### 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 three preliminary exams and two core courses (described below). The exams are officially referred to as “the written part of the qualifying exam”.
- Pass an oral exam (called general 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 and Core Course Requirements

#### General information

Students entering the Mathematics PhD program in Fall 2017 or later need to pass three prelim exams and get a grade B or better in two core courses, chosen from one of the options below (prelims are indicated by the course for that prelim).

Pure Mathematics

- Three prelims from Math 5111, Math 5120, Math 5210 and Math 5310.
- Two core courses from Math 5111, Math 5120, Math 5160, Math 5210, Math 5211, Math 5260, Math 5310, and Math 5360.

Applied Mathematics

- Three prelims from Math 5111, Math 5120, Math 5310, Math 5410 and Math 5510.
- Two core courses from Math 5111, Math 5120, Math 5310, Math 5160, Math 5410, Math 5440, Math 5510, and Math 5520.

In this requirement, a core course is any course in the list except for prelim courses that correspond to prelims the student passed. For example, if a student completes the Pure Math prelim requirements by passing the Real Analysis (Math 5111), Algebra (Math 5210), and Topology (Math 5310) prelims, then Complex Analysis (Math 5120) or Abstract Algebra II (Math 5211) may count as a core course, but Abstract Algebra I (Math 5210) may not. Students cannot mix and match different requirements from the different tracks, so they should consult with their advisors upon arrival about which track to take. A student is considered to have passed this requirement after doing so from either track.

For core courses, instructors are expected to have a rigorous assessment of students’ performance.

#### Timeframe and Progress Requirements

Students are expected to pass at least one prelim exam after each semester for the first three semesters of their graduate study and finish all prelim exam requirements by the beginning of the spring semester in their second year and finish all core course requirements by the end of their second year of graduate study. Failure to meet the requirements could result in a loss of funding for the following year.

#### 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. 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, but students are not encouraged to take prelim exams without proper preparation. While a student is allowed to take a prelim exam without taking the corresponding prelim course, this should be discussed with an advisor if it is after the first semester.

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.

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 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.