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ISBN13: 978-0412345500

ISBN10: 0412345501

Edition: 2ND 90

Copyright: 1990

Publisher: Chapman & Hall

Published: 1990

International: No

ISBN10: 0412345501

Edition: 2ND 90

Copyright: 1990

Publisher: Chapman & Hall

Published: 1990

International: No

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- Includes photographs of historical documents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 **

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

**Other Editions for Galois Theory**

ISBN10: 0412345501

Edition: 2ND 90

Copyright: 1990

Publisher: Chapman & Hall

Published: 1990

International: No

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

- Marketplace
- From

**Other Editions for Galois Theory**