Abstract Algebra II

Catalog description

The first four main components of this course are an axiomatic continuation and a more in-depth study of the components of Abstract Algebra I: (i) groups; (ii) homomorphism and isomorphisms; (iii) rings; and (iv) fields, with concentration on the latter two. The fifth component is special topics (chosen by the instructor) that may include Sylow Theorems, Finite Simple Groups, Generators and Relations, Frieze Groups and Crystallographic Groups and Algebraic Coding Theory. After successfully completing this course, students will be able to: (1) Prove properties of an algebraic system working from basic axioms in each of the five components. (2) Use theorems and techniques to solve problems in each of the five components. (3) Solve problems involving a standard set of examples in each of the five components. (4) Identify real-world applications of abstract algebra and solve problems related to those applications.