Authors:
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
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“This book covers a lot of interesting material and is surely a valuable addition to the literature, but is certainly not for the timid. It brings together a broad array of sophisticated mathematics … and it does so in a very general and abstract way, with an exposition that gives whole new meaning to the word ‘concise’.” (Mark Hunacek, MAA Reviews, April 5, 2021)
Authors and Affiliations
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Université Paris Denis-Diderot, Paris, France
Régine Douady
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Université Paris-Sud Orsay, Paris, France
Adrien Douady
About the authors
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.
Bibliographic Information
Book Title: Algebra and Galois Theories
Authors: Régine Douady, Adrien Douady
Translated by: Urmie Ray
DOI: https://doi.org/10.1007/978-3-030-32796-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-32795-8Published: 14 July 2020
Softcover ISBN: 978-3-030-32798-9Published: 14 July 2021
eBook ISBN: 978-3-030-32796-5Published: 13 July 2020
Edition Number: 1
Number of Pages: XXIII, 462
Number of Illustrations: 27 b/w illustrations, 6 illustrations in colour
Topics: Algebra