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

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
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