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Abstract Algebra

Abstract Algebra - 3rd edition

Abstract Algebra - 3rd edition

ISBN13: 9781577664437

ISBN10: 1577664434

Abstract Algebra by John A. Beachy and William D. Blair - ISBN 9781577664437
Cover type: Hardback
Edition: 3RD 06
Copyright: 2006
Publisher: Waveland Press, Inc.
International: No
Abstract Algebra by John A. Beachy and William D. Blair - ISBN 9781577664437

ISBN13: 9781577664437

ISBN10: 1577664434

Cover type: Hardback
Edition: 3RD 06
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Highly regarded by instructors in past editions for its sequencing of topics as well as its concrete approach, slightly slower beginning pace, and extensive set of exercises, the latest edition of Abstract Algebra extends the thrust of the widely used earlier editions as it introduces modern abstract concepts only after a careful study of important examples. Beachy and Blair's clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student's background and linking the subject matter of the chapter to the broader picture.

Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers.

Table of Contents

Table of Contents

1. Integers

Integers Modulo n

2. Functions

Equivalence Relations

3. Groups

Definition of a Group
Constructing Examples
Cyclic Groups
Permutation Groups
Cosets, Normal Subgroups, and Factor Groups

4. Polynomials

Fields; Roots of Polynomials
Existence of Roots
Polynomials over Z, Q, R, and C

5. Commutative Rings

Commutative Rings; Integral Domains
Ring Homomorphisms
Ideals and Factor Rings
Quotient Fields

6. Fields

Algebraic Elements
Finite and Algebraic Extensions
Geometric Constructions
Splitting Fields
Finite Fields
Irreducible Polynomials over Finite Fields
Quadratic Reciprocity

7. Structure of Groups

Isomorphism Theorems; Automorphisms
Groups Acting on Sets
The Sylow Theorems
Finite Abelian Groups
Solvable Groups
Simple Groups

8. Galois Theory

The Galois Group of a Polynomial
Multiplicity of Roots
The Fundamental Theorem of Galois Theory
Solvability by Radicals
Cyclotomic Polynomials
Computing Galois Groups

9. Unique Factorization

Principal Ideal Domains
Unique Factorization Domains
Some Diophantine Equations


Construction of the Number Systems
Basic Properties of the Integers
Complex Numbers
Solution of Cubic and Quartic Equations
Dimension of a Vector Space

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Other Editions of Abstract Algebra

Abstract Algebra by John A. Beachy - ISBN 9780881338669