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Galois theory and advanced linear al...

Sinha, Rajnikant.

Galois theory and advanced linear algebra /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Galois theory and advanced linear algebra // Rajnikant Sinha.
作者:	Sinha, Rajnikant.
出版者:	Singapore :Springer, : c2020.,
面頁冊數:	ix, 351 p. ;24 cm.;
標題:	Galois theory. -
ISBN:	9811398488

Galois theory and advanced linear algebra /
Sinha, Rajnikant.

Galois theory and advanced linear algebra /Rajnikant Sinha. - Singapore :Springer,c2020. - ix, 351 p. ;24 cm.

Includes bibliographical references (p. 351).

Intro -- Preface -- Contents -- About the Author -- 1 Galois Theory I -- 1.1 Euclidean Rings -- 1.2 Polynomial Rings -- 1.3 The Eisenstein Criterion -- 1.4 Roots of Polynomials -- 1.5 Splitting Fields -- Exercises -- 2 Galois Theory II -- 2.1 Simple Extensions -- 2.2 Galois Groups -- 2.3 Applications of Galois Theory -- 2.4 Solvability By Radicals -- 3 Linear Transformations -- 3.1 Eigenvalues -- 3.2 Canonical Forms -- 3.3 The Cayley-Hamilton Theorem -- 4 Sylvester's Law of Inertia -- 4.1 Positive Definite Matrices -- 4.2 Sylvester's Law -- 4.3 Application to Riemannian Geometry.

"This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley-Hamilton theorem, Galois groups, Sylvester's law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial"--Provided by the publisher.

ISBN: 9811398488Subjects--Topical Terms:

677326
Galois theory.

LC Class. No.: QA214 / .S56 2020

Dewey Class. No.: 512/.32

Galois theory and advanced linear algebra /
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245 1 0 $a Galois theory and advanced linear algebra / $c Rajnikant Sinha.
260 # $a Singapore : $b Springer, $c c2020.
300 $a ix, 351 p. ; $c 24 cm.
504 $a Includes bibliographical references (p. 351).
505 0 # $a Intro -- Preface -- Contents -- About the Author -- 1 Galois Theory I -- 1.1 Euclidean Rings -- 1.2 Polynomial Rings -- 1.3 The Eisenstein Criterion -- 1.4 Roots of Polynomials -- 1.5 Splitting Fields -- Exercises -- 2 Galois Theory II -- 2.1 Simple Extensions -- 2.2 Galois Groups -- 2.3 Applications of Galois Theory -- 2.4 Solvability By Radicals -- 3 Linear Transformations -- 3.1 Eigenvalues -- 3.2 Canonical Forms -- 3.3 The Cayley-Hamilton Theorem -- 4 Sylvester's Law of Inertia -- 4.1 Positive Definite Matrices -- 4.2 Sylvester's Law -- 4.3 Application to Riemannian Geometry.
520 # $a "This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley-Hamilton theorem, Galois groups, Sylvester's law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial"--Provided by the publisher.
650 # 0 $a Galois theory. $3 677326
650 # 0 $a Algebras, Linear. $3 528115