Product Description

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.

Product Details

• Amazon Sales Rank: #143261 in Books
• Published on: 2001-10-05
• Original language: English
• Number of items: 1
• Binding: Paperback
• 332 pages

About the Author
Andrew Pressley is Professor of Mathematics at King’s College London, UK.

Customer Reviews

Very good textbook, clearly aimed at undergraduates.
This is one of the clearest and easiest to follow textbooks I have had the pleasure to use in the last year. It happened to be one of the recommended texts for our 2nd year "Geometry of Surfaces Course".

It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with.

The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot.

What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds.

Topics covered here include: curvature, smooth surfaces, tangents normals & orientability, first & second fundametal forms, curvatures of surfaces, gaussian curvature, geodesics, and the amazing Gauss-Bonet theorem. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities.

So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.