Galois’ Dream: Group Theory and Differential Equations: Group Theory and Differential Equations

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Springer Science & Business Media, Dec 6, 2012 - Mathematics - 150 pages
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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. Michio Kuga’s lectures on Group Theory and Differential Equations are a realization of two dreams---one to see Galois groups used to attack the problems of differential equations---the other to do so in such a manner as to take students from a very basic level to an understanding of the heart of this fascinating mathematical problem. 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.

 

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Contents

0th Week No prerequisites
3
2nd Week Equivalence Classes
19
4th Week Fundamental Groups of Surfaces
33
6th Week Examples of Fundamental Groups
45
8th Week Coverings
53
9th Week Covering Surfaces and Fundamental Groups
59
11th Week The Group of Covering Transformations
70
12th Week The Universal Covering Space
77
13th Week The Correspondence Between Coverings of DO
83
15th Week Function Theory on Covering Surfaces
93
16th Week Differential Equations
105
18th Week Regular Singularities
114
19th Week Differential Equations of Fuchsian Type
129
References
141
Copyright

Other editions - View all

Galois’ Dream: Group Theory and Differential Equations: Group Theory and ...
Michio Kuga
Limited preview - 1993
Galois' Dream: Group Theory and Differential Equations
Michio Kuga
Snippet view - 1993
Galois’ Dream: Group Theory and Differential Equations: Group Theory and ...
Michio Kuga
No preview available - 2012
View all »

Common terms and phrases

algebraic arbitrary assigns automorphism C1 and C2 choose closed curve complex numbers consider continuous deformations continuous function copiable neighborhood copy covering map covering space curve C# define endpoint equivalence class equivalence relation Fe O(D Figure finite Formula Fuchsian differential equation Fuchsian type function F fundamental group Galois covering Group Theory Hence holomorphic function homeomorphism homotopy class implies indicial equation infinite initial point injective integer isomorphic Kuga lecture Let C# Let f lift linear log(z map f meromorphic function Michio Kuga monodromy group monodromy representation natural numbers notation null-homotopic obtain operation of type point of C1 point Q points with tail pole Preparation Theorem 18.2 Proposition quotient rational number real numbers regular singular points satisfying Similarly simply connected solution starting at P2 subgroup of T1(D;O subset surjective T-invariant terminal point topology two-dimensional manifold type L0 universal covering surface week words

Bibliographic information

QR code for Galois’ Dream: Group Theory and Differential Equations
TitleGalois’ Dream: Group Theory and Differential Equations: Group Theory and Differential Equations
AuthorMichio Kuga
Translated bySusan Addington, Motohico Mulase
Editionillustrated
PublisherSpringer Science & Business Media, 2012
ISBN1461203295, 9781461203292
Length150 pages
Subjects ›  › 

Mathematics / Algebra / Abstract
Mathematics / Algebra / General
Mathematics / Differential Equations / General
Mathematics / Group Theory
  
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