Textbooks in Mathematics
2 total works
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.
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.
Student Solutions Manual for Gallian's Contemporary Abstract Algebra
by Joseph A Gallian
Whereas many partial solutions and sketches for the odd-numbered exercises appear in the book, the Student Solutions Manual, written by the author, has comprehensive solutions for all odd-numbered exercises and large number of even-numbered exercises. This Manual also offers many alternative solutions to those appearing in the text. These will provide the student with a better understanding of the material.
This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Tenth Edition and is designed to supplement that text.
Table of Contents
Integers and Equivalence Relations
0. Preliminaries
Groups1. 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
Rings12. 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 Fields
Fields19. Extension Fields
20. Algebraic Extensions
21. Finite Fields
22. Geometric Constructions
Special Topics23. 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
Biography
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.