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Quintic equations and how to solve them

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quintic equations and how to solve them / by C.M. Linton.
作者:	Linton, C. M.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xii, 210 p. :ill. (some col.), digital ;24 cm.
內容註:	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
標題:	Quintic equations. -
電子資源:	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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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
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