Hidden Harmony - Geometric Fantasies: The Rise Of Complex Function Theory (sources And Studies In The History Of Mathematics And Physical Sciences)
by Jeremy Gray /
2013 / English / PDF
7.6 MB Download
This book is a 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published and unpublished sources.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 authors from d’Alembert to Hilbert, and Laplace to Weyl.
This book is a 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published and unpublished sources.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 authors from d’Alembert to Hilbert, and Laplace to Weyl.
Particular 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
devoted to the creation of a textbook tradition in complex
analysis by considering some seventy textbooks in nine different
languages. The 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 actors lived and
worked by paying attention to the rise of mathematical schools
and of contrasting national traditions.
Particular 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
devoted to the creation of a textbook tradition in complex
analysis by considering some seventy textbooks in nine different
languages. The 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 actors lived and
worked by paying attention to the rise of mathematical schools
and of contrasting national traditions.
The book is unrivaled for its breadth and depth, both in the core
theory and its implications for other fields of mathematics. It
documents the motivations for the early ideas and their gradual
refinement into a rigorous theory.
The book is unrivaled for its breadth and depth, both in the core
theory and its implications for other fields of mathematics. It
documents the motivations for the early ideas and their gradual
refinement into a rigorous theory.