Lectures on Galois Theory of Algebraic Equations - Bookswagon
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Lectures on Galois Theory of Algebraic Equations

Lectures on Galois Theory of Algebraic Equations


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About the Book

This book is an account of the development of the theory of algebraic equations from its origins in ancient times to its completion by Galois in the 19th century. The main emphasis is placed on developments arising between the 16th and the 19th centuries. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying a sense of the evolution of the theory of algebraic equations, and its giving rise to such basic mathematical notions as "group" and "field". A brief discussion of the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the more technical details can be omitted by readers interested primarily in a broad survey of the theory. The book is intended for postgraduate and undergraduate students in mathematics and the history of science, and also for teachers and mathematicians seeking an historical perspective on this field. The text is designed to be self-contained, but some familiarity with basic mathematical structures and elementary notions is needed for the technical aspects of the later chapters.

Table of Contents:
Quadratic equations; cubic equations; quartic equations; the creation of polynomials in one indeterminate; a modern approach to polynomials in one indeterminate; alternative methods for cubic and quartic equations; roots of unity; symmetric functions; the fundamental theorem of algebra; Lagrange; Vandermonde; Gauss on cyclotomic equations; Ruffini and Abel on general equations; Galois.


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Product Details
  • ISBN-13: 9780582002906
  • Publisher: Longman
  • Publisher Imprint: Longman Higher Education
  • Height: 230 mm
  • Width: 150 mm
  • ISBN-10: 0582002907
  • Publisher Date: /02/1988
  • Binding: Hardback
  • Weight: 831 gr


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Lectures on Galois Theory of Algebraic Equations
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