Elementary Differential Geometry [Paperback]

A.N. Pressley (Author)

Book Description

ISBN-10: 1852331526 | ISBN-13: 978-1852331528 | Publication Date: December 12, 2000 | Edition: Corrected

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there. The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecturers, and for all others interested in the subject. Andrew Pressley is Professor of Mathematics at King’s College London, UK. The Springer Undergraduate Mathematics Series (SUMS) is a series designed for undergraduates in mathematics and the sciences worldwide. From core foundational material to final year topics, SUMS books take a fresh and modern approach and are ideal for self-study or for a one- or two-semester course. Each book includes numerous examples, problems and fully worked solutions.

Editorial Reviews

Review

From the 1st edition reviews:"By the inclusion of 200 exercises with full solutions, this book has become a helpful tool for everyone teaching in its field. Summing up, it is a very good first book on the topic." (Internationale Mathematische Nachrichten, 187, August 2001) "…Pressley takes the simplest route with respect to all the technical setup: avoid it all. Instead of covariant derivatives, use derivatives with respect to local coordinates. Use moving frames without mentioning connections. Mention the Christoffel symbols very quickly, but don’t do very much with them. For the most part, it works…the book does include several versions of the Gauss-Bonnett theorem, allowing the professor to end the course with a bang. All in all, I was quite happy with the book." (MAA Online)

From the Back Cover

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com Praise for the first edition: "The text is nicely illustrated, the definitions are well-motivated and the proofs are particularly well-written and student-friendly…this book would make an excellent text for an undergraduate course, but could also well be used for a reading course, or simply read for pleasure." Australian Mathematical Society Gazette "Excellent figures supplement a good account, sprinkled with illustrative examples." Times Higher Education Supplement --This text refers to an alternate Paperback edition.

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Product Details

• Paperback: 332 pages
• Publisher: Springer; Corrected edition (December 12, 2000)
• Language: English
• ISBN-10: 1852331526
• ISBN-13: 978-1852331528
• Product Dimensions: 9.2 x 6.9 x 0.7 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #882,309 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

54 of 55 people found the following review helpful:

4.0 out of 5 stars A quick introduction to differential geometry, October 26, 2001

By A Customer

This review is from: Elementary Differential Geometry (Paperback)

Pressley's gives you a very comprehensible and down to earth introduction to differential geometry.
By avoiding the more modern and abstract generalizations of differential geometry to more than three dimensions you really feel that you grasp what the theorems and methods are about. In this way you are able to work your way quickly through the book and avoid getting stuck and loosing interest. Another plus is that the book contains lots of examples and fully worked answers to all exercises, which makes it perfect for self-study.
The downside is that the book is not as exhuastive as you perhaps would like, when you have looked at books like O'Neills and DoCarmos ... on the other hand, you only need to spend a fraction of the time to get through Pressleys.
I definitely think that this is a much better book that Struiks classical work (by being more structured and goal oriented) and an excellent introduction to further studies in differential and Riemann geometry.

20 of 20 people found the following review helpful:

5.0 out of 5 stars Written to teach rather than to impress, January 17, 2008

By 

Thomas Meyer (Storrs, Connecticut) - See all my reviews
(REAL NAME)   

This review is from: Elementary Differential Geometry (Paperback)

I have purchased hundreds of technical books and really treasure the ones that seem to have been written in order to really convey the material rather than impress the reader with how smart the author is. This is such a book. The material is remarkably clear and the author's style strikes me as a notable example of the mathematical writing styles put forth in the articles comprising the text "How to Write Mathematics." For example, the material proceeds in a logical chain such that the reader is never confronted with a term or concept before it has been explained. The notation is defined meticulously and repeatedly so the reader is not forced to continually refer backwards through the text to remember the meaning of the symbols. This also is a boon for "grasshopper readers" who will use the text as a reference, as opposed to a linear reader. Symbols don't change meaning, are not overloaded, and seem to have been chosen for intuitive appeal. For example, a lower-case gamma denotes a parametric function for a curve and, to me, the shape of the gamma suggests the sorts of curves being discussed. In my experience, this book is best in class.

13 of 14 people found the following review helpful:

4.0 out of 5 stars An enjoyable text on the subject!, October 19, 2007

By 

From Detroit (Michigan, USA) - See all my reviews

Amazon Verified Purchase

This review is from: Elementary Differential Geometry (Paperback)

I've been looking for a decent book on differential geometry for years now. Most of the good ones are fairly pricey, or require the reader to have a deep knowledge of mathematics. This fits in neither category. You only need multi variable calculus, linear algebra, and some experience with reading/writing proofs. This book will also appeal to those who want to learn on their own, as every problem has a hint/solution in the back.