Lectures On Differential Galois Theory PDF Download
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Author | : Andy R. Magid |
Publisher | : American Mathematical Soc. |
Total Pages | : 119 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821870041 |
Download Lectures on Differential Galois Theory Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 105 |
Release | : 1994 |
Genre | : Differential equations |
ISBN | : 9781470421564 |
Download Lectures on Differential Galois Theory Book in PDF, ePub and Kindle
Author | : Jacques Sauloy |
Publisher | : American Mathematical Soc. |
Total Pages | : 303 |
Release | : 2016-12-07 |
Genre | : Mathematics |
ISBN | : 1470430959 |
Download Differential Galois Theory through Riemann-Hilbert Correspondence Book in PDF, ePub and Kindle
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.
Author | : Michio Kuga |
Publisher | : Springer Science & Business Media |
Total Pages | : 147 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461203295 |
Download Galois’ Dream: Group Theory and Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Marius van der Put |
Publisher | : Springer |
Total Pages | : 182 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354069241X |
Download Galois Theory of Difference Equations Book in PDF, ePub and Kindle
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.
Author | : Frédéric Fauvet |
Publisher | : European Mathematical Society |
Total Pages | : 284 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9783037190739 |
Download Renormalization and Galois Theories Book in PDF, ePub and Kindle
This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.
Author | : Marius van der Put |
Publisher | : Springer Science & Business Media |
Total Pages | : 446 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642557503 |
Download Galois Theory of Linear Differential Equations Book in PDF, ePub and Kindle
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Author | : D. J. H. Garling |
Publisher | : Cambridge University Press |
Total Pages | : 180 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 9780521312493 |
Download A Course in Galois Theory Book in PDF, ePub and Kindle
This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.
Author | : Qing Han |
Publisher | : American Mathematical Soc. |
Total Pages | : 161 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821853139 |
Download Elliptic Partial Differential Equations Book in PDF, ePub and Kindle
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
Author | : V.B. Alekseev |
Publisher | : Springer Science & Business Media |
Total Pages | : 278 |
Release | : 2007-05-08 |
Genre | : Mathematics |
ISBN | : 1402021879 |
Download Abel’s Theorem in Problems and Solutions Book in PDF, ePub and Kindle
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.