Abstract Algebra I: Group Theory ((4 Credits))

Catalog description

In this upper level study, students explore the theory and applications of the algebraic structures known as groups. In addition, group theory will be used to develop the skill in proofs and abstraction that are essential to further study of higher mathematics. Topics covered in this course include: an introduction to the abstract idea of a group; example groups; subgroups and cyclic subgroups; permutations and Cayley’s Theorem; cosets, normal groups and their relationship to homomorphisms; and Lagrange's Theorem. Relevant topics from those courses are logic, proofs, if and only if proofs, proof by induction, equivalence relations, properties of functions such as one to one and onto, and matrix operations. These topics will be used extensively. This course contains elements which rely on vision to complete. If you have a visual impairment and are considering registering for this course, it is recommended that you reach out to Accessibility Resources and Services ([email protected]) in advance of registration to determine if this course is appropriate and what alternatives may be available. This course was previously SMT-274404 Abstract Algebra 1: Group Theory. Prerequisites: It is assumed that students are acquainted with logic and the construction of proofs, usually from having completed a study in at least two out of three of the following topics: Discrete Math, Proofs, and Linear Algebra.