Ph.D. in Mathematics
General Information
Degree Requirements
Course Credits
- Total requirement: 45 credits, including 15 doctoral dissertation research credits (GRAD 6950).
- Course level: All courses must be 5000-level or above.
- Field study option: MATH 5850 – Graduate Field Study Internship, if taken, must be included in the Plan of Study and may count toward research.
- With a prior UConn master’s in mathematics: Only 30 credits are required, including 15 doctoral dissertation research credits.
Core Courses & Prelims
- Pass three preliminary exams ("prelims") and two core courses (see below).
- Pass at least one preliminary exam after each semester (strongly recommend two in August) for the first three semesters.
- Complete all preliminary exam requirements by the start of the spring semester of the second year.
- Complete all core course requirements by the end of the second year.
General/Oral Exam
- Must be passed before the fourth year begins (by the end of year three).
- Public portion: A 50-minute presentation on a broad area related to the intended dissertation. The talk should not focus on the candidate’s own research; original results, if any, may be presented briefly at the end.
- Private portion: Only the candidate and the advisory committee are present. The committee will ask questions about the presentation topic and the candidate’s major field of study before deciding on the outcome.
Dissertation
- Write, defend, and submit the dissertation.
- Specifications: See Dissertation Information for details.
- Formatting support: Thesis templates (LaTeX) are available on the Thesis Formatting page.
Preliminary Exams
Thesis in Pure Mathematics
Pass 3 prelims from the following list:
- Math 5111/Measure and Integration
- Math 5120/Complex Function Theory
- Math 5210/Abstract Algebra
- Math 5310/Introduction to Geometry and Topology I
Thesis in Applied Mathematics
Pass 3 prelims from the following list:
- Math 5111/Measure and Integration
- Math 5120/Complex Function Theory
- Math 5310/Introduction to Geometry and Topology I
- Math 5410/Introduction to Applied Mathematics I
- Math 5510/Numerical Analysis and Approximation Theory I
Thesis in Actuarial Science
Pass both of the following prelims:
- Math 5160/Probability Theory and Stochastic Processes I
- Math 5639/Actuarial Loss Models
Pass 1 additional prelim from the following list:
- Math 5111/Measure and Integration
- Math 5120/Complex Function Theory
- Math 5210/Abstract Algebra
- Math 5310/Introduction to Geometry and Topology I
- Math 5410/Introduction to Applied Mathematics I
- Math 5510/Numerical Analysis and Approximation Theory I
Core Courses
Thesis in Pure Mathematics
Pass 2 courses from the following list in addition to prelim courses:
- Math 5111/Measure and Integration
- Math 5120/Complex Function Theory
- Math 5160/Probability Theory and Stochastic Processes I
- Math 5210/Abstract Algebra I
- Math 5211/Abstract Algebra II
- Math 5250/Linear Algebra
- Math 5260/Mathematical Logic I
- Math 5310/Introduction to Geometry and Topology I
- Math 5360/Differential Geometry
- Math 5440/Partial Differential Equations
Thesis in Applied Mathematics
Pass 2 courses from the following list in addition to prelim courses:
- Math 5111/Measure and Integration
- Math 5120/Complex Function Theory
- Math 5310/Introduction to Geometry and Topology I
- Math 5160/Probability Theory and Stochastic Processes I
- Math 5250/Linear Algebra
- Math 5410/Introduction to Applied Mathematics I
- Math 5440/Partial Differential Equations
- Math 5510/Numerical Analysis and Approximation Theory I
- Math 5520/Finite Element Solution Methods I
Thesis in Actuarial Science
Pass 2 courses from the following list in addition to prelim courses:
- Math 5111/Measure and Integration
- Math 5120/Complex Function Theory
- Math 5161/Probability Theory and Stochastic Processes II
- Math 5210/Abstract Algebra I
- Math 5211/Abstract Algebra II
- Math 5250/Linear Algebra
- Math 5310/Introduction to Geometry and Topology I
- Math 5360/Differential Geometry
- Math 5410/Introduction to Applied Mathematics I
- Math 5440/Partial Differential Equations
- Math 5510/Numerical Analysis and Approximation Theory I
- Math 5520/Finite Element Solution Methods I
Advising
After arriving at UConn, each student in the Ph.D. program is assigned a initial advisor. The initial advisor assists the student in choosing courses and guides them towards successfully passing their prelim requirements (see below).
