Sinossi
This volume is based on the Mathematical Advanced Study Semesters course in geometry given at Penn State U. by Katok and his teaching assistant Climenhaga in the Research Experiences for Undergraduates program in the fall semester of 2007. It contains 36 lectures on surfaces, with a focus on the Euler characteristics. It introduces concepts such as the round sphere, flat torus, Möbius strip, Klein Bottle, and elliptic plane, methods of describing surfaces, metric geometry, and fundamental structures such as topology, combinatorial structure, and Riemannian metrics. It is assumed that readers (advanced undergraduates) have knowledge of calculus, some linear algebra, and rudiments of ODE and real analysis. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)
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Lectures on Surfaces (Student Mathematical Library)
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Paperback. Condizione: New. 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 articolo LU-9780821846797
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Paperback. Condizione: new. 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 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. 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. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780821846797
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Lectures on Surfaces : Almost Everything You Wanted to Know About Them
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ISBN 13: 9780821846797
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ISBN 13: 9780821846797
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Condizione: New. 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. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle. Series: Student Mathematical Library. Num Pages: 286 pages, Illustrations. BIC Classification: PB. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 171 x 214 x 16. Weight in Grams: 376. . 2008. Paperback. . . . . Codice articolo V9780821846797
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Lectures on Surfaces : Almost Everything You Wanted to Know About Them
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American Mathematical Society, 2008
ISBN 10: 0821846795
ISBN 13: 9780821846797
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