Field theory and its classical problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Washington]
Math. Assoc. of America
1978
|
| Ausgabe: | 1. print. |
| Schriftenreihe: | The Carus mathematical monographs
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 323 S. |
| ISBN: | 0883850206 |
Internformat
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| 650 | 4 | |a Equations |x Numerical solutions | |
| 650 | 4 | |a Geometry |x Famous problems | |
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Datensatz im Suchindex
| _version_ | 1804136070467551232 |
|---|---|
| adam_text | CONTENTS
PAGE
Preface ix
Introduction 1
Chapter 1—The Three Greek Problems
1.1 Constructible Lengths 9
1.2 Doubling the Cube 24
1.3 Trisecting the Angle 26
1.4 Squaring the Circle 31
1.5 Polynomials and Their Roots 33
1.6 Symmetric Functions 39
1.7 The Transcendence of it 47
References and Notes 57
Chapter 2—Field Extensions
2.1 Arithmetic of Polynomials 59
2.2 Simple, Multiple, and Finite Extensions 71
2.3 Geometric Constructions Revisited 80
2.4 Roots of Complex Numbers 84
2.5 Constructibility of Regular Polygons 1 92
2.6 Congruences 98
2.7 Constructibility of Regular Polygons II 104
References and Notes 119
Chapter 3—Solution By Radicals
3.1 Statement of the Problem 123
3.2 Automorphisms and Groups 127
3.3 The Group of an Extension 136
3.4 Two Fundamental Theorems 141
3.5 Galois Theorem 151
XV
XVi CONTENTS
3.6 Abel s Theorem 165
3.7 Some Solvable Equations 174
References and Notes 177
Chapter 4—Polynomials With Symmetric Groups
4.1 Background Information 181
4.2 Hilbert s Irreducibility Theorem 198
4.3 Existence of Polynomials over Q with Group Sn 210
References and Notes 219
Solutions to the problems 221
Index 319
|
| adam_txt |
CONTENTS
PAGE
Preface ix
Introduction 1
Chapter 1—The Three Greek Problems
1.1 Constructible Lengths 9
1.2 Doubling the Cube 24
1.3 Trisecting the Angle 26
1.4 Squaring the Circle 31
1.5 Polynomials and Their Roots 33
1.6 Symmetric Functions 39
1.7 The Transcendence of it 47
References and Notes 57
Chapter 2—Field Extensions
2.1 Arithmetic of Polynomials 59
2.2 Simple, Multiple, and Finite Extensions 71
2.3 Geometric Constructions Revisited 80
2.4 Roots of Complex Numbers 84
2.5 Constructibility of Regular Polygons 1 92
2.6 Congruences 98
2.7 Constructibility of Regular Polygons II 104
References and Notes 119
Chapter 3—Solution By Radicals
3.1 Statement of the Problem 123
3.2 Automorphisms and Groups 127
3.3 The Group of an Extension 136
3.4 Two Fundamental Theorems 141
3.5 Galois' Theorem 151
XV
XVi CONTENTS
3.6 Abel's Theorem 165
3.7 Some Solvable Equations 174
References and Notes 177
Chapter 4—Polynomials With Symmetric Groups
4.1 Background Information 181
4.2 Hilbert's Irreducibility Theorem 198
4.3 Existence of Polynomials over Q with Group Sn 210
References and Notes 219
Solutions to the problems 221
Index 319 |
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| discipline | Mathematik |
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| edition | 1. print. |
| format | Book |
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| id | DE-604.BV022095411 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:14:56Z |
| indexdate | 2024-07-09T20:50:33Z |
| institution | BVB |
| isbn | 0883850206 |
| language | English |
