Pre-Analysis & Probability II : Groups, Rings & Fields

This course is about algebraic structures. It includes an introduction to identity, inverse and idempotent elements. We'll see that Boolean conjunction and disjunction can be seen as multiplication and addition and investigate possible additive and multiplicative identities and inverses. This is followed by power sets and basic operations on elements of power sets (union, intersection, complement, difference). All concepts are then combined in a discussion of algebraic structures including groups, rings and fields. We end with Boolean rings and describe set algebra as an example Boolean ring. In the review session we complete an example proof from CH1 of W. Rudin's Principles Of Mathematical Analysis using the axioms of a field.