Modern Algebra I

An introduction to abstract algebra with a focus on group theory, including the following topics: Binary operations; semigroups and monoids; submonoids; inverses in monoids; groups; subgroups; various examples of groups, monoids, and semigroups; the integers modulo n; direct products; the order of an element; cyclic groups; isomorphisms and homomorphisms; Cayley's Theorem; cosets and Lagrange's Theorem; normal subgroups and congruence; quotient groups; kernels; the universal property of the quotient group; the First Isomorphism Theorem for groups; rings and ring homomorphisms (definitions and examples). Credit cannot be held for both this course and 62:331.