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Abstract Algebra: An Introduction is set apart by its thematic development and organization. The chapters are organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. New to this edition is a "groups first" option that enables those who prefer to cover groups before rings to do so easily.
- Extensively revised to include an alternate path allowing instructors to cover Rings before Groups as in previous editions OR Groups before Rings.
- For the benefit of beginners, the proofs early in the book are broken into clearly marked steps, each of which is carefully explained and proved in detail.
- There are many more examples and exercises than in the previous edition: There are about 350 examples and 1600 exercises (18% of which are new).
- The text may be used for either courses that cover rings before groups (as in earlier editions) OR courses that cover groups before rings.
- The flexible design of this text makes it suitable for courses of various lengths and different levels of mathematical sophistication.
- The chapters are organized around two themes, arithmetic and congruence, that are developed first for the integers and then for rings, polynomials, and groups.
- The emphasis throughout is on clarity of exposition.
2. Congruence in Z and Modular Arithmetic.
4. Arithmetic in F[x].
5. Congruence in F[x] and Congruence-Class Arithmetic.
6. Ideals and Quotient Rings.
8. Normal Subgroups and Quotient Groups
9. Topics in Group Theory.
10. Arithmetic in Integral Domains.
11. Field Extensions.
12. Galois Theory.
13. Public-Key Cryptography.
14. The Chinese Remainder Theorem.
15. Geometric Constructions.
16. Algebraic Coding Theory.
17. Lattices and Boolean Algebras (available online only).
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. www.cengage.com/solutionbuilder.
Complete Solutions Manual
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