Abstract Algebra with Applications

Front cover
Title
Contents
Preface
1. Preliminaries
2. Groups
3. Subgroups
4. Classification Properties of Groups
5. The Group C*
6. The Groups Z_n*
7. Permutation Groups
8. Isomorphism
9. Direct Products
10. The Fundamental Theorem of Finite Abelian Groups
11. Lagrange’s Theorem
12. Group Homomorphisms
13. Factor Groups
14. Geometric and Matrix Groups
15. An Introduction to Coding Theory
16. Counting
17. Sylow Theorems
18. Lattices of Subgroups
19. Rings and Subrings
20. Classification Properties of Rings
21. Polynomial Rings
22. Ring Homomorphisms
23. Untitled
24. Extension Fields
25. Unique Factorization
26. Polynomial Codes
27. Lattices and Boolean Algebras
28. Introduction to Galois Theory
Appendix: Matrices and Vector Spaces
References
Answers and Suggestions for Selected Exercises
Index