Curved Spaces

From Classical Geometries to Elementary Differential Geometry

P. M. H. Wilson (University of Cambridge)

$74.95

Paperback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Cambridge University Press
11 February 2008

Mathematics & Sciences; Calculus & mathematical analysis; Differential & Riemannian geometry

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.

By: P. M. H. Wilson (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 244mm, Width: 170mm, Spine: 11mm
Weight: 330g
ISBN: 9780521713900
ISBN 10: 0521713900
Pages: 198
Publication Date: 11 February 2008
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Pelham Wilson is Professor of Algebraic Geometry in the Department of Pure Mathematics, University of Cambridge. He has been a Fellow of Trinity College since 1981 and has held visiting positions at universities and research institutes worldwide, including Kyoto University and the Max-Planck-Institute for Mathematics in Bonn. Professor Wilson has over 30 years of extensive experience of undergraduate teaching in mathematics, and his research interests include complex algebraic varieties, Calabi-Yau threefolds, mirror symmetry, and special Lagrangian submanifolds.

Reviews for Curved Spaces: From Classical Geometries to Elementary Differential Geometry

'... 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