Ph.D. in Mathematics

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”.
  • Student is expected to choose a thesis advisor no later than the end of the fall semester in their third year.
  • Submit Plan of Study prior to the oral (general) 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.
  • Write a dissertation under the direction of a member of the Graduate Faculty. The Graduate School has required specifications for the dissertation here.
    (More generally, this page has useful information.)
  • 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

Applied Mathematics

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.

Time Frame 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.

Plan of Study

Your committee must be established prior to completing the Plan of Study for PhD.  This should be done before or at the same time as the general (oral) exam, but at the very latest, in the first four weeks of your final semester.

Language Requirement – The Language Requirement was waived by the Graduate Program committee starting in Fall 2020.

General/Oral Exams, Dissertation Proposal and Applying for Graduation

The doctoral General Exam usually is undertaken when the student has completed at least 75% of the content coursework listed on the approved Plan of Study.   The student should not take the General Exam before the Plan of Study has been approved.

The Dissertation Proposal for Doctoral Degree must be submitted at least six months before your expected date of degree completion and must be fully approved at least three months prior to the date of your defense.  After approval of the committee, the form must be submitted to the Director of Graduate Studies, who must find two reviewers to read the proposal and provide feedback prior to signing the form.

Instructions for applying for graduation in Student Admin. Applications must be made during the first four weeks of your last semester.

Update your diploma (DIPL) address in Student Admin:   In Self-Service/Student Center/Personal Information choose “addresses” in the pull down menu.   Select “ADD A NEW ADDRESS” and fill in the form.  Once you hit, OK, check “DIPL addr” and SAVE.  Also update any other address, if applicable.   NOTE:  It takes approximately three months to get your diploma.