書誌事項

Galois theory

Ian Stewart

(Chapman and Hall mathematics series)

Chapman and Hall, 1989

2nd ed

  • : pbk

大学図書館所蔵 件 / 9

この図書・雑誌をさがす

内容説明・目次

巻冊次

ISBN 9780412345401

内容説明

This book is an attempt to present the Galois theory as a showpiece of mathematical unification, bringing together several different branches of the subject and creating a powerful machine for the study of problems of considerable historical and mathematical importance. The central theme is the application of the Galois group to the quintic equation. As well as the traditional approach by way of the "general" polynomial equation, the author has included a direct approach which demonstrates the insolubility by radicals of a specific quintic polynomial with integer coefficients.

目次

  • Factorization of polynomials
  • field extensions
  • the degree of an extension
  • ruler and compasses
  • transcendental numbers
  • the idea behind Galois theory
  • normality and separability
  • field degrees and group orders
  • monomorphisms, automorphisms and normal closures
  • the Galois correspondence
  • soluble and simple groups
  • solution of equations by radicals
  • the general polynomial equation
  • finite fields
  • regular polygons
  • calculating Galois groups
  • the fundamental theorem of algebra.
巻冊次

: pbk ISBN 9780412345500

内容説明

This book is an attempt to present the Galois theory as a showpiece of mathematical unification, bringing together several different branches of the subject and creating a powerful machine for the study of problems of considerable historical and mathematical importance. The central theme is the applicaiton of the Galois group to the quintic equation. As well as the traditional approach by way of the "general" polynomial equation, the author has included a direct approach which demonstrates the insolubility by radicals of a specific quintic polynomial with integer coefficeints.

目次

  • factorization of polynomials
  • field extensions
  • the degree of an extension
  • ruler and compasses
  • transcendental numbers
  • the idea behind Galois theory
  • normality and separability
  • field degrees and group orders
  • monomorphisms, automorphisms and normal closures
  • the Galois correspondence
  • soluble and simple groups
  • solution of equations by radicals
  • the general polynomial equation
  • finite fields
  • regular polygons
  • calculating Galois groups
  • the fundamental theorem of algebra.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

  • NII書誌ID(NCID)
    BA07539612
  • ISBN
    • 0412345404
    • 0412345501
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    London ; New York
  • ページ数/冊数
    xxx, 202 p.
  • 大きさ
    22 cm
  • 分類
  • 件名
  • 親書誌ID
ページトップへ