Mathematics 321. Abstract Algebra
This course is an introduction to the study of abstract algebra. We begin with sets, and operations on those sets, that satisfy just a few basic properties and deduce many more properties, creating an impressive body of knowledge from just these few initial ideas. We use this approach to focus on structures known as groups. Symmetry, permutation groups, isomorphisms and homorphisms, cosets and factor groups will be covered, as well as an introduction to rings, domains and fields. A secondary focus will be developing the student’s ability to write rigorous and well-crafted proofs.