Bottazzini, Umberto.
Hidden Harmony—Geometric Fantasies The Rise of Complex Function Theory / [electronic resource] : by Umberto Bottazzini, Jeremy Gray. - XVII, 848 p. 38 illus., 2 illus. in color. online resource. - Sources and Studies in the History of Mathematics and Physical Sciences . - Sources and Studies in the History of Mathematics and Physical Sciences .
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is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources.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.
9781461457251
10.1007/978-1-4614-5725-1 doi
Mathematics.
Functional analysis.
Functions of complex variables.
History.
Number theory.
Mathematics.
Functional Analysis.
History of Mathematical Sciences.
Functions of a Complex Variable.
Number Theory.
QA319-329.9
515.7
Hidden Harmony—Geometric Fantasies The Rise of Complex Function Theory / [electronic resource] : by Umberto Bottazzini, Jeremy Gray. - XVII, 848 p. 38 illus., 2 illus. in color. online resource. - Sources and Studies in the History of Mathematics and Physical Sciences . - Sources and Studies in the History of Mathematics and Physical Sciences .
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.
9781461457251
10.1007/978-1-4614-5725-1 doi
Mathematics.
Functional analysis.
Functions of complex variables.
History.
Number theory.
Mathematics.
Functional Analysis.
History of Mathematical Sciences.
Functions of a Complex Variable.
Number Theory.
QA319-329.9
515.7