Lectures on Surfaces: Almost Everything You Wanted to Know About Them

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9780821846797: Lectures on Surfaces: Almost Everything You Wanted to Know About Them

Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. At the same time, many of those notions appear in a technically simpler and more graphic form than in their general 'natural' settings. The first, primarily expository, chapter introduces many of the principal actors - the round sphere, flat torus, Mobius strip, Klein bottle, elliptic plane, etc. - as well as various methods of describing surfaces, beginning with the traditional representation by equations in three-dimensional space, proceeding to parametric representation, and also introducing the less intuitive, but central for our purposes, representation as factor spaces.It concludes with a preliminary discussion of the metric geometry of surfaces, and the associated isometry groups. Subsequent chapters introduce fundamental mathematical structures - topological, combinatorial (piecewise linear), smooth, Riemannian (metric), and complex - in the specific context of surfaces. The focal point of the book is the Euler characteristic, which appears in many different guises and ties together concepts from combinatorics, algebraic topology, Morse theory, ordinary differential equations, and Riemannian geometry.The repeated appearance of the Euler characteristic provides both a unifying theme and a powerful illustration of the notion of an invariant in all those theories. The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background. This book is a result of the MASS course in geometry in the fall semester of 2007.

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Anatole Katok and Vaughn Climenhaga
Editore: American Mathematical Society (2008)
ISBN 10: 0821846795 ISBN 13: 9780821846797
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Sequitur Books
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Descrizione libro American Mathematical Society, 2008. Paperback. Condizione libro: New. Brand new. We distribute directly for the publisher. Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. At the same time, many of those notions appear in a technically simpler and more graphic form than in their general "natural" settings.The first, primarily expository, chapter introduces many of the principal actors--the round sphere, flat torus, Möbius strip, Klein bottle, elliptic plane, etc.--as well as various methods of describing surfaces, beginning with the traditional representation by equations in three-dimensional space, proceeding to parametric representation, and also introducing the less intuitive, but central for our purposes, representation as factor spaces. It concludes with a preliminary discussion of the metric geometry of surfaces, and the associated isometry groups. Subsequent chapters introduce fundamental mathematical structures--topological, combinatorial (piecewise linear), smooth, Riemannian (metric), and complex--in the specific context of surfaces.The focal point of the book is the Euler characteristic, which appears in many different guises and ties together concepts from combinatorics, algebraic topology, Morse theory, ordinary differential equations, and Riemannian geometry. The repeated appearance of the Euler characteristic provides both a unifying theme and a powerful illustration of the notion of an invariant in all those theories.The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background.This book is a result of the MASS course in geometry in the fall semester of 2007. Codice libro della libreria 1006100170

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Descrizione libro American Mathematical Society. Paperback. Condizione libro: new. BRAND NEW, Lectures on Surfaces: (Almost) Everything You Wanted to Know About Them, Anatole Katok, Vaughn Climenhaga, Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. At the same time, many of those notions appear in a technically simpler and more graphic form than in their general 'natural' settings. The first, primarily expository, chapter introduces many of the principal actors - the round sphere, flat torus, Mobius strip, Klein bottle, elliptic plane, etc. - as well as various methods of describing surfaces, beginning with the traditional representation by equations in three-dimensional space, proceeding to parametric representation, and also introducing the less intuitive, but central for our purposes, representation as factor spaces.It concludes with a preliminary discussion of the metric geometry of surfaces, and the associated isometry groups. Subsequent chapters introduce fundamental mathematical structures - topological, combinatorial (piecewise linear), smooth, Riemannian (metric), and complex - in the specific context of surfaces. The focal point of the book is the Euler characteristic, which appears in many different guises and ties together concepts from combinatorics, algebraic topology, Morse theory, ordinary differential equations, and Riemannian geometry.The repeated appearance of the Euler characteristic provides both a unifying theme and a powerful illustration of the notion of an invariant in all those theories. The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background. This book is a result of the MASS course in geometry in the fall semester of 2007. Codice libro della libreria B9780821846797

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Descrizione libro American Mathematical Society, 2008. Paperback. Condizione libro: New. Codice libro della libreria DADAX0821846795

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Descrizione libro American Mathematical Society, 2008. Paperback. Condizione libro: New. book. Codice libro della libreria 0821846795

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Descrizione libro Amer Mathematical Society, 2008. Paperback. Condizione libro: New. 13.97 x 21.59 cm. Our orders are sent from our warehouse locally or directly from our international distributors to allow us to offer you the best possible price and delivery time. Book. Codice libro della libreria MM-27229908

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Descrizione libro Amer Mathematical Society, 2008. Paperback. Condizione libro: Brand New. 303 pages. 8.40x5.40x0.60 inches. In Stock. Codice libro della libreria __0821846795

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Descrizione libro 2008. Paperback. Condizione libro: New. 171mm x 214mm x. Paperback. Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex .Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 286 pages. 0.376. Codice libro della libreria 9780821846797

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Descrizione libro 2008. Paperback. Condizione libro: New. 171mm x 214mm x. Paperback. Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topol.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 286 pages. 0.376. Codice libro della libreria 9780821846797

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