rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Fields and Galois Theory
  name:
    name part: Howie, John M.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxk
    date issued: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 226 p. 22 illus. online resource.
  abstract: 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.
  table of contents: 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.
  note: by John M. Howie.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Field Theory and Polynomials
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Undergraduate Mathematics Series
  identifier: 9781846281815
  identifier: http://dx.doi.org/10.1007/978-1-84628-181-5
  record info:
    record creation date: 100301
    record change date: 20150207101145.0
    record identifier: 978-1-84628-181-5