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Contemporary Abstract Algebra

By Joseph A. Gallian

9th Edition © 2017
Discipline:Mathematics
Course:Post-Calculus
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CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students.

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About this product

CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students.

A good mixture of now more that 1750 computational and theoretical exercises appearing in each chapter and in Supplementary Exercise sets that synthesize concepts from multiple chapters.

"Why Is Abstract Algebra Useful?" essay on the author’s website shows students the importance of studying abstract algebra and its applicability to everyday life. This motivational essay can be incorporated into a lesson on the first day of class, or can serve as a motivational tool further along in the course.

Coverage of proof writing is provided on the instructor’s website in the updated essay "Advice for students learning proofs." This essay provides basic guidance for students encountering proof writing for the first time or needing to freshen their skills.

This text focuses on abstract algebra as a contemporary subject, with concepts and methodologies currently being used by computer scientists, physics, and chemists.

Table of contents

Chapters

PART I: INTEGERS AND EQUIVALENCE RELATIONS.
Preliminaries. Properties of Integers. Complex Numbers. Modular Arithmetic. Mathematical Induction. Equivalence Relations. Functions (Mappings). Exercises.
PART I!: 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.
PART III: 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.
PART IV: FIELDS.
19. Vector Spaces.
20. Extension Fields.
21. Algebraic Extensions.
22. Finite Fields.
23. Geometric Constructions.
PART V: SPECIAL TOPICS.
24. Sylow Theorems.
25. Finite Simple Groups.
26. Generators and Relations.
27. Symmetry Groups.
28. Frieze Groups and Crystallographic Groups.
29. Symmetry and Counting.
30. Cayley Digraphs of Groups.
31. Introduction to Algebraic Coding Theory.
33. Cyclotomic Extensions.
Show more

1. Introduction to Groups.

Symmetries of a Square. The Dihedral Groups. Exercises. Biography of Neils Abel

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