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Modern algebra with applications [[electronic resource] /] / William J. Gilbert, W. Keith Nicholson
| Modern algebra with applications [[electronic resource] /] / William J. Gilbert, W. Keith Nicholson |
| Autore | Gilbert William J. <1941-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2004 |
| Descrizione fisica | 1 online resource (353 p.) |
| Disciplina | 512 |
| Altri autori (Persone) | NicholsonW. Keith |
| Collana | Pure and applied mathematics |
| Soggetto topico | Algebra, Abstract |
| ISBN |
1-280-34418-0
9786610344185 0-470-31340-4 0-471-46989-0 0-471-46988-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
MODERN ALGEBRA WITH APPLICATIONS; CONTENTS; Preface to the First Edition; Preface to the Second Edition; List of Symbols; 1 Introduction; Classical Algebra; Modern Algebra; Binary Operations; Algebraic Structures; Extending Number Systems; 2 Boolean Algebras; Algebra of Sets; Number of Elements in a Set; Boolean Algebras; Propositional Logic; Switching Circuits; Divisors; Posets and Lattices; Normal Forms and Simplification of Circuits; Transistor Gates; Representation Theorem; Exercises; 3 Groups; Groups and Symmetries; Subgroups; Cyclic Groups and Dihedral Groups; Morphisms
Permutation GroupsEven and Odd Permutations; Cayley's Representation Theorem; Exercises; 4 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; 5 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; 6 Pólya-Burnside Method of Enumeration; Burnside's Theorem Necklace ProblemsColoring Polyhedra; Counting Switching Circuits; Exercises; 7 Monoids and Machines; Monoids and Semigroups; Finite-State Machines; Quotient Monoids and the Monoid of a Machine; Exercises; 8 Rings and Fields; Rings; Integral Domains and Fields; Subrings and Morphisms of Rings; New Rings from Old; Field of Fractions; Convolution Fractions; Exercises; 9 Polynomial and Euclidean Rings; Euclidean Rings; 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 TheoremExercises; 10 Quotient Rings; Ideals and Quotient Rings; Computations in Quotient Rings; Morphism Theorem; Quotient Polynomial Rings That Are Fields; Exercises; 11 Field Extensions; Field Extensions; Algebraic Numbers; Galois Fields; Primitive Elements; Exercises; 12 Latin Squares; Latin Squares; Orthogonal Latin Squares; Finite Geometries; Magic Squares; Exercises; 13 Geometrical Constructions; Constructible Numbers; Duplicating a Cube; Trisecting an Angle; Squaring the Circle; Constructing Regular Polygons Nonconstructible Number of Degree 4Exercises; 14 Error-Correcting Codes; The Coding Problem; Simple Codes; Polynomial Representation; Matrix Representation; Error Correcting and Decoding; BCH Codes; Exercises; Appendix 1: Proofs; Appendix 2: Integers; Bibliography and References; Answers to Odd-Numbered Exercises; Index |
| Record Nr. | UNINA-9910146070503321 |
Gilbert William J. <1941->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Modern algebra with applications [[electronic resource] /] / William J. Gilbert, W. Keith Nicholson
| Modern algebra with applications [[electronic resource] /] / William J. Gilbert, W. Keith Nicholson |
| Autore | Gilbert William J. <1941-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2004 |
| Descrizione fisica | 1 online resource (353 p.) |
| Disciplina | 512 |
| Altri autori (Persone) | NicholsonW. Keith |
| Collana | Pure and applied mathematics |
| Soggetto topico | Algebra, Abstract |
| ISBN |
1-280-34418-0
9786610344185 0-470-31340-4 0-471-46989-0 0-471-46988-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
MODERN ALGEBRA WITH APPLICATIONS; CONTENTS; Preface to the First Edition; Preface to the Second Edition; List of Symbols; 1 Introduction; Classical Algebra; Modern Algebra; Binary Operations; Algebraic Structures; Extending Number Systems; 2 Boolean Algebras; Algebra of Sets; Number of Elements in a Set; Boolean Algebras; Propositional Logic; Switching Circuits; Divisors; Posets and Lattices; Normal Forms and Simplification of Circuits; Transistor Gates; Representation Theorem; Exercises; 3 Groups; Groups and Symmetries; Subgroups; Cyclic Groups and Dihedral Groups; Morphisms
Permutation GroupsEven and Odd Permutations; Cayley's Representation Theorem; Exercises; 4 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; 5 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; 6 Pólya-Burnside Method of Enumeration; Burnside's Theorem Necklace ProblemsColoring Polyhedra; Counting Switching Circuits; Exercises; 7 Monoids and Machines; Monoids and Semigroups; Finite-State Machines; Quotient Monoids and the Monoid of a Machine; Exercises; 8 Rings and Fields; Rings; Integral Domains and Fields; Subrings and Morphisms of Rings; New Rings from Old; Field of Fractions; Convolution Fractions; Exercises; 9 Polynomial and Euclidean Rings; Euclidean Rings; 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 TheoremExercises; 10 Quotient Rings; Ideals and Quotient Rings; Computations in Quotient Rings; Morphism Theorem; Quotient Polynomial Rings That Are Fields; Exercises; 11 Field Extensions; Field Extensions; Algebraic Numbers; Galois Fields; Primitive Elements; Exercises; 12 Latin Squares; Latin Squares; Orthogonal Latin Squares; Finite Geometries; Magic Squares; Exercises; 13 Geometrical Constructions; Constructible Numbers; Duplicating a Cube; Trisecting an Angle; Squaring the Circle; Constructing Regular Polygons Nonconstructible Number of Degree 4Exercises; 14 Error-Correcting Codes; The Coding Problem; Simple Codes; Polynomial Representation; Matrix Representation; Error Correcting and Decoding; BCH Codes; Exercises; Appendix 1: Proofs; Appendix 2: Integers; Bibliography and References; Answers to Odd-Numbered Exercises; Index |
| Record Nr. | UNINA-9910830132703321 |
|
Gilbert William J. <1941->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Modern algebra with applications [[electronic resource] /] / William J. Gilbert, W. Keith Nicholson
| Modern algebra with applications [[electronic resource] /] / William J. Gilbert, W. Keith Nicholson |
| Autore | Gilbert William J. <1941-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2004 |
| Descrizione fisica | 1 online resource (353 p.) |
| Disciplina | 512 |
| Altri autori (Persone) | NicholsonW. Keith |
| Collana | Pure and applied mathematics |
| Soggetto topico | Algebra, Abstract |
| ISBN |
1-280-34418-0
9786610344185 0-470-31340-4 0-471-46989-0 0-471-46988-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
MODERN ALGEBRA WITH APPLICATIONS; CONTENTS; Preface to the First Edition; Preface to the Second Edition; List of Symbols; 1 Introduction; Classical Algebra; Modern Algebra; Binary Operations; Algebraic Structures; Extending Number Systems; 2 Boolean Algebras; Algebra of Sets; Number of Elements in a Set; Boolean Algebras; Propositional Logic; Switching Circuits; Divisors; Posets and Lattices; Normal Forms and Simplification of Circuits; Transistor Gates; Representation Theorem; Exercises; 3 Groups; Groups and Symmetries; Subgroups; Cyclic Groups and Dihedral Groups; Morphisms
Permutation GroupsEven and Odd Permutations; Cayley's Representation Theorem; Exercises; 4 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; 5 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; 6 Pólya-Burnside Method of Enumeration; Burnside's Theorem Necklace ProblemsColoring Polyhedra; Counting Switching Circuits; Exercises; 7 Monoids and Machines; Monoids and Semigroups; Finite-State Machines; Quotient Monoids and the Monoid of a Machine; Exercises; 8 Rings and Fields; Rings; Integral Domains and Fields; Subrings and Morphisms of Rings; New Rings from Old; Field of Fractions; Convolution Fractions; Exercises; 9 Polynomial and Euclidean Rings; Euclidean Rings; 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 TheoremExercises; 10 Quotient Rings; Ideals and Quotient Rings; Computations in Quotient Rings; Morphism Theorem; Quotient Polynomial Rings That Are Fields; Exercises; 11 Field Extensions; Field Extensions; Algebraic Numbers; Galois Fields; Primitive Elements; Exercises; 12 Latin Squares; Latin Squares; Orthogonal Latin Squares; Finite Geometries; Magic Squares; Exercises; 13 Geometrical Constructions; Constructible Numbers; Duplicating a Cube; Trisecting an Angle; Squaring the Circle; Constructing Regular Polygons Nonconstructible Number of Degree 4Exercises; 14 Error-Correcting Codes; The Coding Problem; Simple Codes; Polynomial Representation; Matrix Representation; Error Correcting and Decoding; BCH Codes; Exercises; Appendix 1: Proofs; Appendix 2: Integers; Bibliography and References; Answers to Odd-Numbered Exercises; Index |
| Record Nr. | UNINA-9910841889503321 |
|
Gilbert William J. <1941->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||