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| spelling | Hadlock, Charles Robert Verfasser aut Field theory and its classical problems by Charles Robert Hadlock 1. print. [Washington] Math. Assoc. of America 1978 323 S. txt rdacontent n rdamedia nc rdacarrier The Carus mathematical monographs 19 Corps algébrique ram Corps algébriques Equation algébrique Jussieu Exercice algèbre Jussieu Géométrie Géométrie - Problèmes classiques ram Lichamen (wiskunde) gtt Polygone régulier Jussieu Radicaux, Théorie des Radicaux, Théorie des ram Théorie Galois Jussieu Théorie corps Jussieu Théorème irréductibilité Hilbert Jussieu Équations - Solutions numériques Équations - Solutions numériques ram Algebraic fields Equations Numerical solutions Geometry Famous problems Radical theory Körper Algebra (DE-588)4308063-7 gnd rswk-swf Körpererweiterung (DE-588)4164435-9 gnd rswk-swf Körpertheorie (DE-588)4164455-4 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Polynom (DE-588)4046711-9 s DE-604 Galois-Theorie (DE-588)4155901-0 s Körper Algebra (DE-588)4308063-7 s Körpererweiterung (DE-588)4164435-9 s 1\p DE-604 Körpertheorie (DE-588)4164455-4 s 2\p DE-604 The Carus mathematical monographs 19 (DE-604)BV001887236 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015310263&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hadlock, Charles Robert Field theory and its classical problems The Carus mathematical monographs Corps algébrique ram Corps algébriques Equation algébrique Jussieu Exercice algèbre Jussieu Géométrie Géométrie - Problèmes classiques ram Lichamen (wiskunde) gtt Polygone régulier Jussieu Radicaux, Théorie des Radicaux, Théorie des ram Théorie Galois Jussieu Théorie corps Jussieu Théorème irréductibilité Hilbert Jussieu Équations - Solutions numériques Équations - Solutions numériques ram Algebraic fields Equations Numerical solutions Geometry Famous problems Radical theory Körper Algebra (DE-588)4308063-7 gnd Körpererweiterung (DE-588)4164435-9 gnd Körpertheorie (DE-588)4164455-4 gnd Galois-Theorie (DE-588)4155901-0 gnd Polynom (DE-588)4046711-9 gnd |
| subject_GND | (DE-588)4308063-7 (DE-588)4164435-9 (DE-588)4164455-4 (DE-588)4155901-0 (DE-588)4046711-9 |
| title | Field theory and its classical problems |
| title_auth | Field theory and its classical problems |
| title_exact_search | Field theory and its classical problems |
| title_exact_search_txtP | Field theory and its classical problems |
| title_full | Field theory and its classical problems by Charles Robert Hadlock |
| title_fullStr | Field theory and its classical problems by Charles Robert Hadlock |
| title_full_unstemmed | Field theory and its classical problems by Charles Robert Hadlock |
| title_short | Field theory and its classical problems |
| title_sort | field theory and its classical problems |
| topic | Corps algébrique ram Corps algébriques Equation algébrique Jussieu Exercice algèbre Jussieu Géométrie Géométrie - Problèmes classiques ram Lichamen (wiskunde) gtt Polygone régulier Jussieu Radicaux, Théorie des Radicaux, Théorie des ram Théorie Galois Jussieu Théorie corps Jussieu Théorème irréductibilité Hilbert Jussieu Équations - Solutions numériques Équations - Solutions numériques ram Algebraic fields Equations Numerical solutions Geometry Famous problems Radical theory Körper Algebra (DE-588)4308063-7 gnd Körpererweiterung (DE-588)4164435-9 gnd Körpertheorie (DE-588)4164455-4 gnd Galois-Theorie (DE-588)4155901-0 gnd Polynom (DE-588)4046711-9 gnd |
| topic_facet | Corps algébrique Corps algébriques Equation algébrique Exercice algèbre Géométrie Géométrie - Problèmes classiques Lichamen (wiskunde) Polygone régulier Radicaux, Théorie des Théorie Galois Théorie corps Théorème irréductibilité Hilbert Équations - Solutions numériques Algebraic fields Equations Numerical solutions Geometry Famous problems Radical theory Körper Algebra Körpererweiterung Körpertheorie Galois-Theorie Polynom |
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