Share

Lectures on Differential Galois Theory

1994 Mathematics
Download Lectures on Differential Galois Theory PDF Online Free

Author :
Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 041/5 ( reviews)

GET EBOOK


Book Synopsis Lectures on Differential Galois Theory by : Andy R. Magid

Download or read book Lectures on Differential Galois Theory written by Andy R. Magid. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: Differential Galois theory studies solutions of differential equations over a differential base field. In much the same way that ordinary Galois theory is the theory of field extensions generated by solutions of (one variable) polynomial equations, differential Galois theory looks at the nature of the differential field extension generated by the solution of differential equations. An additional feature is that the corresponding differential Galois groups (of automorphisms of the extension fixing the base and commuting with the derivation) are algebraic groups. This book deals with the differential Galois theory of linear homogeneous differential equations, whose differential Galois groups are algebraic matrix groups. In addition to providing a convenient path to Galois theory, this approach also leads to the constructive solution of the inverse problem of differential Galois theory for various classes of algebraic groups. Providing a self-contained development and many explicit examples, this book provides a unique approach to differential Galois theory and is suitable as a textbook at the advanced graduate level.

Lectures on Differential Galois Theory

1994 Differential equations
Download Lectures on Differential Galois Theory PDF Online Free

Author :
Release : 1994
Genre : Differential equations
Kind : eBook
Book Rating : 564/5 ( reviews)

GET EBOOK


Book Synopsis Lectures on Differential Galois Theory by :

Download or read book Lectures on Differential Galois Theory written by . This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt:

Differential Galois Theory through Riemann-Hilbert Correspondence

2016-12-07 Mathematics
Download Differential Galois Theory through Riemann-Hilbert Correspondence PDF Online Free

Author :
Release : 2016-12-07
Genre : Mathematics
Kind : eBook
Book Rating : 959/5 ( reviews)

GET EBOOK


Book Synopsis Differential Galois Theory through Riemann-Hilbert Correspondence by : Jacques Sauloy

Download or read book Differential Galois Theory through Riemann-Hilbert Correspondence written by Jacques Sauloy. This book was released on 2016-12-07. Available in PDF, EPUB and Kindle. Book excerpt: Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equations, the main prerequisites are complex function theory, linear algebra, and an elementary knowledge of groups and of polynomials in many variables. A large variety of examples, exercises, and theoretical constructions, often via explicit computations, offers first-year graduate students an accessible entry into this exciting area.

Galois’ Dream: Group Theory and Differential Equations

2012-12-06 Mathematics
Download Galois’ Dream: Group Theory and Differential Equations PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 295/5 ( reviews)

GET EBOOK


Book Synopsis Galois’ Dream: Group Theory and Differential Equations by : Michio Kuga

Download or read book Galois’ Dream: Group Theory and Differential Equations written by Michio Kuga. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.

Galois Theory of Difference Equations

2006-11-14 Mathematics
Download Galois Theory of Difference Equations PDF Online Free

Author :
Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 41X/5 ( reviews)

GET EBOOK


Book Synopsis Galois Theory of Difference Equations by : Marius van der Put

Download or read book Galois Theory of Difference Equations written by Marius van der Put. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

You may also like...