Field Theory and Its Classical Problems, Volume 14

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Cambridge University Press, Dec 7, 2000 - Mathematics - 323 pages
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 π, 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.
 

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Contents

Introduction
1
Chapter 1The Three Greek Problems
9
Chapter 2Field Extensions
59
Chapter 3Solution By Radicals
123
Chapter 4Polynomials With Symmetric Groups
181
Solutions to the problems
221
Index
319
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