Research Experience for Undergraduates
Mathematics REU: May 29 – July 21, 2017
Students will work on research in groups of three that are each led by a faculty advisor. The research groups will be centered around three exciting areas of mathematical research.
Mentors and Subject Areas:
- Dr. Kassie Archer – Pattern Avoidance
- A permutation is said to avoid a given pattern if there is no subsequence of the permutation in the same relative order as that pattern. This notion of pattern avoidance has been extended to several other combinatorial objects, including set partitions, trees, graphs, etc. We will extend the notion of pattern avoidance to a new set of combinatorial objects and study their properties.
- Dr. Christina Graves – Reliability Polynomials
- The all-terminal reliability polynomial of a graph is the probability that a graph remains connected if each edge is included independently with fixed probability p. This concept can be generalized to the two-terminal reliability polynomial of a graph where we find the probability that two specified vertices remain connected. We will look at all possible graphs on a fixed number of vertices and edges and see if there exists a graph whose two-terminal reliability polynomial is greater than all others.
- Dr. David Milan – Inverse Semigroups
- We will study various ways to build inverse semigroups having interesting and useful algebraic properties. Inverse semigroups are a bit like groups in that they are sets with an associative multiplication and an "inverse" operation. Where groups are naturally represented by permutations, inverse semigroups are represented by partial permutations. That is, any inverse semigroup can realized as a set of bijections on subsets of some fixed set X. Inverse semigroup theory has found a number of applications, including the study of local symmetry present in quasi-crystals, and in the theory of partial isometries on vector spaces (both finite and infinite dimensional).
- A stipend of $4500 for the eight-week program.
- Travel funding to Tyler and partial funding to attend a national conference.
- Free on-campus housing at the Patriot Village or Eagle's Landing apartments, only a short walk from the Mathematics Department facilities in Ratliff Building North.
- Work daily with faculty during the research experience.
- Full access to The University of Texas at Tyler's facilities, including the Herrington Patriot Center (fitness facilities, available at a discounted rate) and the Muntz Library.
- Work closely with faculty in gaining valuable research experience.
- Learn how to write and typeset a professional mathematics article using LaTeX.
- Learn how to prepare and deliver an excellent talk on mathematics.
- Get information on the process of selecting and applying for graduate programs
- Participate in fun team-building social activities. Past activities have included: