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Inhaltsangabe
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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Visual Geometry and Topology
Anbieter: Bookbot, Prague, Tschechien
Verkäuferbewertung 5 von 5 Sternen
Hardcover. Zustand: As New. Leichte Kratzer / Abnutzungen / Druckstellen. Geometry and topology are driven by the visualization of ideal objects with unique characteristics. A clear understanding of specific properties or proofs often emerges when mathematicians can "see" the concepts at play. These visualizations serve as signposts to mathematical comprehension and possess their own inherent beauty. This book aims to narrate, in an accessible and visual manner, classical and modern achievements in geometry and topology, addressing both intrinsic mathematical problems and their applications in mathematical physics. It begins with classical topology and progresses to notable advancements in Hamiltonian geometry. Fomenko emphasizes visual explanations over abstract calculations, allowing readers to quickly grasp the new theory of topological descriptions of integrable Hamiltonian differential equations. The book features numerous graphical illustrations created by the author, presented in dedicated "Visual material" sections, which elucidate the mathematical ideas and results discussed. These visuals enable readers to engage with contemporary mathematical concepts and methods. Although focused on mathematics, the book is crafted to appeal to students and researchers across the natural sciences, as well as artists and art students, ensuring a wide range of interest. Bestandsnummer des Verkäufers 591efec9-002a-432e-a342-75957c61ffb6
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