Book of Abstract Algebra (Dover Publications Inc.)

Chapter 1 Why Abstract AlgebraChapter 2 OperationsChapter 3 The Definition of GroupsChapter 4 Elementary Properties of GroupsChapter 5 SubgroupsChapter 6 FunctionsChapter 7 Groups of PermutationsChapter 8 Permutations of a Finite SetChapter 9 IsomorphismChapter 10 Order of Group ElementsChapter 11 Cyclic GroupsChapter 12 Partitions and Equivalence RelationsChapter 13 Counting CosetsChapter 14 HomomorphismChapter 15 Quotient GroupsChapter 16 The Fundamental Homomorphism TheoremChapter 17 Rings: Definitions and Elementary PropertiesChapter 18 Ideals and HomomorphismChapter 19 Quotient RingsChapter 20 Integral DomainsChapter 21 The IntegersChapter 22 Factoring into PrimesChapter 23 Elements of Number Theiory (Optional)Chapter 24 Rings of PolynomialsChapter 25 Factoring PolynomialsChapter 26 Substitution in PolynomialsChapter 27 Extensions of FieldsChapter 28 Vector SpacesChapter 29 Degrees of Field ExtensionsChapter 30 Ruler and CompassChapter 31 Galois Theory: PreambleChapter 32 Galois Theory: The Heart of the MatterChapter 33 Solving Equations by RadicalsAppendix A Review of Set TheoryAppendix B Review of the IntegersAppendix C Review of Mathematical Integers Answers to Selected Exercises Index