Preface Chapter I.Preliminaries-Groups and Rings 1. Introduction to Groups 2. Quotient Groups and Sylow Subgroups 3. Finite Abelian Groups and Solvable Groups 4. Introduction to Rings 5. Factoring in F[x] Chapter II. Field Extensions 1. Simple Extensions 2. Algebraic Extensions 3. Splitting Fields and Normal Extensions Chapter III. The Galois Correspondence 1. The Fundamental Correspondence 2. The Solvable Correspondence Chapter IV. Applications 1. Constructibility 2. Roots of Unity 3. Wedderburn's Theorem 3. Dirichlet's Theorem and Finite Abelian Groups Appendix A - Groups 1. Group Actions and the Sylow Theorems 2. Free Groups, Generators and Relations Appendix B - Factoring in Integral Domains 1. Euclidean Domains and Principal Ideal Domains 2. Prime and Irreducible Elements 3. Unique Factorization Domains Appendix C - Vector Spaces 1. Subspaces, Linear Independence and Spanning 2. Bases and Dimension Bibliogr
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