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Quintic equations and how to solve them

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quintic equations and how to solve them / by C.M. Linton.
Author:	Linton, C. M.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xii, 210 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Chapter 1. Introduction -- Chapter 2. Quadratics, cubics, quartics and complex numbers -- Chapter 3. Polynomials and their roots -- Chapter 4. Symmetric polynomials and groups -- Chapter 5. Field extensions -- Chapter 6. Galois theory -- Chapter 7. There is no general quintic formula -- Chapter 8. Tschirnhaus transformations -- Chapter 9. Solvable quintics and how to solve them -- Chapter 10. Epilogue.
Contained By:	Springer Nature eBook
Subject:	Quintic equations. -
Online resource:	https://doi.org/10.1007/978-3-032-01658-4
ISBN:	9783032016584

Quintic equations and how to solve them
Linton, C. M.

Quintic equations and how to solve them [electronic resource] /by C.M. Linton. - Cham :Springer Nature Switzerland :2025. - xii, 210 p. :ill. (some col.), digital ;24 cm.

Chapter 1. Introduction -- Chapter 2. Quadratics, cubics, quartics and complex numbers -- Chapter 3. Polynomials and their roots -- Chapter 4. Symmetric polynomials and groups -- Chapter 5. Field extensions -- Chapter 6. Galois theory -- Chapter 7. There is no general quintic formula -- Chapter 8. Tschirnhaus transformations -- Chapter 9. Solvable quintics and how to solve them -- Chapter 10. Epilogue.

This monograph explores the well-known problem of the solvability of polynomial equations. While equations up to the fourth degree are solvable, there are, as demonstrated by Niels Henrik Abel, no general algebraic formulas leading to the solution of equations of fifth or higher degree. Nevertheless, some fifth degree (quintic) equations are indeed solvable. The author describes how Galois theory can be used to identify those quintic equations that can be solved algebraically and then shows how the solutions can be found. This involves shining a light on some little known works dating back to the late 19th century, bringing new life to a classical problem. This book is a valuable resource for both students and researchers and it constitutes a good basis for a seminar on polynomials and the solvability of equations.

ISBN: 9783032016584

Standard No.: 10.1007/978-3-032-01658-4doiSubjects--Topical Terms:

523886
Quintic equations.

LC Class. No.: QA215

Dewey Class. No.: 512.9422

Quintic equations and how to solve them
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245 1 0 $a Quintic equations and how to solve them $h [electronic resource] / $c by C.M. Linton.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2025.
300 $a xii, 210 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a Chapter 1. Introduction -- Chapter 2. Quadratics, cubics, quartics and complex numbers -- Chapter 3. Polynomials and their roots -- Chapter 4. Symmetric polynomials and groups -- Chapter 5. Field extensions -- Chapter 6. Galois theory -- Chapter 7. There is no general quintic formula -- Chapter 8. Tschirnhaus transformations -- Chapter 9. Solvable quintics and how to solve them -- Chapter 10. Epilogue.
520 $a This monograph explores the well-known problem of the solvability of polynomial equations. While equations up to the fourth degree are solvable, there are, as demonstrated by Niels Henrik Abel, no general algebraic formulas leading to the solution of equations of fifth or higher degree. Nevertheless, some fifth degree (quintic) equations are indeed solvable. The author describes how Galois theory can be used to identify those quintic equations that can be solved algebraically and then shows how the solutions can be found. This involves shining a light on some little known works dating back to the late 19th century, bringing new life to a classical problem. This book is a valuable resource for both students and researchers and it constitutes a good basis for a seminar on polynomials and the solvability of equations.
650 0 $a Quintic equations. $3 523886
650 1 4 $a Field Theory and Polynomials. $3 891077
650 2 4 $a Linear Algebra. $3 3338825
650 2 4 $a Algebra. $3 516203
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-032-01658-4
950 $a Mathematics and Statistics (SpringerNature-11649)