By the beginning of the 3rd semester students are expected to pass at least 2 prelim exams; by the beginning of the 5th semester students are expected to pass at least 4 prelim exams. Under special circumstances (e.g. students entering in the Spring) the Graduate Program Committee may allow the student extra time to fulfill these requirements. The written portion of the preliminary exams will be administered every year, shortly before each semester (i.e. in August, January, or both), based on approved student’s requests. A request for a prelim has to be submitted before the end of the previous semester to the Graduate Program Director (with a copy sent to the student’s advisor).
- There is no limit on the number of times prelim exams can be taken, but if the same exam is failed two times, the student must petition the Graduate Program Committee in order to sit for further attempts at that prelim.
- No later than the fifth semester, to remain in good standing, each student is expected to find a Ph.D. advisor.

It is strongly recommended that students take at least 5 prelim courses during the first 5 semesters, unless the advisor has a different study plan.

The continued support of a student who failed to meet these expectations is contingent on approval, by the student’s advisor and the Graduate Program Committee, of a petition by the student, and on availability of funds.

#### The Philosophy behind Prelims

The role of prelims is distinct from the role of final examinations in undergraduate courses. Prelims, as comprehensive examinations, require the student to gather together knowledge, skills and insights from diverse mathematical areas. Traditionally, exams in different areas are given during short time periods, which forces the students to study different areas concurrently. The desired effect, proved over the years, is for students to develop a sense of mathematical ideas that span the discipline and, thereby, to prepare the student for independent research.

The UConn implementation of the prelims requires students to take two or more exams after one year of study. Among the reasons to do so, is to start the process of students being actively involved in mathematics and to speed along those students with unusually strong preparation. Contrast is drawn here with the passive activity of taking courses.

Well prepared entering students are encouraged to take prelim exams before the first semester. If a student passes a prelim exam without taking the corresponding prelim course (for example, if she passes in August when she first arrives), this prelim pass also counts as a prelim course pass.

Graduate study in mathematics is a rigorous enterprise and requires a sincere commitment. The faculty has a responsibility both to the student body at large and to the profession to maintain adequate standards for the Ph.D. degree. Piecemeal passing of prelims over an extended number of years is not, in the opinion of this committee, generally compatible with the goals of a mathematics Ph.D. program.

In some cases the Graduate Program Committee may recommend the student to take the corresponding prelim course again if the same exam is failed two times and, in general, students are not encouraged to take prelim exams without proper preparation. Students, with the approval of the Graduate Program Committee, may be permitted to take the prelims during or beyond the third year of study under either of the following circumstances: a clearly defined individualized course of study has been established for a student with a non-standard background or life circumstances which preclude the usual progress toward degree; it has been demonstrated, on previous tries and/or in course work, that the candidate should be afforded an unusual opportunity.

At times, individual circumstances will dictate that the pace and/or content of the doctoral program should be altered. The Graduate Program Committee welcomes petitions from students and/or their advisors which will recognize the students’ individual interests, backgrounds and goals, within the constraints established by the Graduate School, the College and the Department.

#### Past Exams

The Department maintains a collection of past prelims going back to August 2000. Students are encouraged to peruse these in preparation for their own examinations.

#### Language Requirements

All PhD students must satisfy the Graduate School’s Related Area and/or Foreign Language Requirement. This requirement can be met in one of two ways. A PhD student can demonstrate appropriate reading knowledge of mathematics in Russian, German, French or Chinese. Most often this demonstration is done through a doctoral reading exam, although there are a number of different options. Alternately, with the approval of a PhD student’s advisory committee, the student may take six credits of related area coursework. The courses must be approved by the advisory committee, be at least 4000 level and be outside the Math Department.