Field theory and its classical problems

Field theory and its classical problems

by Hadlock, Charles R.

Type Book
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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 constructibility 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 groups, fields, or abstract algebra is assumed. Notable to…

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Title Statements

  • Full title :Field theory and its classical problems / Charles R. Hadlock.

Summary

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 constructibility 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 groups, fields, or abstract algebra is assumed. Notable topics treated along this route include the transcendence of e and of 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. Field Theory and its Classical Problems is a winner of the MAA Edwin Beckenbach Book Prize for excellence in mathematical exposition.

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Edition Statements

  • Publication Date:©1978

Publication Statements

The Physical Object

  • Description:1 online resource (340 pages) : : illustrations.

Edition Identifiers

  • ISBN:9781614440192, 1614440190, 088385032X, 9780883850329, 0883850206, 9780883850206
  • oclc:ocn880452826
  • LC Classification:QA247
  • Dewey Decimal:512/.32

Table of Contents

""Front Cover""; ""Field Theory and its Classical Problems""; ""Copyright Page""; ""Preface""; ""Contents""; ""Introduction""; ""Chapter 1�The Three Greek Problems""; ""1.1. Constructible Lengths""; ""1.2. Doubling the Cube""; ""1 3 Trisecting the Angle""; ""1.4. Squaring the Circle""; ""1.5. Polynomials and Their Roots""; ""1.6. Symmetric Functions""; ""1.7. The Transcendence of π""; ""References and Notes""; ""Chapter 2�Field Extensions""; ""2.1. Arithmetic of Polynomials""; ""2.2. Simple, Multiple, and Finite Extensions""; ""2.3. Geometric Constructions Revisited""

""2.4. Roots of Complex Numbers""""2.5. Constructibility of Regular Polygons I""; ""2.6. Congruences""; ""2.7. Constructibility of Regular Polygons II""; ""References and Notes""; ""Chapter 3�Solution by Radicals""; ""3.1. Statement of the Problem""; ""3.2. Automorphisms and Groups""; ""3.3. The Group of an Extension""; ""3.4. Two Fundamental Theorems""; ""3.5. Galois' Theorem""; ""3.6. Abel's Theorem""; ""3.7. Some Solvable Equations""; ""References and Notes""; ""Chapter 4�Polynomials with Symmetric Groups""; ""4.1. Background Information""; ""4.2. Hubert's Irreducibility Theorem""

""4.3. Existence of Po…

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Subjects

Equations -- Numerical solutions Équations -- Solutions numériques Géométrie -- Problèmes classiques Geometry -- Famous problems

Writers

Hadlock, Charles R.

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