Modern Algebra: An Introduction, 5th Edition

by John R. Durbin (The Univ. of Texas, Austin)

• ISBN13: 9780471433354
• ISBN10: 0471433357
• Edition: 5th
• Format: Hardcover
• Copyright: 2004-05-01
• Publisher: Wiley

Summary

This text is appropriate for any one-semester junior/senior level course in Modern Algebra, Abstract Algebra, Algebraic Structures, or Groups, Rings and Fields. Durbin has two main goals: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas. The first six chapters present the core of the subject; the remainder are designed to be as flexible as possible. Durbin covers groups before rings, which is a matter of personal preference for instructors. The course is mostly comprised of mathematics majors, but you will find engineering and computer science majors as well.

Table of Contents

1. Mappings and Operations.

2. Introduction to Groups.

3. Equivalence. Congruence. Divisibility.

4. Groups.

5. Group Homomorphisms.

6. Introduction to Rings.

7. The Familiar Number Systems.

8. Polynomials.

9. Quotient Rings.

10. Field Extensions.

11. Galois Theory.

12. Geometric Constructions.

13. Applications of Permutation Groups.

14. Symmetry.

15. Cryptography. Algebraic Coding.

16. Lattices and Boolean Algebras.

Appendix A: Sets.

Appendix B: Proofs.

Appendix C: Mathematical Induction.

Appendix D: Linear Algebra.

Appendix E: Solutions to Selected Problems.

Index.