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Visual Geometry and Topology

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9783642762376: Visual Geometry and Topology
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Book by Fomenko Anatolij T

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Geometry and topology are strongly motivated by the visualization of ideal objects that have certain special characteristics. A clear formulation of a specific property or a logically consistent proof of a theorem often comes only after the mathematician has correctly "seen" what is going on. These pictures which are meant to serve as signposts leading to mathematical understanding, frequently also contain a beauty of their own. The principal aim of this book is to narrate, in an accessible and fairly visual language, about some classical and modern achievements of geometry and topology in both intrinsic mathematical problems and applications to mathematical physics. The book starts from classical notions of topology and ends with remarkable new results in Hamiltonian geometry. Fomenko lays special emphasis upon visual explanations of the problems and results and downplays the abstract logical aspects of calculations. As an example, readers can very quickly penetrate into the new theory of topological descriptions of integrable Hamiltonian differential equations. The book includes numerous graphical sheets drawn by the author, which are presented in special sections of "Visual material". These pictures illustrate the mathematical ideas and results contained in the book. Using these pictures, the reader can understand many modern mathematical ideas and methods. Although "Visual Geometry and Topology" is about mathematics, Fomenko has written and illustrated this book so that students and researchers from all the natural sciences and also artists and art students will find something of interest within its pages.

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Anatolij T. Fomenko
Verlag: Springer Berlin Heidelberg (2011)
ISBN 10: 3642762379 ISBN 13: 9783642762376
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Buchbeschreibung Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware -Geometry and topology are strongly motivated by thevisualization of ideal objects that have certain specialcharacteristics. A clear formulation of a specific propertyor a logically consistent proof of a theorem often comesonly after the mathematician has correctly 'seen' what isgoing on. These pictures which are meant to serve assignposts leading to mathematical understanding, frequentlyalso contain a beauty of their own.The principal aim of this book is to narrate, in anaccessible and fairly visual language, about some classicaland modern achievements of geometry and topology in bothintrinsic mathematical problems and applications tomathematical physics. The book starts from classical notionsof topology and ends with remarkable new results inHamiltonian geometry. Fomenko lays special emphasis uponvisual explanations of the problems and results anddownplays the abstract logical aspects of calculations. Asan example, readers can very quickly penetrate into the newtheory of topological descriptions of integrable Hamiltoniandifferential equations. The book includes numerous graphicalsheets drawn by the author, which are presented in specialsections of 'Visual material'. These pictures illustrate themathematical ideas and results contained in the book. Usingthese pictures, the reader can understand many modernmathematical ideas and methods.Although 'Visual Geometry and Topology' is aboutmathematics, Fomenko has written and illustrated this bookso that students and researchers from all the naturalsciences and also artists and art students will findsomething of interest within its pages. 344 pp. Englisch. Artikel-Nr. 9783642762376

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