Galois theory and its algebraic background /
Galois theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects in pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals, that is, determin...
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| Format: | Book |
| Language: | English |
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Cambridge ; New York :
Cambridge University Press,
[2022]
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| Edition: | Second edition. |
| Subjects: |
| Summary: | Galois theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects in pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals, that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois theory and the algebra that it needs and is suitable for both those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois theory). This second edition has been significantly revised and reordered, the first part develops the basic algebra that is needed, and the second part gives a comprehensive account of Galois theory. There are applications to ruler-and-compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully selected examples will help the reader develop a clear understanding of the mathematical theory. |
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| Item Description: | First edition published as Course in Galois theory, Cambridge University Press, 1986. |
| Physical Description: | x, 195 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781108838924 1108838928 9781108969086 1108969089 |