Book:T.S. Blyth/Set Theory and Abstract Algebra

Subject Matter

 * Set Theory
 * Abstract Algebra

Contents

 * Set Theory and the Natural Numbers
 * Sets; inclusion; intersection; union; complementation; number systems
 * Sets of sets
 * Ordered pairs; cartesian product sets
 * Relations; functional relations; mappings
 * Induced mappings; composition; injections; surjections; bijections
 * Indexed families; partitions; equivalence relations
 * Order relations; ordered sets; order isomorphisms; lattices
 * Equipotent sets; cardinal arithmetic; $$\N$$
 * Recursion; characterisation of $$\N$$
 * Algebraic Structures and the Number System
 * Laws of composition; semigroups; morphisms
 * Groups; subgroups; group morphisms
 * Embedding a cancellable abelian semigroup in a group; $$\Z$$
 * Compatible equivalence relations on groups; quotient groups; isomorphism theorems; cyclic groups
 * Rings; subrings; compatible equivalences on rings; ideals; ring morphisms
 * Integral domains; division rings; fields
 * Arithmetic properties in commutative integral domains; unique factorisation domains; principal ideal domains; euclidean domains
 * Fields of quotients of a commutative integral domain; $$\Q$$; characteristic of a ring; ordered integral domains
 * Archimedean, Cauchy complete and Dedekind complete ordered fields; $$\R$$
 * Polynomials; $$\C$$