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Cover: 9783030327989 | Algebra and Galois Theories | Régine Douady (u. a.) | Taschenbuch
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Algebra and Galois Theories
Taschenbuch von Régine Douady (u. a.)
Sprache: Englisch

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Beschreibung
Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings.
This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.
Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings.
This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.
Über den Autor
Adrien DOUADY was born in 1935. After receiving his Ph.d. in mathematics in the field of complex analytic geometry, he later joined the University Paris-Sud (Orsay). A recipient of the Ampere prize, he was a member of the French Academy of Sciences, as well as of the highly influential informal Bourbaki group. Throughout his life, he remained interested in several areas. Yet his odyssey always brought back to complex numbers. He passed away in 2006, and is notably survived by his wife, Regine Douady.
Regine Douady, born in 1934, after a Ph.d. in the didactics of mathematics, she became a lecturer at the University Paris Denis-Diderot, as well as the head of the IREM (Institut de Recherche sur l' Enseignement des Mathematiques). She was made a chevalier dans l'ordre des palmes academiques. Now retired, she has ceaselessly endeavoured to introduce into teaching the necessity to address concepts from different standpoints-the motivating idea behind this book.
Zusammenfassung

This book aims to transfer geometric intuition to the algebraic framework of Galois theory

Gives a parallel presentation of Galois theory and the theory of covering spaces and highlights this similarity between the two

Useful both for undergraduates and graduates, as well as to any researcher wishing to go beyond a purely algebraic approach to Galois theory

Inhaltsverzeichnis
Introduction.- Chapter 1. Zorn's Lemma.- Chapter 2. Categories and Functors.- Chapter 3. Linear Algebra.- Chapter 4. Coverings.- Chapter 5. Galois Theory.- Chapter 6. Riemann Surfaces.- Chapter 7. Dessins d'Enfants.- Bibliography.- Index of Notation
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xxiii
462 S.
27 s/w Illustr.
6 farbige Illustr.
462 p. 33 illus.
6 illus. in color.
ISBN-13: 9783030327989
ISBN-10: 3030327981
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Douady, Régine
Douady, Adrien
Übersetzung: Ray, Urmie
Auflage: 1st ed. 2020
Hersteller: Springer International Publishing
Springer International Publishing AG
Maße: 235 x 155 x 27 mm
Von/Mit: Régine Douady (u. a.)
Erscheinungsdatum: 14.07.2021
Gewicht: 0,733 kg
Artikel-ID: 120255355
Über den Autor
Adrien DOUADY was born in 1935. After receiving his Ph.d. in mathematics in the field of complex analytic geometry, he later joined the University Paris-Sud (Orsay). A recipient of the Ampere prize, he was a member of the French Academy of Sciences, as well as of the highly influential informal Bourbaki group. Throughout his life, he remained interested in several areas. Yet his odyssey always brought back to complex numbers. He passed away in 2006, and is notably survived by his wife, Regine Douady.
Regine Douady, born in 1934, after a Ph.d. in the didactics of mathematics, she became a lecturer at the University Paris Denis-Diderot, as well as the head of the IREM (Institut de Recherche sur l' Enseignement des Mathematiques). She was made a chevalier dans l'ordre des palmes academiques. Now retired, she has ceaselessly endeavoured to introduce into teaching the necessity to address concepts from different standpoints-the motivating idea behind this book.
Zusammenfassung

This book aims to transfer geometric intuition to the algebraic framework of Galois theory

Gives a parallel presentation of Galois theory and the theory of covering spaces and highlights this similarity between the two

Useful both for undergraduates and graduates, as well as to any researcher wishing to go beyond a purely algebraic approach to Galois theory

Inhaltsverzeichnis
Introduction.- Chapter 1. Zorn's Lemma.- Chapter 2. Categories and Functors.- Chapter 3. Linear Algebra.- Chapter 4. Coverings.- Chapter 5. Galois Theory.- Chapter 6. Riemann Surfaces.- Chapter 7. Dessins d'Enfants.- Bibliography.- Index of Notation
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xxiii
462 S.
27 s/w Illustr.
6 farbige Illustr.
462 p. 33 illus.
6 illus. in color.
ISBN-13: 9783030327989
ISBN-10: 3030327981
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Douady, Régine
Douady, Adrien
Übersetzung: Ray, Urmie
Auflage: 1st ed. 2020
Hersteller: Springer International Publishing
Springer International Publishing AG
Maße: 235 x 155 x 27 mm
Von/Mit: Régine Douady (u. a.)
Erscheinungsdatum: 14.07.2021
Gewicht: 0,733 kg
Artikel-ID: 120255355
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