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.

Part 1 The Core Course 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 Part 2 Advanced Topics 9. Topics in Group Theory 10. Arithmetic in Integral Domains. 11. Field Extensions. 12. Galois Theory. Part 3 Excursions and Applications 13. Public-Key Cryptography. 14. The Chinese Remainder Theorem. 15. Geometric Constructions. 16. Algebraic Coding Theory. Part 4 Appendices

Thomas W. Hungerford received his M.S. and Ph.D. from the University of Chicago. He has taught at the University of Washington and at Cleveland State University, and is now at St. Louis University. His research fields are algebra and mathematics education. He is the author of many notable books for undergraduate and graduate level courses. These include: ALGEBRA (Springer Verlag, Graduate Texts in Mathematics #73, 1974); ABSTRACT ALGEBRA: AN INTRODUCTION, Second Edition (Harcourt, 1997); MATHEMATICS WITH APPLICATIONS, Eighth Edition (Addison-Wesley, 2003; with M. Lial); and CONTEMPORARY PRECALCULUS: A GRAPHING APPROACH, Fourth Edition (Brooks/Cole, 2004).

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