A first study of abstracted algebraic structures including investigation of groups, rings, integral domains, and fields. This study investigates, conjectures, and proves key properties on various concrete and abstracted sets of objects (sets of numbers, permultations, polynomials, matrices, symmetries, etc.) including the division algorithm in the integers, Euclid's Algorithm, unique factorization in the integers, permutations of finite sets, abstracted group properties, subgroup properties, cyclic groups, modular arithmetic, normal subgroups, cosets of subgroups, quotient groups, mappings, group isomorphisms, group homomorphisms, Cayley's Theorem, abstracted ring properties, subring properties, ring homomorphisms, ideals, abstracted integral domain properties, abstracted field properties, and applications to specific sets.

**Credit hours:** 3

Last updated:
05/23/2022