A classical introduction to Galois theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, N.J.
Wiley
2012
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Includes index. -- "This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematics, and a fundamental question to be considered is: For a given polynomial equation (over a given field), does a solution in terms of radicals exist? That the need to investigate the very existence of a solution is perhaps surprising and invites an overview of the history of mathematics. The classical material within the book includes theorems on polynomials, fields, and groups due to such luminaries as Gauss, Kronecker, Lagrange, Ruffini and, of course, Galois. These results figured prominently in earlier expositions of Galois theory, but seem to have gone out of fashion. This is unfortunate since, aside from being of intrinsic mathematical interest, such material provides powerful motivation for the more modern treatment of Galois theory presented later in the book. Over the course of the book, three versions of the Impossibility Theorem are presented: the first relies entirely on polynomials and fields, the second incorporates a limited amount of group theory, and the third takes full advantage of modern Galois theory. This progression through methods that involve more and more group theory characterizes the first part of the book. The latter part of the book is devoted to topics that illustrate the power of Galois theory as a computational tool, b Newman, Stephen C., 1952-: Classical introduction to Galois theory |
| Beschreibung: | 1 Online-Ressource (xii, 284 p.) |
| ISBN: | 9781118336816 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.32 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV040365146 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-06T00:05:14Z |
| institution | BVB |
| isbn | 9781118336816 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025218889 |
| oclc_num | 809181034 |
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| physical | 1 Online-Ressource (xii, 284 p.) |
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| publishDate | 2012 |
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| spelling | Newman, Stephen C. 1952- Verfasser (DE-588)138482829 aut A classical introduction to Galois theory Stephen C. Newman Hoboken, N.J. Wiley 2012 1 Online-Ressource (xii, 284 p.) txt rdacontent c rdamedia cr rdacarrier Includes index. -- "This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematics, and a fundamental question to be considered is: For a given polynomial equation (over a given field), does a solution in terms of radicals exist? That the need to investigate the very existence of a solution is perhaps surprising and invites an overview of the history of mathematics. The classical material within the book includes theorems on polynomials, fields, and groups due to such luminaries as Gauss, Kronecker, Lagrange, Ruffini and, of course, Galois. These results figured prominently in earlier expositions of Galois theory, but seem to have gone out of fashion. This is unfortunate since, aside from being of intrinsic mathematical interest, such material provides powerful motivation for the more modern treatment of Galois theory presented later in the book. Over the course of the book, three versions of the Impossibility Theorem are presented: the first relies entirely on polynomials and fields, the second incorporates a limited amount of group theory, and the third takes full advantage of modern Galois theory. This progression through methods that involve more and more group theory characterizes the first part of the book. The latter part of the book is devoted to topics that illustrate the power of Galois theory as a computational tool, b Newman, Stephen C., 1952-: Classical introduction to Galois theory Galois theory MATHEMATICS / Applied bisacsh Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 s DE-604 https://onlinelibrary.wiley.com/doi/book/10.1002/9781118336816 Verlag Volltext |
| spellingShingle | Newman, Stephen C. 1952- A classical introduction to Galois theory Galois theory MATHEMATICS / Applied bisacsh Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4155901-0 |
| title | A classical introduction to Galois theory |
| title_auth | A classical introduction to Galois theory |
| title_exact_search | A classical introduction to Galois theory |
| title_full | A classical introduction to Galois theory Stephen C. Newman |
| title_fullStr | A classical introduction to Galois theory Stephen C. Newman |
| title_full_unstemmed | A classical introduction to Galois theory Stephen C. Newman |
| title_short | A classical introduction to Galois theory |
| title_sort | a classical introduction to galois theory |
| topic | Galois theory MATHEMATICS / Applied bisacsh Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Galois theory MATHEMATICS / Applied Galois-Theorie |
| url | https://onlinelibrary.wiley.com/doi/book/10.1002/9781118336816 |
| work_keys_str_mv | AT newmanstephenc aclassicalintroductiontogaloistheory |