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Introduction to galois theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to galois theoryby David Hernandez, Yves Laszlo.
Author:	Hernandez, David.
other author:	Laszlo, Yves.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xvii, 193 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Galois theory.
Online resource:	https://doi.org/10.1007/978-3-031-66182-2
ISBN:	9783031661822$q(electronic bk.)

Introduction to galois theory
Hernandez, David.

Introduction to galois theory[electronic resource] /by David Hernandez, Yves Laszlo. - Cham :Springer Nature Switzerland :2024. - xvii, 193 p. :ill. (some col.), digital ;24 cm. - Springer undergraduate mathematics series,2197-4144. - Springer undergraduate mathematics series..

1 Invitation to Galois Theory -- 2 Basic Concepts of Group Theory -- 3 Basic Concepts of Ring Theory -- 4 Basic Concepts of Algebras Over a Field -- 5 Finite Fields, Perfect Fields -- 6 The Galois Correspondence -- 7 Addendum: Infinite Galois Correspondence -- 8 Cyclotomy and Constructibility -- 9 Solvability by Radicals -- 10 Reduction Modulo p -- 11 Complements -- 12 Review Exercises -- 13 Solutions to Exercises.

This textbook provides an undergraduate introduction to Galois theory and its most notable applications. Galois theory was born in the 19th century to study polynomial equations. Both powerful and elegant, this theory was at the origin of a substantial part of modern algebra and has since undergone considerable development. It remains an extremely active research subject and has found numerous applications beyond pure mathematics. In this book, the authors introduce Galois theory from a contemporary point of view. In particular, modern methods such as reduction modulo prime numbers and finite fields are introduced and put to use. Beyond the usual applications of ruler and compass constructions and solvability by radicals, the book also includes topics such as the transcendence of e and π, the inverse Galois problem, and infinite Galois theory. Based on courses of the authors at the École Polytechnique, the book is aimed at students with a standard undergraduate background in (mostly linear) algebra. It includes a collection of exam questions in the form of review exercises, with detailed solutions.

ISBN: 9783031661822$q(electronic bk.)

Standard No.: 10.1007/978-3-031-66182-2doiSubjects--Topical Terms:

190982
Galois theory.

LC Class. No.: QA214

Dewey Class. No.: 512.32

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490 1 $a Springer undergraduate mathematics series, $x 2197-4144
505 0 $a 1 Invitation to Galois Theory -- 2 Basic Concepts of Group Theory -- 3 Basic Concepts of Ring Theory -- 4 Basic Concepts of Algebras Over a Field -- 5 Finite Fields, Perfect Fields -- 6 The Galois Correspondence -- 7 Addendum: Infinite Galois Correspondence -- 8 Cyclotomy and Constructibility -- 9 Solvability by Radicals -- 10 Reduction Modulo p -- 11 Complements -- 12 Review Exercises -- 13 Solutions to Exercises.
520 $a This textbook provides an undergraduate introduction to Galois theory and its most notable applications. Galois theory was born in the 19th century to study polynomial equations. Both powerful and elegant, this theory was at the origin of a substantial part of modern algebra and has since undergone considerable development. It remains an extremely active research subject and has found numerous applications beyond pure mathematics. In this book, the authors introduce Galois theory from a contemporary point of view. In particular, modern methods such as reduction modulo prime numbers and finite fields are introduced and put to use. Beyond the usual applications of ruler and compass constructions and solvability by radicals, the book also includes topics such as the transcendence of e and π, the inverse Galois problem, and infinite Galois theory. Based on courses of the authors at the École Polytechnique, the book is aimed at students with a standard undergraduate background in (mostly linear) algebra. It includes a collection of exam questions in the form of review exercises, with detailed solutions.
650 0 $a Galois theory. $3 190982
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650 2 4 $a Number Theory. $3 274059
700 1 $a Laszlo, Yves. $3 984439
710 2 $a SpringerLink (Online service) $3 273601
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830 0 $a Springer undergraduate mathematics series. $3 544774
856 4 0 $u https://doi.org/10.1007/978-3-031-66182-2
950 $a Mathematics and Statistics (SpringerNature-11649)