An Introduction to Abstract Algebra

Abstract algebra is a cornerstone to modern mathematics. Other areas of mathematics heavily depend upon abstract algebra, and abstract algebra is found in a multitude of disciplines. The goal of this textbook is to be a source for a first undergraduate course in abstract algebra. You can download the book via the link below. Content 1. Preliminaries 1.1. Introduction to Abstract Algebra 1.2. Logic and Proof 1.3. Set Theory 1.4. Mappings and Equivalence Relations 2. Group Theory 2.1. Binary Operations 2.2. Introduction to Groups 2.3. Cyclic Groups 2.4. Dihedral Groups 2.5. Groups of Permutations 2.6. Alternating Groups 2.7. Subgroups 2.8. Homomorphisms and Isomorphisms 2.9. Cosets and Normal Subgroups 2.10. Quotient Groups 2.11. Direct Products 2.12. Catalog of Finite Groups 3. Field Theory 3.1. Introduction to Fields 3.2. Polynomials 3.3. Irreduciblity 3.4. Vector Spaces 3.5. Extension Fields 3.6. Algebraic Extensions 3.7. Geometric Constructions 4. Ring Theory 4.1. Introduction to Rings 4.2. Integral Domains 4.3. Ideals 5. Bibliography Sisältö Preliminaries Introduction to Abstract Algebra Logic and Proof Set Theory Mappings and Equivalence Relations Group Theory Binary Operations Introduction to Groups Cyclic Groups Dihedral Groups Groups of Permutations Alternating Groups Subgroups Homomorphisms and Isomorphisms Cosets and Normal Subgroups Quotient Groups Direct Products Catalog of Finite Groups Field Theory Introduction to Fields Polynomials Irreduciblity Vector Spaces Extension Fields Algebraic Extensions Geometric Constructions Ring Theory Introduction to Rings Integral Domains Ideals Bibliography Abstract algebra is a cornerstone to modern mathematics. Other areas of mathematics heavily depend upon abstract algebra, and abstract algebra is found in a multitude of disciplines. You can download the book for free via the link below.