Galois' theory of algebraic equations
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TextPublication details: New Jersey : World Scientific, 2021 Edition: 2nd edDescription: xvi, 308 pages ; 24 cmISBN: 9780000990112Subject(s): Equations, Theory of | Galois theoryDDC classification: 512.623.3 Online resources: Table of contents | Reviews Summary: The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. 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 to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as "group" and "field".
A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory.
In this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.
| Item type | Current library | Call number | Status | Date due | Barcode |
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Book
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NISER LIBRARY | 512.623.3 TIG-G (Browse shelf(Opens below)) | Available | 25342 |
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| 512.623.3 SZA-G Galosis groups and fundamental groups | 512.623.3 TIG-G Galois theory of algebraic equations | 512.623.3 TIG-G Galois theory of algebraic equations | 512.623.3 TIG-G Galois' theory of algebraic equations | 512.623.3 WEI-G Galois theory | 512.623.3/.73 SER-G Galois cohomology | 512.624 ANA-X XOR Count and light weight multiplication in finite field with application to MDS matrices |
Originally published in English in 1988 jointly by: Harlow, Essex, England : Longman Scientific & Technical; and, New York : Wiley.
Includes bibliographical references (pages 299-304) and index.
The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. 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 to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as "group" and "field".
A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory.
In this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.
Upper level undergraduates, graduate students and mathematicians in algebra.
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