Student Solutions Manual for Gallian's Contemporary Abstract Algebra

10th Auflage
ISBN: 978-0-367-76680-1
Verlag: CRC Press

Buch, Englisch, 137 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 222 g

Reihe: Textbooks in 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.

Autoren/Hrsg.

Gallian, Joseph A

Fachgebiete

• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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.

Über Autor(innen)

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.