Abstract Algebra I: Group Theory


Empire State College

  • Semester
    Fall 2021
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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. 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. 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 was previously SMT-274404 Abstract Algebra 1: Group Theory.
Course Area: Mathematics
Level: Upper Level Undergraduate
Dates: 09-07-2021 - 12-17-2021
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Instructor: TBD
Local Course ID: 21FA_ESC_MATH4010_01
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