Galois Dream Group Theory And Differential Equations

Author : Michio Kuga
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203292

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

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 : Claude Mitschi,David Sauzin
Publisher : Springer
Page : 298 pages
File Size : 55,6 Mb
Release : 2016-08-27
Category : Mathematics
ISBN : 9783319287362

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Divergent Series, Summability and Resurgence I by Claude Mitschi,David Sauzin Pdf

Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.

Author : Michael Grinfeld
Publisher : John Wiley & Sons
Page : 634 pages
File Size : 48,8 Mb
Release : 2015-01-12
Category : Science
ISBN : 9783527411887

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Mathematical Tools for Physicists by Michael Grinfeld Pdf

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Author : Andreas Arvanitogeōrgos
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 41,5 Mb
Release : 2003
Category : Homogeneous spaces
ISBN : 9780821827789

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An Introduction to Lie Groups and the Geometry of Homogeneous Spaces by Andreas Arvanitogeōrgos Pdf

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.

Author : John P. Harnad,Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 387 pages
File Size : 47,6 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 9780821870426

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Groups and Symmetries by John P. Harnad,Pavel Winternitz Pdf

Author : Terry Gannon
Publisher : Cambridge University Press
Page : 493 pages
File Size : 46,6 Mb
Release : 2023-07-31
Category : Science
ISBN : 9781009401586

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Moonshine beyond the Monster by Terry Gannon Pdf

Author : Gilbert Baumslag
Publisher : Birkhäuser
Page : 174 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885874

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Topics in Combinatorial Group Theory by Gilbert Baumslag Pdf

Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.

Author : Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 49,7 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821870343

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Group Theory and Numerical Analysis by Pavel Winternitz Pdf

The Workshop on Group Theory and Numerical Analysis brought together scientists working in several different but related areas. The unifying theme was the application of group theory and geometrical methods to the solution of differential and difference equations. The emphasis was on the combination of analytical and numerical methods and also the use of symbolic computation. This meeting was organized under the auspices of the Centre de Recherches Mathematiques, Universite de Montreal (Canada). This volume has the character of a monograph and should represent a useful reference book for scientists working in this highly topical field.

Author : Edited by: Kisak
Publisher : CreateSpace
Page : 250 pages
File Size : 41,9 Mb
Release : 2015-07-12
Category : Electronic
ISBN : 151505554X

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Lie Group Mathematics by Edited by: Kisak Pdf

Mathematical Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. Lie groups provide a natural framework for analyzing the continuous symmetries of differential equations in much the same way as permutation groups are used in Galois theory for analyzing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.

Author : Jean-Francois Pommaret
Publisher : Unknown
Page : 146 pages
File Size : 55,8 Mb
Release : 2018-06
Category : Mathematical physics
ISBN : 1536134104

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New Mathematical Methods for Physics by Jean-Francois Pommaret Pdf

The concept of "group" has been introduced in mathematics for the first time by E. Galois (1830) and slowly passed from algebra to geometry with the work of S. Lie on Lie groups (1880) and Lie pseudogroups (1890) of transformations. The concept of a finite length differential sequence, now called the Janet sequence, had been described for the first time by M. Janet (1920). Then, the work of D. C. Spencer (1970) has been the first attempt to use the formal theory of systems of partial differential equations (PDE) in order to study the formal theory of Lie pseudogroups. However, the linear and nonlinear Spencer sequences for Lie pseudogroups, though never used in physics, largely supersede the "Cartan structure equations " (1905) and are quite different from the "Vessiot structure equations " (1903), introduced for the same purpose but never acknowledged by E. Cartan or successors. Meanwhile, mixing differential geometry with homological algebra, M. Kashiwara (1970) created "algebraic analysis" in order to study differential modules and double duality. By chance, unexpected arguments have been introduced by the brothers E. and F. Cosserat (1909) in order to revisit elasticity and by H. Weyl (1918) in order to revisit electromagnetism through a unique differential sequence only depending on the structure of the conformal group of space-time.The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of the extension. It has been the dream of many mathematicians at the end of the nineteenth century to generalize these results to systems of linear or algebraic PDE and the corresponding finitely generated differential extensions, in order to be able to add the word differential in front of any classical statement. The achievement of the Picard-Vessiot theory by E. Kolchin and coworkers between 1950 and 1970 is now well-known. However, the work of Vessiot on the differential Galois theory (1904), that is on the possibility to extend the classical Galois theory to systems of algebraic PDE and algebraic Lie pseudogroups, namely groups of transformations solutions for systems of algebraic PDE, has also never been acknowledged. His main idea has been to notice that the Galois theory (old and new) is a study of principal homogeneous spaces (PHS) for algebraic groups or pseudogroups described by what he called "automorphic systems" of PDE.The purpose of this book is first to revisit Gauge Theory and General Relativity in light of the latest developments just described and then to apply the differential Galois theory in order to revisit various domains of mechanics (Shell theory, Chain theory, Frenet-Serret formulas, Hamilton-Jacobi equations). All the results presented are new. (Nova)

Author : Lawrence Friedman Markus
Publisher : Unknown
Page : 227 pages
File Size : 49,5 Mb
Release : 1960*
Category : Electronic
ISBN : OCLC:702496055

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Group Theory and Differential Equations by Lawrence Friedman Markus Pdf

Author : Anonim
Publisher : Unknown
Page : 764 pages
File Size : 42,9 Mb
Release : 2000
Category : Mathematics
ISBN : UVA:X006088869

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Mathematical Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,6 Mb
Release : 1992
Category : Computer software
ISBN : CORNELL:31924074863436

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The Bulletin of Mathematics Books by Anonim Pdf

Author : American Mathematical Society
Publisher : Unknown
Page : 604 pages
File Size : 44,5 Mb
Release : 1993
Category : Mathematics
ISBN : UCSD:31822017710104

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Notices of the American Mathematical Society by American Mathematical Society Pdf

Author : Lawrence Markus
Publisher : Unknown
Page : 128 pages
File Size : 54,9 Mb
Release : 1959
Category : Electronic
ISBN : OCLC:900694178

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Group Theory and Differential Equations by Lawrence Markus Pdf