Modern Algebra with Applications

ISBN-10: 0471414514
ISBN-13: 9780471414513
Edition: 2nd 2004 (Revised)
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Description: Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject-effectively holding your interest and creating a more  More...

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Book details

List price: $186.00
Edition: 2nd
Copyright year: 2004
Publisher: John Wiley & Sons, Incorporated
Publication date: 11/5/2003
Binding: Hardcover
Pages: 352
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 1.342
Language: English

Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject-effectively holding your interest and creating a more seamless method of instruction. Filled with in-depth insights and over six hundred exercises of varying difficulty, this invaluable text can help anyone appreciate and understand this subject.

Introduction
Classical Algebra
Modern Algebra
Binary Operations
Algebraic Structures
Extending Number Systems
Boolean Algebras
Algebra of Sets
Number of Elements in a Set
Boolean Algebras
Switching Circuits
Posets and Lattices
Normal Forms and Simplification of Circuits
Transistor Gates
Representation Theorem
Exercises
Groups
Groups and Symmetries
Subgroups
Cyclic Groups and Dihedral Groups
Morphisms
Permutation Groups
Even and Odd Permutations
Cayley's Representation Theorem
Exercises
Quotient Groups
Equivalence Relations
Cosets and Lagrange's Theorem
Normal Subgroups and Quotient Groups
Morphism Theorem
Direct Products
Groups of Low Order
Action of a Group on a Set
Exercises
Symmetry Groups in Three Dimensions
Translations and the Euclidean Group
Matrix Groups
Finite Groups in Two Dimensions
Proper Rotations of Regular Solids
Finite Rotation Groups in Three Dimensions
Crystallographic Groups
Exercises
Polya-Burnside Method of Enumeration
Burnside's Theorem
Necklace Problems
Coloring Polyhedra
Counting Switching Circuits
Exercises
Monoids and Machines
Monoids and Semigroups
Finite-State Machines
Quotient Monoids and the Monoid of a Machine
Exercises
Rings and Fields
Rings
Integral Domains and Fields
Subrings and Morphisms of Rings
New Rings from Old
Field of Fractions
Convolution Fractions
Exercises
Polynomial and Euclidean Rings
Division Algorithm
Euclidean Algorithm
Unique Factorization
Factoring Real and Complex Polynomials
Factoring Rational and Integral Polynomials
Factoring Polynomials over Finite Fields
Linear Congruences and the Chinese Remainder Theorem
Exercises
Quotient Rings
Ideals and Quotient Rings
Computations in Quotient Rings
Morphism Theorem
Quotient Polynomial Rings that are Fields
Exercises
Field Extensions
Field Extensions
Algebraic Numbers
Galois Fields
Primitive Elements
Exercises
Latin Squares
Latin Squares
Orthogonal Latin Squares
Finite Geometries
Magic Squares
Exercises
Geometrical Constructions
Constructible Numbers
Duplicating the Cube
Trisecting an Angle
Squaring the Circle
Constructing Regular Polygons
A Nonconstructible Number of Degree Four
Exercises
Error-Correcting Codes
The Coding Problem
Simple Codes
Polynomial Representation
Matrix Representation
Error Correcting and Decoding
BCH Codes
Exercises
Bibliography and References
Answers to the Odd-Numbered Exercises
Glossary of Symbols
Index

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