Galois' dream : group theory and differential equations
著者
書誌事項
Galois' dream : group theory and differential equations
Birkhäuser, c1993
- タイトル別名
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ガロアの夢
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注記
Includes bibliographical references (p. 141) and index
内容説明・目次
- 巻冊次
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ISBN 9780817636883
内容説明
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.
目次
- Preface.-Pre-Mathematics.-No Prerequisites.-Sets and Maps.-Equivalence Classes.-The Story of Free Groups.-Heave Ho! (Pull it Tight).-Fundamental Groups of Surfaces.-Fundamental Groups.-Examples of Fundamental Groups.-Examples of Fundamental Groups, Continued.-Men Who Don't Realize That Their Wives Have Been Interchanged.-Coverings.-Covering surfaces and Fundamental Groups.-Covering Surfaces and Fundamental Groups, Continued.-The Group of Covering Transformations.-Everyone has a Tail.-The Universal Covering Space.-The Correspondence Between Coverings of (D
- O) and Subgroups of pi1(D
- O).-Seeing Galois Theory.-Continuous Functions of Covering Surfaces.-Solvable or Not?.-Differential Equations.-Elementary methods of Solving Differential Equations.-Regular Singularities.-Differential Equations of Fuchsian Type.-References.-Notation.-Index.
- 巻冊次
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ISBN 9783764336882
内容説明
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, and the other to do so in a way that takes students from a basic level to an understanding of the heart of the problem.
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