This grant is for an Research Experiences For Undergraduates site for 4 students at Moravian College during the summer. The project will offer the undergraduates an opportunity for mathematical study and research by providing them a graduate school type experience. The Principal Investigator will supervise a seminar throughout the entire eight weeks of the program. Initially the seminar will introduce necessary background material, and gradually the students will become actively involved in the seminar, giving talks on outside readings as well as doing their own research. The student research projects have been chosen so that they are accessible to undergraduates. The main focus of the project is in the area of explicit reciprocity laws in algebraic number theory. Each student's research topic will relate to this central problem but focus on a particular aspect which may be chosen from one of the following: finite fields, polynomials and algebraic functions in one variable over finite fields, reciprocity maps, and explicit factorization of certain polynomials.
