Text: Algebra and Geometry, (Cambridge University Press, 2005) by Alan F. Beardon.
Catalog description: Exploration of groups, symmetry, and permutations. This course is especially designed for the MAT program, and will not satisfy the requirements of other mathematics degree programs.
Content: This course is designed especially for students in the MAT program at the University of Idaho. Our goal is to explore connections between geometry and modern abstract algebra, specifically group theory. We will not assume any previous knowledge of group theory, but will provide a brief development of the tools we need. Our goals include developing an understanding of the symmetries of two- and three-space from an algebraic perspective, and also proving Burnside's Theorem -- a surprisingly powerful tool for counting the number of possible arrangements of geometric objects.
Prerequisites: None formally (beyond admission to the MAT program). You should probably have some experience with writing mathematical proofs.
Grades:
Exams: The four exams follow lectures 9, 19, 29, and 39 and each exam focuses on material from the nine-or-ten lectures since the previous exam. They are not comprehensive. The format of the exams is as follows:
Homework: There are four sets of homework problems -- one due with each exam. Most of the problems are from the text. Some comments: