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Galois theory [[electronic resource] /] / David A. Cox
| Galois theory [[electronic resource] /] / David A. Cox |
| Autore | Cox David A |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, NJ, : John Wiley & Sons, c2012 |
| Descrizione fisica | 1 online resource (603 p.) |
| Disciplina | 512/.32 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Galois theory
Equations, Theory of |
| ISBN |
1-280-58836-5
9786613618191 1-118-21844-2 1-118-21845-0 1-118-21842-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Galois Theory; CONTENTS; Preface to the First Edition; Preface to the Second Edition; Notation; 1 Basic Notation; 2 Chapter-by-Chapter Notation; PART I POLYNOMIALS; 1 Cubic Equations; 1.1 Cardan's Formulas; Historical Notes; 1.2 Permutations of the Roots; A Permutations; B The Discriminant; C Symmetric Polynomials; Mathematical Notes; Historical Notes; 1.3 Cubic Equations over the Real Numbers; A The Number of Real Roots; B Trigonometric Solution of the Cubic; Historical Notes; References; 2 Symmetric Polynomials; 2.1 Polynomials of Several Variables; A The Polynomial Ring in n Variables
B The Elementary Symmetric PolynomialsMathematical Notes; 2.2 Symmetric Polynomials; A The Fundamental Theorem; B The Roots of a Polynomial; C Uniqueness; Mathematical Notes; Historical Notes; 2.3 Computing with Symmetric Polynomials (Optional); A Using Mathematica; B Using Maple; 2.4 The Discriminant; Mathematical Notes; Historical Notes; References; 3 Roots of Polynomials; 3.1 The Existence of Roots; Mathematical Notes; Historical Notes; 3.2 The Fundamental Theorem of Algebra; Mathematical Notes; Historical Notes; References; PART II FIELDS; 4 Extension Fields 4.1 Elements of Extension FieldsA Minimal Polynomials; B Adjoining Elements; Mathematical Notes; Historical Notes; 4.2 Irreducible Polynomials; A Using Maple and Mathematica; B Algorithms for Factoring; C The Schönemann-Eisenstein Criterion; D Prime Radicals; Historical Notes; 4.3 The Degree of an Extension; A Finite Extensions; B The Tower Theorem; Mathematical Notes; Historical Notes; 4.4 Algebraic Extensions; Mathematical Notes; References; 5 Normal and Separable Extensions; 5.1 Splitting Fields; A Definition and Examples; B Uniqueness; 5.2 Normal Extensions; Historical Notes 5.3 Separable ExtensionsA Fields of Characteristic 0; B Fields of Characteristic p; C Computations; Mathematical Notes; 5.4 Theorem of the Primitive Element; Mathematical Notes; Historical Notes; References; 6 The Galois Group; 6.1 Definition of the Galois Group; Historical Notes; 6.2 Galois Groups of Splitting Fields; 6.3 Permutations of the Roots; Mathematical Notes; Historical Notes; 6.4 Examples of Galois Groups; A The pth Roots of 2; B The Universal Extension; C A Polynomial of Degree 5; Mathematical Notes; Historical Notes; 6.5 Abelian Equations (Optional); Historical Notes; References 7 The Galois Correspondence7.1 Galois Extensions; A Splitting Fields of Separable Polynomials; B Finite Separable Extensions; C Galois Closures; Historical Notes; 7.2 Normal Subgroups and Normal Extensions; A Conjugate Fields; B Normal Subgroups; Mathematical Notes; Historical Notes; 7.3 The Fundamental Theorem of Galois Theory; 7.4 First Applications; A The Discriminant; B The Universal Extension; C The Inverse Galois Problem; Historical Notes; 7.5 Automorphisms and Geometry (Optional); A Groups of Automorphisms; B Function Fields in One Variable; C Linear Fractional Transformations D Stereographic Projection |
| Record Nr. | UNINA-9910141299903321 |
Cox David A
|
||
| Hoboken, NJ, : John Wiley & Sons, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Galois theory / / David A. Cox
| Galois theory / / David A. Cox |
| Autore | Cox David A |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, NJ, : John Wiley & Sons, c2012 |
| Descrizione fisica | 1 online resource (603 p.) |
| Disciplina | 512/.32 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Galois theory
Equations, Theory of |
| ISBN |
1-280-58836-5
9786613618191 1-118-21844-2 1-118-21845-0 1-118-21842-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Galois Theory; CONTENTS; Preface to the First Edition; Preface to the Second Edition; Notation; 1 Basic Notation; 2 Chapter-by-Chapter Notation; PART I POLYNOMIALS; 1 Cubic Equations; 1.1 Cardan's Formulas; Historical Notes; 1.2 Permutations of the Roots; A Permutations; B The Discriminant; C Symmetric Polynomials; Mathematical Notes; Historical Notes; 1.3 Cubic Equations over the Real Numbers; A The Number of Real Roots; B Trigonometric Solution of the Cubic; Historical Notes; References; 2 Symmetric Polynomials; 2.1 Polynomials of Several Variables; A The Polynomial Ring in n Variables
B The Elementary Symmetric PolynomialsMathematical Notes; 2.2 Symmetric Polynomials; A The Fundamental Theorem; B The Roots of a Polynomial; C Uniqueness; Mathematical Notes; Historical Notes; 2.3 Computing with Symmetric Polynomials (Optional); A Using Mathematica; B Using Maple; 2.4 The Discriminant; Mathematical Notes; Historical Notes; References; 3 Roots of Polynomials; 3.1 The Existence of Roots; Mathematical Notes; Historical Notes; 3.2 The Fundamental Theorem of Algebra; Mathematical Notes; Historical Notes; References; PART II FIELDS; 4 Extension Fields 4.1 Elements of Extension FieldsA Minimal Polynomials; B Adjoining Elements; Mathematical Notes; Historical Notes; 4.2 Irreducible Polynomials; A Using Maple and Mathematica; B Algorithms for Factoring; C The Schönemann-Eisenstein Criterion; D Prime Radicals; Historical Notes; 4.3 The Degree of an Extension; A Finite Extensions; B The Tower Theorem; Mathematical Notes; Historical Notes; 4.4 Algebraic Extensions; Mathematical Notes; References; 5 Normal and Separable Extensions; 5.1 Splitting Fields; A Definition and Examples; B Uniqueness; 5.2 Normal Extensions; Historical Notes 5.3 Separable ExtensionsA Fields of Characteristic 0; B Fields of Characteristic p; C Computations; Mathematical Notes; 5.4 Theorem of the Primitive Element; Mathematical Notes; Historical Notes; References; 6 The Galois Group; 6.1 Definition of the Galois Group; Historical Notes; 6.2 Galois Groups of Splitting Fields; 6.3 Permutations of the Roots; Mathematical Notes; Historical Notes; 6.4 Examples of Galois Groups; A The pth Roots of 2; B The Universal Extension; C A Polynomial of Degree 5; Mathematical Notes; Historical Notes; 6.5 Abelian Equations (Optional); Historical Notes; References 7 The Galois Correspondence7.1 Galois Extensions; A Splitting Fields of Separable Polynomials; B Finite Separable Extensions; C Galois Closures; Historical Notes; 7.2 Normal Subgroups and Normal Extensions; A Conjugate Fields; B Normal Subgroups; Mathematical Notes; Historical Notes; 7.3 The Fundamental Theorem of Galois Theory; 7.4 First Applications; A The Discriminant; B The Universal Extension; C The Inverse Galois Problem; Historical Notes; 7.5 Automorphisms and Geometry (Optional); A Groups of Automorphisms; B Function Fields in One Variable; C Linear Fractional Transformations D Stereographic Projection |
| Record Nr. | UNINA-9910811064503321 |
|
Cox David A
|
||
| Hoboken, NJ, : John Wiley & Sons, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra / / by David A. Cox, John Little, Donal O'Shea
| Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra / / by David A. Cox, John Little, Donal O'Shea |
| Autore | Cox David A |
| Edizione | [4th ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (XVI, 646 p. 95 illus., 10 illus. in color.) |
| Disciplina | 516.35 |
| Collana | Undergraduate Texts in Mathematics |
| Soggetto topico |
Geometry, Algebraic
Commutative algebra Commutative rings Logic, Symbolic and mathematical Computer software Algebraic Geometry Commutative Rings and Algebras Mathematical Logic and Foundations Mathematical Software |
| ISBN | 3-319-16721-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Notation for Sets and Functions -- 1. Geometry, Algebra, and Algorithms -- 2. Groebner Bases -- 3. Elimination Theory -- 4.The Algebra-Geometry Dictionary -- 5. Polynomial and Rational Functions on a Variety -- 6. Robotics and Automatic Geometric Theorem Proving -- 7. Invariant Theory of Finite Groups -- 8. Projective Algebraic Geometry -- 9. The Dimension of a Variety -- 10. Additional Groebner Basis Algorithms -- Appendix A. Some Concepts from Algebra -- Appendix B. Pseudocode -- Appendix C. Computer Algebra Systems -- Appendix D. Independent Projects -- References -- Index. . |
| Record Nr. | UNINA-9910299766603321 |
|
Cox David A
|
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A study of singularities on rational curves via Syzygies / / David Cox [and three others]
| A study of singularities on rational curves via Syzygies / / David Cox [and three others] |
| Autore | Cox David A |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (116 p.) |
| Disciplina | 514/.746 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Singularities (Mathematics)
Commutative algebra |
| ISBN | 0-8218-9513-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 0. Introduction, terminology, and preliminary results""; ""1. Introduction""; ""2. Terminology""; ""3. Preliminary results""; ""Chapter 1. The General Lemma""; ""Chapter 2. The Triple Lemma""; ""Chapter 3. The BiProj Lemma""; ""Chapter 4. Singularities of multiplicity equal to degree divided by two""; ""Chapter 5. The space of true triples of forms of degree : the base point free locus, the birational locus, and the generic Hilbert-Burch matrix""; ""Chapter 6. Decomposition of the space of true triples""
""Chapter 7. The Jacobian matrix and the ramification locus""""Chapter 8. The conductor and the branches of a rational plane curve""; ""Chapter 9. Rational plane quartics: a stratification and the correspondence between the Hilbert-Burch matrices and the configuration of singularities""; ""Bibliography"" |
| Record Nr. | UNINA-9910796029303321 |
|
Cox David A
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A study of singularities on rational curves via Syzygies / / David Cox [and three others]
| A study of singularities on rational curves via Syzygies / / David Cox [and three others] |
| Autore | Cox David A |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (116 p.) |
| Disciplina | 514/.746 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Singularities (Mathematics)
Commutative algebra |
| ISBN | 0-8218-9513-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 0. Introduction, terminology, and preliminary results""; ""1. Introduction""; ""2. Terminology""; ""3. Preliminary results""; ""Chapter 1. The General Lemma""; ""Chapter 2. The Triple Lemma""; ""Chapter 3. The BiProj Lemma""; ""Chapter 4. Singularities of multiplicity equal to degree divided by two""; ""Chapter 5. The space of true triples of forms of degree : the base point free locus, the birational locus, and the generic Hilbert-Burch matrix""; ""Chapter 6. Decomposition of the space of true triples""
""Chapter 7. The Jacobian matrix and the ramification locus""""Chapter 8. The conductor and the branches of a rational plane curve""; ""Chapter 9. Rational plane quartics: a stratification and the correspondence between the Hilbert-Burch matrices and the configuration of singularities""; ""Bibliography"" |
| Record Nr. | UNINA-9910819069403321 |
|
Cox David A
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||