The Department offers the degree of Doctor of Philosophy in Mathematical Sciences in three areas of concentration: Pure Mathematics, Applied Mathematics, and Statistics. This document focuses on the first two: Pure and Applied Mathematics. A reference to a document on the PhD degree in Statistics is found in the next paragraph. Research interests of the Mathematics faculty include: 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.

The Department also supports Master’s degree programs in Mathematics, Statistics, and Biostatistics as well as Doctoral and Master’s degree programs in Complex Systems and Data

Why choose UVM?

  • Our Department is large enough to offer classes and research experiences in a broad range of mathematical subjects, while small enough to give students ample opportunity to interact with our active research faculty. 
  • We offer a variety of graduate classes, as well as flexible independent studies. For example, graduate students take classes in:
    • Applied mathematics: complex systems, differential equations, Fourier analysis, mathematical modeling, mathematical biology, numerical analysis,…
    • Pure mathematics: algebra, real/complex analysis, combinatorics, cryptography, geometry, number theory, algebraic and computational topology, topological data analysis, …
  • We have a regular Department Colloquium and regular seminars, such as the Combinatorics Seminar and the Quebec-Vermont Number Theory Seminar, as well as seminars in related departments, such as complex systems, computer science, engineering, physics and statistics.
  • Burlington, Vermont has been ranked as a top college town by the New York Times. Find out more about living in Burlington here.

Admission Requirements

  • Bachelor's degree with a major in mathematics or a closely related discipline (e.g., statistics, engineering, or physics, with a substantial mathematics foundation).
  • Please review the Application Instructions for graduate admission to UVM. The information listed below supplements some of the general instruction on that page. 
  • The is no GRE score requirement. However, if you have taken the GRE test(s), we encourage you to submit your official score(s). 
  • Resume/CV is required
  • No Writing Sample is required. 
  • Please try to contain your Statement of Purpose to about 600 words, which is approximately one page. 
  • It is required that you address the following two aspects in this document:
    1. Which of the Department faculty you plan on doing your thesis with (you may include more than one faculty member here), and 
    2. How your background has prepared you for that.

Your statement about being interested to work with particular faculty member(s) will not constitute a commitment to do so; you will be free to explore the opportunities to work with any of our faculty as your thesis advisor if you join UVM. However, your being specific in your narrative will help the Admissions Committee to select candidates who can best fit into our program. 
You may also include any other information about yourself that you consider relevant, such as your teaching and research experience. We encourage you to emphasize specific facts rather than make generic or emotional statements. 

  • An application fee will not be waived based only on financial constraints of the applicant. It can be waived in two circumstances:
    1. Please see the link to Application Fee Waiver Requests in Application Instructions by UVM. 
    2. In addition, the Department of Mathematics & Statistics will provide a very limited number of application fee waivers. To be considered for this highly selective pool of applicants, please send to the Graduate Program Director, Dr. T.I. Lakoba,  the following documents by December 20 as separate pdf files: 
    • An unofficial copy of your academic transcript;
    • An unofficial copy of your general GRE score (which is not required for fee-paying applicants);
    • And a draft of the Statement of Purpose addressing the two requirements listed in its description above. (It does not need to contain anything except your answers to those two questions.);
    • International applicants must provide an unofficial copy of their English Proficiency examination. 

Applicants for the Application Fee Waiver by the Department will be notified of the decision by January 15. 

  • International students are to satisfy English Proficiency requirements; further information can be found on this webpage
  • The application deadlines are found on this webpage (click on the link for Mathematical Sciences). 
  • Everyone applying for Fall admission will be automatically considered for financial support in the form of Graduate Teaching Assistantship. No financial support is available for Spring admission.  
  • All applications must be completed online.

University-wide Requirements for the Doctor of Philosophy degree

UVM requirements for the Doctor of Philosophy Degree

Requirements specific to Doctoral degree in Mathematical Sciences

  • A total of at least 75 credit hours as combination of course work 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.

More information can be found in the Mathematics Graduate Handbook

Graduate Teaching Assistantship and Comprehensive fee

  • The majority of Graduate Teaching Assistants (GTA) teach for 9 months (September – May); their stipend is $20,958 for the 2021/22 Academic Year. In exceptional cases, an experienced GTA may be assigned to teach in the Summer, in which case their stipend will be proportionally increased.
  • Graduate Teaching Assistantship also covers 9 credit hours of tuition per semester and also the Student Health Insurance premium.
  • Information on tuition and fees is found on this website. In particular, all graduate students are required to pay a Mandatory comprehensive fee, which covers access to the UVM gymnasium and medical and mental health services; in the 2022/23 Academic Year it will be $1018 per semester. 

Please the Mathematics Graduate Director, Dr. T.I. Lakoba, if you have any questions or would like further information.