MATH 4361 - Modern Algebra I

3 Class Hours 0 Laboratory Hours 3 Credit Hours
Prerequisite: A grade of “C” or better in MATH 2390 or MATH 3390.
This course is an introduction to fundamental abstract algebraic structures, focusing on groups and monoids. Strong emphasis will be on theory, proofs, and the generalization and abstraction of familiar notions of equivalence, identities, inverses, and binary operations. Topics include: basic properties of groups, subgroups, normal subgroups, isomorphisms, homomorphisms, quotient groups, Lagrange’s Theorem, as well as permutation, dihedral, and cyclic groups. Selected topics such as finitely-generated Abelian groups, group actions, Cayley graphs, and automorphism groups may be discussed.