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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.
1. Arithmetic in Z Revisited. 2. Congruence in Z and Modular Arithmetic. 3. Rings. 4. Arithmetic in F[x]. 5. Congruence in F[x] and Congruence-Class Arithmetic. 6. Ideals and Quotient Rings. 7. Groups. 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).
Posted September 3, 2002
I find that this book needs many more explicit examples for each section and subsection, as well as better and more descriptive solutions to the exercises. As a self study guide, one will get lost and desperate easily. Text is good to read, but again more explanations is needed. A better preference would be Dummit Foote Abstract Algebra, which feels very complete and detailed but may have too many topics that one wants to give up on the subject. I bought both books to study abstract algebra and group theory on my own in my spare time.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.