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

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 |

141 | |

### 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: Group Theory and ... Michio Kuga No preview available - 2012 |