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Introduction to galois theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to galois theory/ by David Hernandez, Yves Laszlo.
作者:	Hernandez, David.
其他作者:	Laszlo, Yves.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xvii, 193 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Number Theory. -
電子資源:	https://doi.org/10.1007/978-3-031-66182-2
ISBN:	9783031661822

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

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

672023
Number Theory.

LC Class. No.: QA214

Dewey Class. No.: 512.32

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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 2 4 $a Number Theory. $3 672023
650 2 4 $a Group Theory and Generalizations. $3 672112
650 1 4 $a Field Theory and Polynomials. $3 672025
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700 1 $a Laszlo, Yves. $3 1462189
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