This book presents an introduction to modern abstract algebra covering the basic ideas of groups, rings, and fields. The first part of the book treats ideas that are important but neither abstract nor complicated, and provides practice in handling mathematical statements - their meaning, quantification, negation, and proof. This edition features a new section to give more substance to the introduction to Galois theory, updated lists of references and discussions of topics such as Fermat's Last Theorem and the finite simple groups.
Mappings and Operations.
Introduction to Groups.
Equivalence. Congruence. Divisibility.
Introduction to Rings.
The Familiar Number Systems.
Application of Permutation Groups.
Lattices and Boolean Algebras.
Photo Credit List.