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Differential Galois Theory (Mathematics and Its Applications)
Differential Galois Theory (Mathematics and Its Applications)
Date: 12 June 2011, 02:31

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On 31st May 1832, Evariste Galois died at the age of 21. At that time the word "group" was not even used in mathematics, and the work of Galois that introduced it for the first time did not become known until eleven years later. Then group theory attracted more and more people, passing slowly from the field of pure algebra to other domains. This process has been particularly well described by Felix Klein in his 1872 "Erlangen Program." However, most of the comments of that Program simply focus on the words "group" and "geometry," while forgetting completely the word "field." As a result, at the end of the last century and at the beginning of this, many mathematicians had the dream of finding a Galois theory for systems of partial differential equations.
The purpose of this book is to provide for the first time the complete solution of this problem by means of new methods from differential and algebraic geometry.

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