Cargando…
Fields and Galois Theory
The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteri...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Springer London : Imprint: Springer,
2006.
|
| Edición: | 1st ed. 2006. |
| Colección: | Springer Undergraduate Mathematics Series,
|
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-1-84628-181-5 | ||
| 003 | DE-He213 | ||
| 005 | 20220114084811.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2006 xxk| s |||| 0|eng d | ||
| 020 | |a 9781846281815 |9 978-1-84628-181-5 | ||
| 024 | 7 | |a 10.1007/978-1-84628-181-5 |2 doi | |
| 050 | 4 | |a QA150-272 | |
| 072 | 7 | |a PBF |2 bicssc | |
| 072 | 7 | |a MAT002000 |2 bisacsh | |
| 072 | 7 | |a PBF |2 thema | |
| 082 | 0 | 4 | |a 512 |2 23 |
| 100 | 1 | |a Howie, John M. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Fields and Galois Theory |h [electronic resource] / |c by John M. Howie. |
| 250 | |a 1st ed. 2006. | ||
| 264 | 1 | |a London : |b Springer London : |b Imprint: Springer, |c 2006. | |
| 300 | |a X, 226 p. 22 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Springer Undergraduate Mathematics Series, |x 2197-4144 | |
| 505 | 0 | |a Rings and Fields -- Integral Domains and Polynomials -- Field Extensions -- Applications to Geometry -- Splitting Fields -- Finite Fields -- The Galois Group -- Equations and Groups -- Some Group Theory -- Groups and Equations -- Regular Polygons -- Solutions. | |
| 520 | |a The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra. This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection. Topics covered include: rings and fields integral domains and polynomials field extensions and splitting fields applications to geometry finite fields the Galois group equations Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. | ||
| 650 | 0 | |a Algebra. | |
| 650 | 0 | |a Algebraic fields. | |
| 650 | 0 | |a Polynomials. | |
| 650 | 1 | 4 | |a Algebra. |
| 650 | 2 | 4 | |a Field Theory and Polynomials. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9781848008854 |
| 776 | 0 | 8 | |i Printed edition: |z 9781852339869 |
| 830 | 0 | |a Springer Undergraduate Mathematics Series, |x 2197-4144 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-1-84628-181-5 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||