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Galois Theory

Galois Theory - 2nd edition

ISBN13: 978-0412345500

Cover of Galois Theory 2ND 90 (ISBN 978-0412345500)
ISBN13: 978-0412345500
ISBN10: 0412345501
Cover type: Paperback
Edition/Copyright: 2ND 90
Publisher: Chapman & Hall
Published: 1990
International: No

List price: $44.95

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Galois Theory - 2ND 90 edition

ISBN13: 978-0412345500

Ian N. Stewart

ISBN13: 978-0412345500
ISBN10: 0412345501
Cover type: Paperback
Edition/Copyright: 2ND 90
Publisher: Chapman & Hall

Published: 1990
International: No
Summary

Galois Theory is a showpiece of mathematical unification and "technology transfer." Abstract algebraic techniques, such as group theory and field theory, answer important questions in geometry and the theory of equations. Applications include:

  • the impossibility of trisecting the angle
  • duplicating the cube
  • squaring the circle
  • solving equations of the fifth degree


the possibility of constructing regular polygons with 17, 257, or 65537 sides
This revised edition of a popular text includes an introductory overview, a chapter on the calculation of Galois groups, further clarification of proofs, extra motivating examples, and modified exercises.

  • Provides a rigorous treatment, motivated by discussion and examples
  • Contains historical materials, including a description of the turbulent life of Evariste Galois
  • Includes photographs of historical documents
  • Supplies more than 200 exercises

Author Bio

Stewart, I. N. : University of Warwick

Table of Contents

Historical Introduction
The Life of Galois
Overview


Background
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 Order
Monomorphisms, Automorphisms, and Normal Closures
The Galois Correspondence
A Specific Example
Soluble and Simple Groups
Solution of Equation by Radicals
The General Polynomial Equation
Finite Fields
Regular Polygons
Calculating Galois Groups
The Fundamental Theorem of Algebra

Selected Solutions
References
Index
Symbol Index

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