Contemporary abstract algebra / Joseph A. Gallian, University of Minnesota Duluth.

Includes indexes.

Includes bibliographical references.

Part 1. Integers and equivalence relations -- Preliminaries -- Part 2. Groups -- 1. Introduction to groups -- 2. Groups -- 3. Finite groups; subgroups -- 4. Cyclic groups -- 5. Permutation groups -- 6. Isomorphisms -- 7. Cosets and Lagrange's Theorem -- 8. External direct products -- 9. Normal subgroups and factor groups -- 10. Group homomorphisms -- 11. Fundamental theorem of finite Abelian groups -- Part 3. Rings -- 12. Introduction to rings -- 13. Integral domains -- 14. Ideals and factor rings -- 15. Ring homomorphisms -- 16. Polynomial rings -- 17. Factorization of polynomials -- 18. Divisibility in integral domains -- Part 4. Fields -- 19. Vector spaces -- 20. Extension fields -- 21. Algebraic extensions -- 22. Finite fields -- 23. Geometric constructions -- Part 5. Special topics -- 24. Sylow theorems -- 25. Finite simple groups -- 26. Generators and relations -- 27. Symmetry groups -- 28. Frieze groups and crystallographic groups -- 29. Symmetry and counting -- 30. Cayley digraphs of groups -- 31. Introduction to algebraic coding theory -- 32. An introduction to Galois Theory -- 33. Cyclotomic extensions.

his book is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. The text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.