Program Overview

Ph.D. in Mathematical Sciences

The Department of Mathematics and Statistics at the University of Vermont offers a Ph.D. in Mathematical Sciences, with concentrations in Pure Mathematics, Applied Mathematics, and Statistics.

Program Overview

The Ph.D. program in Mathematical Sciences is designed to provide students with a solid foundation in mathematical sciences, as well as the opportunity to pursue advanced research in their area of interest. The program requires a total of at least 75 credit hours, including coursework and dissertation research.

Concentrations

• Pure Mathematics
• Applied Mathematics
• Statistics

Curriculum

The curriculum for the Ph.D. program in Mathematical Sciences includes:

• A total of at least 75 credit hours as a combination of coursework and dissertation research
• Successful completion of two written qualifying examinations
• A comprehensive examination, consisting of a written and oral presentation, on a topic chosen in consultation with the candidate's research studies committee
• Writing a doctoral dissertation and passing its oral defense

Admissions

Admission to the Ph.D. program in Mathematical Sciences requires:

• A bachelor's degree with a major in mathematics or a closely related discipline
• No GRE score requirement, but scores may be submitted if taken
• Resume/CV is required
• No writing sample is required
• A statement of purpose, addressing the applicant's research interests and goals

Outcomes

Graduating students from the Ph.D. program in Mathematical Sciences should:

• Have a solid understanding of graduate-level real and complex analysis
• Be able to write a clear, precise, and logically rigorous multi-step proof
• Demonstrate mastery of the core mathematical concepts in at least one area of specialty
• Be an expert in their field of research
• Have created original research
• Have successfully taught a semester-long university-level course as the primary instructor
• Be able to formulate new research problems
• Be able to clearly communicate their research both orally and in writing
• Be qualified for a post-doctoral position or for a faculty position at a teaching or research institution

Costs and Funding

Everyone applying for Fall admission will be automatically considered for financial support in the form of a Graduate Teaching Assistantship. No financial support is available for Spring admission. The Graduate Teaching Assistantship includes:

• A stipend of $20,958 for the 2021/22 Academic Year
• 9 credit hours of tuition per semester
• Student Health Insurance premium

Research Areas

The Department of Mathematics and Statistics has research interests in:

• Algebraic geometry
• Algebraic and computational topology
• Arithmetic geometry
• Combinatorics/graph theory
• Complex systems
• Computational social science
• Fourier/harmonic analysis
• Logic
• Mathematical cryptography
• Network science
• Number theory
• Topological data analysis
• Biomathematics
• Fluid mechanics
• Numerical methods for, and analytical theories of, partial differential equations

Related Programs

The University of Vermont also offers related programs in:

• Mathematical Sciences (M.S.)
• Statistics (M.S., AMP)
• Biostatistics (M.S., AMP)