＊ABSTRACT ALGEBRA: AN INTRODUCTION is intended for a first undergraduate course in modern abstract algebra. Its flexible design makes it suitable for courses of various lengths and different levels of mathematical sophistication, ranging from a traditional abstract algebra course to one with a more applied flavor. The book is organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups, so students can see where many abstract concepts come from, why they are important, and how they relate to one another. New Features: ＊A groups-first option that enables those who want to cover groups before rings to do so easily. ＊Proofs for beginners in the early chapters, which are broken into steps, each of which is explained and proved in detail. ＊In the core course (chapters 1-8), there are 35% more examples and 13% more exercises.

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).

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, Tenth Edition (Pearson, 2011; with M. Lial and J. Holcomb); and CONTEMPORARY PRECALCULUS: A GRAPHING APPROACH, Fifth Edition (Brooks/Cole, 2009; with D. Shaw).

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