Student Solutions Manual for Gallian's Contemporary Abstract Algebra

Joseph A. Gallian

• Publisher: Chapman and Hall/CRC
• Year: 2021
• ISBN:
  9781000403589
• Edition: 10
• Topic: Mathematics
• Subtopic: Abstract Algebra
• Index: Mathematics

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
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
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 Fields
Fields 19. Extension Fields
20. Algebraic Extensions
21. Finite Fields
22. Geometric Constructions
Special Topics 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

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.

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• 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