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＜電子ブック＞
Hidden Harmony—Geometric Fantasies : The Rise of Complex Function Theory / by Umberto Bottazzini, Jeremy Gray
(Sources and Studies in the History of Mathematics and Physical Sciences. ISSN:21968829)

版	1st ed. 2013.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2013
大きさ	XVII, 848 p. 38 illus., 2 illus. in color : online resource
著者標目	*Bottazzini, Umberto author Gray, Jeremy author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Mathematics LCSH:History LCSH:Functions of complex variables LCSH:Number theory FREE:Functional Analysis FREE:History of Mathematical Sciences FREE:Functions of a Complex Variable FREE:Number Theory
一般注記	List of Figures -- Introduction -- 1. Elliptic Functions -- 2. From real to complex -- 3. Cauch -- 4. Elliptic integrals -- 5. Riemann -- 6. Weierstrass -- 7. Differential equations -- 8. Advanced topics -- 9. Several variables -- 10. Textbooks Hidden Harmony—Geometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject—Cauchy, Riemann, and Weierstrass—it looks at the contributions of great mathematicians from d’Alembert to Poincaré, and Laplace to Weyl. Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main players lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professional mathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory HTTP:URL=https://doi.org/10.1007/978-1-4614-5725-1

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