Elementary Differential Geometry

by Andrew Pressley

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

Genres: Mathematics, Geometry, Textbooks, Reference

486 pages, Paperback

First published December 12, 2000

Reviews

[Kevin · Rating 3 out of 5]

I've read this book for an undergraduate differential geometry class. It's a good primer for more advanced topics. It mainly covers curves and surfaces, not manifolds in general; this is OK, but many proofs can't be generalized and, worst of all, don't teach you anything except rote computations. Unless you have a teacher who explains the ideas behind these proofs, I wouldn't suggest this for independent learning, as it would give a bad idea of what differential geometry is about.
The exercises vary from trivial to very hard. Some are uninteresting, but there are hidden gems.

After reading this book you'll want to read more general treatments (if interested), like Lee's Introduction to Smooth Manifolds or even Spivak's first 2 volumes if you have the time.
A similar book is do Carmo's, which is also the classic standard (doesn't necessarily mean better)

[Tue Le · Rating 3 out of 5]

I thought this book was alright, though some of the explanations could have been better, I think.

[Aaron Rossi · Rating 4 out of 5]

Excellent introductory textbook for anyone looking to learn differential geometry. Only background assumed is general second year vector calculus.

Author does a very good job of building differential geometry from a ground level, incorporating all the major theorems and concepts, including some more obscure historical theorems. The author includes several graphs and images to help the reader visualize many of the concepts. Each section also contains several exercises and proofs for the reader to test their understanding and engage the content, solutions are provided at the back.

This book also makes for an excellent 3rd or 4th year undergraduate textbook for any introductory course on differential geometry.

[George Malandrakis · Rating 5 out of 5]

A great introduction to Differential Geometry! There are some exercises that could have been explained further, but otherwise this book is among the best undergraduate books I have had

[Robert · Rating 4 out of 5]

One of the reasons I wanted to learn differential geometry was to better understand the general theory of relativity.

I didn't stick with it long enough to really get it, but this book was a great help and it certainly gave me a good solid idea of what the main concepts where.

If I ever decided to circle back to it this book would definitely be my starting point.

I really like the style and in fact the entire "Springer Undergraduate Mathematics Series".

It's about as gentle as you could find with all the things you could typically want, plenty of examples, explanations and exercises with a clear emphasis on key concepts and lots of motivation.

Now this came out a while ago so perhaps there is something newer and better, but on the other hand the basics of complex analysis haven't changed, so it should still be good!

[Steven Tseng · Rating 5 out of 5]

For anyone taking a differential geometry course for the first time, this book is super helpful. It really does make a lot of the concepts easier to understand. The only minus of this book is that it doesn't go into some of the more advanced topics of differential geometry. However, it helped me survive my course so I highly highly recommend it.