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

For nearly four decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.

Students will learn how to do computations and write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop, but rarely do.

Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The hallmark features of previous editions of the book are enhanced in this edition. These include:

• A good mixture of approximately 1900 computational and theoretical exercises appearing in each chapter that synthesizes concepts from multiple chapters • Back-of-the-book skeleton solutions and hints to odd-numbered exercises

• Over 300 worked-out examples ranging from routine computations to the more challenging

• Links to interactive True/False questions with comments

• Links to computer exercises that utilize interactive software available on the author’s website, stressing guessing and making conjectures

• Many applications from scientific and computing fields, as well as some from everyday life

• Numerous historical notes and biographies that spotlight the people and events behind the mathematics • Motivational and humorous quotations

• Hundreds of figures, photographs, and tables

Changes to the eleventh edition include new exercises, examples, biographies, and quotes, and an enrichment of the discussion portions. These changes

accentuate and enhance the hallmark features that have made previous editions of the book a comprehensive, lively, and engaging introduction to the subject.

While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual offers solutions for all the exercises. A Student’s Solution Manual has comprehensive solutions for all odd-numbered exercises, many even-numbered exercises, and numerous alternative solutions as well

Table of Contents

0. Preliminaries

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

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

19. Extension Fields

20. Algebraic Extensions

21. Finite Fields

22. Geometric Constructions

23. Sylow Theorems

24. Finite Simple Groups

25. Generators and Relations

26. Symmetry Groups

27. Symmetry and Counting

28. Cayley Digraphs of Groups

29. Introduction to Algebraic Coding Theory

30. An Introduction to Galois Theory

31. Cyclotomic Extensions

Selected Answers

About the Author

Joseph A. Gallian earned his PhD from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition, he has served terms as the Second Vice President, and the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in the national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.