Algebra Pure and Applied

ISBN-10: 0130882542

ISBN-13: 9780130882547

Edition: 2002

List price: $117.80
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Description:

This book provides thorough coverage of the main topics of abstract algebra while offering nearly 100 pages of applications. Arepetition andexamples first approach introduces learners to mathematical rigor and abstraction while teaching them the basic notions and results of modern algebra. Chapter topics include group theory, direct products and Abelian groups, rings and fields, geometric constructions, historical notes, symmetries, and coding theory. For future teachers of algebra and geometry at the high school level.
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Book details

List price: $117.80
Copyright year: 2002
Publisher: Prentice Hall PTR
Publication date: 5/24/2001
Binding: Paperback
Pages: 550
Size: 7.00" wide x 9.25" long x 1.25" tall
Weight: 2.508
Language: English

Preface
Acknowledgments
Background
Sets and Maps
Equivalence Relations and Partitions
Properties of Z
Complex Numbers
Matrices
Group Theory
Groups
Examples and Basic Concepts
Subgroups
Cyclic Groups
Permutations
Group Homomorphisms
Cosets and Lagrange's Theorem
Homomorphisms
Normal Subgroups
Quotient Groups
Automorphisms
Direct Products and Abelian Groups
Examples and Definitions
Computing Orders
Direct Sums
Fundamental Theorem of Finite Abelian Groups
Group Actions
Group Actions and Cayley's Theorem
Stabilizers and Orbits in a Group Action
Burnside's Theorem and Applications
Conjugacy Classes and the Class Equation
Conjugacy in S[subscript n] and Simplicity of A[subscript 5]
The Sylow Theorems
Applications of the Sylow Theorems
Composition Series
Isomorphism Theorems
The Jordan-Holder Theorem
Solvable Groups
Rings and Fields
Rings
Examples and Basic Concepts
Integral Domains
Fields
Ring Homomorphisms
Definitions and Basic Properties
Ideals
The Field of Quotients
Rings of Polynomials
Basic Concepts and Notation
The Division Algorithm in F[x]
More Applications of the Division Algorithm
Irreducible Polynomials
Cubic and Quartic Polynomials
Ideals in F[x]
Quotient Rings of F[x]
The Chinese Remainder Theorem for F[x]
Euclidean Domains
Division Algorithms and Euclidean Domains
Unique Factorization Domains
Gaussian Integers
Field Theory
Vector Spaces
Algebraic Extensions
Splitting Fields
Finite Fields
Geometric Constructions
Constructible Real Numbers
Classical Problems
Constructions with Marked Ruler and Compass
Cubics and Quartics Revisited
Galois Theory
Galois Groups
The Fundamental Theorem of Galois Theory
Galois Groups of Polynomials
Geometric Constructions Revisited
Radical Extensions
Historical Notes
From Ahmes the Scribe to Omar Khayyam
From Gerolamo Cardano to C. F. Gauss
From Evariste Galois to Emmy Noether
Selected Topics
Symmetries
Linear Transformations
Isometries
Symmetry Groups
Platonic Solids
Subgroups of the Special Orthogonal Group
Further Reading
Grobner Bases
Lexicographic Order
A Division Algorithm
Dickson's Lemma
The Hilbert Basis Theorem
Grobner Bases and the Division Algorithm
Further Reading
Coding Theory
Linear Binary Codes
Error Correction and Coset Decoding
Standard Generator Matrices
The Syndrome Method
Cyclic Codes
Further Reading
Boolean Algebras
Lattices
Boolean Algebras
Circuits
Further Reading
Answers and Hints to Selected Exercises
Bibliography
Index
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