By the middle of the third year, each student chooses a thesis advisor (also called a major advisor). The thesis advisor directs the student in their research, meeting with them regularly and offering constructive feedback. It is possible to have two co-major advisors.
The student, in consultation with the major advisor, will also select an advisory committee, consisting of the thesis advisor and at least two associate advisors (also need two if there are co-major advisors).
The major advisor(s), and at least one of the associate advisors, must be members of the Graduate Faculty.
Timeline of Milestones
First Year
- Complete at least 5 courses.
- Pass two prelims — one in January after the fall semester; and preferably two in August after the spring semester.
Second Year
- Pass your final prelim in or before January (before the start of the spring semester).
- Complete all core courses by the end of spring semester.
- Begin looking for your thesis advisor — attend seminars, learn about available research areas, take independent studies, and chat with faculty about their interests.
- Begin preparation for your general/oral exam.
Third Year
- Have a thesis advisor by no later than the end of the fall semester.
- Which courses to take are now up to you and your advisor, including GRAD 6950/Doctoral Dissertation Research credits.
- Make a plan with your advisor about your general/oral exam, and take the exam by the end of the summer (before the Fall semester begins).
Fourth Year
- Focus on obtaining results for your thesis.
- Ensure that you are on track to complete 30 course credits and 15 GRAD 6950/Doctoral Dissertation Research credits.
- Submit Dissertation Proposal
- Plan of Study can be submitted (or in final year)
Final Year
- Apply for Graduation and submit Plan of Study in Student Admin by the fourth week of the final semester.
- Announce Defense, Defend and Upload Thesis, Submit Approval Page and complete Survey of Earned Doctorates (more information).
- Update diploma information in Student Admin (more information).
Teaching & Financial Support
Graduate Assistantships
Most supported graduate students in Mathematics are Graduate Assistants (GAs). Within this category, students are assigned as either:
- Teaching Assistants (TAs) – primary form of support, usually offered with admission to the PhD program.
- Research Assistants (RAs) – based on availability of individual faculty and research funds.
TA Expectations
Teaching Assistants typically start teaching discussion sections. After some experience, TAs will likely be assigned a course as instructor of record.
All TAs have opportunities to gain training and experience.
- Training: First-year TAs must take MATH 5000 (Pedagogy in Mathematics), a one-credit course in the fall.
- Experience: TAs generally begin with lower-level or service courses, and some may advance to upper-division courses. This experience strengthens the CV for academic jobs.
- Duration: GA support is normally available for up to five years, contingent on continued availability of funds, departmental needs and policies, satisfactory progress in degree program, satisfactory job performance, and eligibility as provided in the Graduate Catalog. Extensions beyond five years are reviewed individually.
Pay Scales
Graduate Assistant pay depends on academic progress and credentials:
- Level 1 (Beginner): Entry with a bachelor’s degree and fewer than 30 UConn graduate credits.
- Level 2 (Master’s): Entry with a relevant master’s degree or 30+ UConn graduate credits.
- Level 3 (P.h.D): For students who have passed required general/oral exam.
See the Graduate Payroll Pay Scales website for current rates.
GAANN Fellowship Program
UConn mathematics Ph.D. students can apply for the Graduate Assistance in Areas of National Need (GAANN) Fellowship Program. Supported by the U.S. Department of Education and administered by the UConn Department of Mathematics, this program awards three-year grants to five Ph.D. students annually who demonstrate academic excellence, financial need, and a commitment to pursuing a doctoral degree in mathematics.
Other Opportunities
- Summer TA Positions — teaching roles during summer terms (must be in Connecticut to hold these positions).
- Predoctoral Fellowships — a limited number of fellowships are awarded to selected PhD students who have passed their preliminary exams, completed their oral exam, and are actively working on their dissertation.
- Graduate School Fellowships and Awards
- External Funding Opportunities