Softcover ISBN:  9781470449605 
Product Code:  CAR/35 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
eBook ISBN:  9781470449612 
Product Code:  CAR/35.E 
List Price:  $70.00 
MAA Member Price:  $52.50 
AMS Member Price:  $52.50 
Softcover ISBN:  9781470449605 
eBook: ISBN:  9781470449612 
Product Code:  CAR/35.B 
List Price:  $145.00 $110.00 
MAA Member Price:  $108.75 $82.50 
AMS Member Price:  $108.75 $82.50 
Softcover ISBN:  9781470449605 
Product Code:  CAR/35 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
eBook ISBN:  9781470449612 
Product Code:  CAR/35.E 
List Price:  $70.00 
MAA Member Price:  $52.50 
AMS Member Price:  $52.50 
Softcover ISBN:  9781470449605 
eBook ISBN:  9781470449612 
Product Code:  CAR/35.B 
List Price:  $145.00 $110.00 
MAA Member Price:  $108.75 $82.50 
AMS Member Price:  $108.75 $82.50 

Book DetailsThe Carus Mathematical MonographsVolume: 35; 1975; 323 ppMSC: Primary 12Recipient of the Mathematical Association of America's Beckenbach Book Prize in 1984!
Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular \(n\)gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of algebra is assumed. Notable topics treated along this route include the transcendence of \(e\) and \(\pi\), cyclotomic polynomials, polynomials over the integers, Hilbert's irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems.

Table of Contents

Chapters

Introduction

Chapter 1. The three Greek problems

Chapter 2. Field extensions

Chapter 3. Solution by radicals

Chapter 4. Polynomials with symmetric groups


Reviews

The presented book is a clear and concise introduction to classical results of Galois theory. The book is an excellent reading for everyone, especially for instructors and first year graduate students in Galois theory.
Acta. Sci. Math.


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Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular \(n\)gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of algebra is assumed. Notable topics treated along this route include the transcendence of \(e\) and \(\pi\), cyclotomic polynomials, polynomials over the integers, Hilbert's irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems.

Chapters

Introduction

Chapter 1. The three Greek problems

Chapter 2. Field extensions

Chapter 3. Solution by radicals

Chapter 4. Polynomials with symmetric groups

The presented book is a clear and concise introduction to classical results of Galois theory. The book is an excellent reading for everyone, especially for instructors and first year graduate students in Galois theory.
Acta. Sci. Math.