Quintic Equations and How to Solve Them
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...
I tiakina i:
| Kaituhi matua: | |
|---|---|
| Kaituhi rangatōpū: | |
| Hōputu: | Tāhiko īPukapuka |
| Reo: | Ingarihi |
| I whakaputaina: |
Cham :
Springer Nature Switzerland : Imprint: Birkhäuser,
2025.
|
| Putanga: | 1st ed. 2025. |
| Ngā marau: | |
| Urunga tuihono: | https://doi.org/10.1007/978-3-032-01658-4 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
|
MARC
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| 100 | 1 | |a Linton, C.M. |e author. |0 (orcid)0000-0002-1930-1351 |1 https://orcid.org/0000-0002-1930-1351 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Quintic Equations and How to Solve Them |h [electronic resource] / |c by C.M. Linton. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Birkhäuser, |c 2025. | |
| 300 | |a 1 online resource (XII, 210 p. 18 illus.). |b 3 illus. in color. | ||
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| 341 | 0 | |b Single logical reading order |2 onix | |
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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. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Algebraic fields. | |
| 650 | 0 | |a Polynomials. | |
| 650 | 0 | |a Algebras, Linear. | |
| 650 | 0 | |a Algebra. | |
| 650 | 1 | 4 | |a Field Theory and Polynomials. |
| 650 | 2 | 4 | |a Linear Algebra. |
| 650 | 2 | 4 | |a Algebra. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783032016577 |
| 776 | 0 | 8 | |i Printed edition: |z 9783032016591 |
| 776 | 0 | 8 | |i Printed edition: |z 9783032016607 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-032-01658-4 |
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| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||