Contemporary Abstract Algebra, Tenth Edition

For more than three 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.

The author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to 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. Applications are included to illustrate the utility of the abstract concepts.

Examples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The exercises often foreshadow definitions, concepts, and theorems to come.

Changes for the tenth edition include new exercises, new examples, new quotes, and a freshening of the discussion portions. 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, including computer exercises, that synthesize concepts from multiple chapters
• Approximately 300 worked-out examples from routine computations to the challenging
• Many applications from scientific and computing fields and everyday life
• Historical notes and biographies that spotlight people and events
• Motivational and humorous quotations
• Numerous connections to number theory and geometry

While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual written by the author has comprehensive solutions for all exercises and some alternative solutions to develop a critical thought and deeper understanding. It is available from CRC Press only. The Student Solution Manual has comprehensive solutions for all odd-numbered exercises and many even-numbered exercises.

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.