Curved Spaces: From Classical Geometries to Elementary Differential Geometry

Wilson, P. M. H.

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This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.

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Recensione:

'… the patient reader will acquire substantial techniques and methods that are part of differential geometry and along with that, much, much more. … The book is certainly a welcome addition to the literature. It is clear to the reviewer the the text is a labour of love' Mathematical Reviews

'This book paves its way through a number of geometries with a clear intent: to promote the understanding of the basic concepts in differential geometry. The classical 2-dimensional geometries such as Euclidean, spherical and hyperbolic geometry are the first few steps. The geometry of the torus, triangulations and Euler numbers are further issues. Every chapter is followed by an assortment of helpful examples. The chapters gently direct the reader [towards] Riemannian metrics and further to geodesics and abstract surfaces. The Theorema Egregium and Gauss-Bonnet Theorem are also given ample attention. What distinguishes this book from other lecture notes on elementary differential geometry? The author does not abruptly define concepts which otherwise never would have come to the reader's mind. He rather conveys the ideas, subtly initiated in the former chapters. In this sense the book is remarkably self-contained. On the other hand the author does not shun detailed proofs. All these ingredients make for a successful volume.' Johann Lang, Zentralblatt MATH

'Curved Spaces provides an elegant, sophisticated treatment of two-dimensional geometries suitable for advanced undergraduates … Overall, Wilson has provided a monograph that could ably serve for an excellent undergraduate capstone experience … Highly recommended.' S.J. Colley, CHOICE

'The book is written in a nice and precise style and explicit computations and proofs make the book easy to understand. A detailed and explicit discussion of the main examples of classical geometries contributes well to a better understanding of later generalisations. A list of examples at the end of each chapter helps as well. It is a very good addition to the literature on the topic and can be very useful for teachers preparing their courses as well as for students.' EMS Newsletter

Descrizione del libro:

The well-known classical geometries, Euclidean, spherical and hyperbolic, are presented here in a general context, each linked by certain geometric themes. This 2007 textbook provides for a thorough introduction to, and examples of, the more general theory of curved spaces, and more generally, abstract surfaces with Riemannian metrics.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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1.Curved Spaces: From Classical Geometries to Elementary Differential Geometry

ISBN 10: 0521713900 ISBN 13: 9780521713900
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Descrizione libro Paperback. Condizione libro: New. Softcover Book, Condition: New. 1st Edition. [Please Read Carefully Before Buying], This Is An International Edition. Printed In Black and White. 196 pages, Book Cover And ISBN No May Be Different From US Edition. Restricted Sales Disclaimer Wordings Not For Sales In USA And Canada May Be Printed On The Cover Of The Book. Standard Shipping 7-14 Business Days. Expedited Shiping 4-8 Business Days. ***WE DO NOT ENTERTAIN BULK ORDERS.*** The Books May Be Ship From Overseas For Inventory Purpose. Codice libro della libreria 287276

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Descrizione libro Paperback. Condizione libro: New. New Softcover International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Codice libro della libreria 1670

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3.Curved Spaces: From Classical Geometries to Elementary Differential Geometry (Paperback)

Editore: CAMBRIDGE UNIVERSITY PRESS, United Kingdom (2008)
ISBN 10: 0521713900 ISBN 13: 9780521713900
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Descrizione libro CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2008. Paperback. Condizione libro: New. 244 x 172 mm. Language: English . Brand New Book. This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra. Codice libro della libreria AAU9780521713900

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4.Curved Spaces: From Classical Geometries to Elementary Differential Geometry (Paperback)

Editore: CAMBRIDGE UNIVERSITY PRESS, United Kingdom (2008)
ISBN 10: 0521713900 ISBN 13: 9780521713900
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Descrizione libro CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2008. Paperback. Condizione libro: New. 244 x 172 mm. Language: English . Brand New Book. This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra. Codice libro della libreria AAU9780521713900

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5.Curved Spaces: From Classical Geometries to Elementary Differential Geometry

Editore: Cambridge University Press
ISBN 10: 0521713900 ISBN 13: 9780521713900
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Descrizione libro Cambridge University Press. Paperback. Condizione libro: new. BRAND NEW, Curved Spaces: From Classical Geometries to Elementary Differential Geometry, P. M. H. Wilson, This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra. Codice libro della libreria B9780521713900

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6.Curved Spaces

Editore: Cambridge University Press 2007-12-13, Cambridge (2007)
ISBN 10: 0521713900 ISBN 13: 9780521713900
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Descrizione libro Cambridge University Press 2007-12-13, Cambridge, 2007. paperback. Condizione libro: New. Codice libro della libreria 9780521713900

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7.Curved Spaces: From Classical Geometries to Elementary Differential Geometry

Editore: Cambridge University Press (2008)
ISBN 10: 0521713900 ISBN 13: 9780521713900
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Descrizione libro Cambridge University Press, 2008. Condizione libro: New. This 2007 textbook uses examples, exercises, diagrams, and unambiguous proof, to help students make the link between classical and differential geometries. Num Pages: 198 pages, 79 b/w illus. 105 exercises. BIC Classification: PBK; PBMP. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 244 x 175 x 12. Weight in Grams: 33. From Classical Geometries to Elementary Differential Geometry. 198 pages, 79 b/w illus. 105 exercises. This 2007 textbook uses examples, exercises, diagrams, and unambiguous proof, to help students make the link between classical and differential geometries. Cateogry: (P) Professional & Vocational; (U) Tertiary Education (US: College). BIC Classification: PBK; PBMP. Dimension: 244 x 175 x 12. Weight: 332. . 2008. 1st Edition. Paperback. . . . . . Codice libro della libreria V9780521713900

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Editore: Cambridge University Press
ISBN 10: 0521713900 ISBN 13: 9780521713900
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Descrizione libro Cambridge University Press. Condizione libro: New. This 2007 textbook uses examples, exercises, diagrams, and unambiguous proof, to help students make the link between classical and differential geometries. Num Pages: 198 pages, 79 b/w illus. 105 exercises. BIC Classification: PBK; PBMP. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 244 x 175 x 12. Weight in Grams: 33. From Classical Geometries to Elementary Differential Geometry. 198 pages, 79 b/w illus. 105 exercises. This 2007 textbook uses examples, exercises, diagrams, and unambiguous proof, to help students make the link between classical and differential geometries. Cateogry: (P) Professional & Vocational; (U) Tertiary Education (US: College). BIC Classification: PBK; PBMP. Dimension: 244 x 175 x 12. Weight: 332. . 2008. 1st Edition. Paperback. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780521713900

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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97805217139000000000

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Editore: Cambridge University Press (2007)
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Descrizione libro Cambridge University Press, 2007. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria BB-9780521713900

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