## Advanced Modern Algebra Third Edition, Part 1 by Joseph J. Rotman

Advanced Modern Algebra Third Edition Contents Preface to Third Edition: Part 1 xi Acknowledgments xiv Part A. Course I 3 Chapter A-1. Classical Formulas 4 Cubics 6 Quartics 9 Chapter A-2. Classical Number Theory 9 Divisibility 16 Euclidean Algorithms 19 Congruence 29 Chapter A-3. Commutative Rings 41 Polynomials 47 Homomorphisms 55 Quotient Rings 62 From Arithmetic to Polynomials 74 Maximal Ideals and Prime Ideals 83 Finite Fields 89 Irreducibility 97 Euclidean Rings and Principal Ideal Domains 104 Unique Factorization Domains Chapter A-4. Groups 115 Permutations 116 Even and Odd 123…

## Elements of Modern Algebra Seventh Edition By Linda Gilbert and Jimmie Gilbert

Contents Preface ……………….. xi 1 Fundamentals ……………….. 1 1.1 Sets ……………….. 1 1.2 Mappings ……………….. 12 1.3 Properties of Composite Mappings (Optional) ……………….. 25 1.4 Binary Operations ……………….. 30 1.5 Permutations and Inverses ……………….. 37 1.6 Matrices ……………….. 42 1.7 Relations ……………….. 55 Key Words and Phrases ……………….. 62 A Pioneer in Mathematics: Arthur Cayley ……………….. 62 2 The Integers ……………….. 65 2.1 Postulates for the Integers (Optional) ……………….. 65 2.2 Mathematical Induction ……………….. 71 2.3 Divisibility ……………….. 81 2.4 Prime Factors and Greatest Common Divisor ……………….. 86 2.5 Congruence…