An Abstract Algebra Research Project: How many solutions does x^2 + 1 = 0 have?
An Abstract Algebra Research Project: How many solutions does x2 + 1 = 0 have?
Abstract of article: This paper describes the implementation of a student research project in an abstract algebra class and includes the rationale for incorporating a research project, the process of developing a successful research question, guidelines for implementation in the classroom, and a description of outcomes. The project centered on the title question and provided a concrete setting for investigating the connections between polynomial equations, matrix rings, modular integers, unique factorization, and roots of -1.
About the author: Suzanne Doree is an Associate Professor and Chair of the Mathematics Department at Augsburg College in Minneapolis, Minnesota, where she has taught since 1989. She earned her Ph.D. in character theory from the University of Wisconsin - Madison. Her research interests include curriculum and materials development and directing undergraduate student research. She enjoys teaching mathematics at all levels, using pedagogies that support active learning, and teaching mathematical thinking, writing, and speaking skills.