Galois Theory of Difference Equations, Marius van der Put; Michael F. Singer

Автор: Van der Put Marius , Singer Michael F.
Название: Galois Theory of Linear Differential Equations
ISBN: 3540442286 ISBN-13(EAN): 9783540442288
Издательство: Springer
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Цена: 13969.00 р.
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Описание: Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.

Автор: Tignol Jean-Pierre
Название: Galois` Theory Of Algebraic Equations (Second Edition)
ISBN: 9814704695 ISBN-13(EAN): 9789814704694
Издательство: World Scientific Publishing
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Описание:

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.

Автор: Escofier Jean-Pierre, Schneps L.
Название: Galois Theory
ISBN: 0387987657 ISBN-13(EAN): 9780387987651
Издательство: Springer
Цена: 11878.00 р.
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Описание: This book presents the fundamentals of Galois Theory, including a set of copious, well-chosen exercises that form an important part of the presentation. The pace is gentle and incorporates interesting historical material, including aspects on the life of Galois. Computed examples, recent developments, and extensions of results into other related areas round out the presentation.