REU Site: Combinatorics, Number Theory, and Graph Theory

位于佐治亚州卡罗尔顿的西乔治亚大学校区将在2014年、2015年和2016年夏季为本科生提供为期八周的研究体验项目。每年将邀请八名学生，其中一名学生通过竞争性选拔程序来自西乔治亚大学。该计划将由布鲁斯·兰德曼教授和阿卜杜拉·霍德卡尔教授领导，涉及组合学、数论和图论领域的研究。研究问题将源于两位导师的主要兴趣领域，组合拉姆齐理论和图论。呈现给学生的问题将代表这些学科中活跃的和最新的领域。图论和组合数论领域都非常适合本科生开始探索他们自己的研究活动，因为研究这些问题需要非常少的背景知识。此外，这些都是相关的、活跃的数学研究领域，与数学科学的其他分支有许多应用和联系。参与者将以两到三名学生为一组，每个学生是两个不同团队的成员。该计划将包括每周一次的研讨会，在研讨会上，学生们将就他们正在研究的问题以及他们在这些问题上的进展进行演讲。在8周的时间里，学生们将得到鼓励和引导，朝着更独立的方向发展。然而，展示学生之间有效沟通的价值，在小团队中研究问题，将是该计划的主要目标之一。该项目旨在向学生介绍数学研究，并使他们能够提出和证明原创猜想，独立学习，在研究项目上与他人合作，并有效地口头和书面交流他们的发现。该计划旨在帮助学生为研究生学习或在数学职业生涯中就业做好准备。

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.