REU Site: Combinatorics, Number Theory, and Graph Theory

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The University of West Georgia campus, in Carrollton, Georgia, will be the site of a Research Experiences for Undergraduates program for eight weeks during the summers of 2014, 2015, and 2016. Eight students will be invited each year, with one student coming from within the University of West Georgia by means of a competitive selection process. The program will be led by Professors Bruce Landman and Abdollah Khodkar, and involve research in the areas of combinatorics, number theory, and graph theory. The research problems will stem from the main areas of interest of the two faculty mentors, combinatorial Ramsey theory and graph theory. The problems presented to students will represent active and recent areas in these disciplines. Both graph theory and the area of combinatorial number theory are well-suited for the undergraduate student to begin the exploration into their own research activities, as very minimal background is needed to work on the problems. Furthermore, these are relevant, active areas of mathematical research with many applications and connections to other branches of the mathematical sciences.The participants will work in teams of two or three students, with each student being a member of two different teams. The program will include weekly seminars in which the students will give presentations concerning the problems they are working on and their progress on these problems. The students will be encouraged and guided, incrementally over the 8-week period, toward more independent work. However, demonstration of the value of effective communication among the students, working in small teams on research problems, will be one of the main goals of the program. The program is designed to introduce the students to mathematical research, and to give them the ability to pose and prove original conjectures, to learn independently, to collaborate with others on research projects, and to effectively communicate their findings, both orally and in writing. The program is intended to help prepare students for graduate study or employment in a mathematical career.