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Elementary Differential Geometry (Springer Undergraduate Mathematics Series) [Paperback]

A.N. Pressley
3.8 out of 5 stars  See all reviews (15 customer reviews)

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Book Description

March 18, 2010 184882890X 978-1848828902 2nd ed. 2012

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

Frequently Bought Together

Elementary Differential Geometry (Springer Undergraduate Mathematics Series) + Differential Geometry (Dover Books on Mathematics) + Introduction to Topology: Third Edition (Dover Books on Mathematics)
Price for all three: $56.89

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Editorial Reviews

Review

From the reviews of the second edition:

“I am very happy to report that the new edition of Pressley’s Elementary Differential Geometry is an even better book than the first edition … . full solutions to all problems given in an appendix. … Most of the problems are in the book and have solutions in the back. … The upshot is that this is still an excellent book and still my first choice for an undergraduate introduction to differential geometry.” (Fernando Q. Gouvêa, The Mathematical Association of America, May, 2010)

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


Product Details

  • Series: Springer Undergraduate Mathematics Series
  • Paperback: 474 pages
  • Publisher: Springer; 2nd ed. 2012 edition (March 18, 2010)
  • Language: English
  • ISBN-10: 184882890X
  • ISBN-13: 978-1848828902
  • Product Dimensions: 1.2 x 6.2 x 9.2 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #125,030 in Books (See Top 100 in Books)

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Customer Reviews

3.8 out of 5 stars
(15)
3.8 out of 5 stars
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Most Helpful Customer Reviews
62 of 63 people found the following review helpful
4.0 out of 5 stars A quick introduction to differential geometry October 26, 2001
By A Customer
Format: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.
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34 of 34 people found the following review helpful
5.0 out of 5 stars Written to teach rather than to impress January 17, 2008
Format: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.
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17 of 18 people found the following review helpful
4.0 out of 5 stars An enjoyable text on the subject! October 19, 2007
Format:Paperback|Verified Purchase
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.
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10 of 10 people found the following review helpful
5.0 out of 5 stars Definately a good begineers book April 23, 2008
By D. Pai
Format:Paperback
If you want a very general introduction of Differential Geometry, this is the book to start. Very nicely written text. Understandable examples. Broad coverage of materials . Explains space curves and surface properties with amazing quality. Recommended as a beginners level introduction
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6 of 6 people found the following review helpful
4.0 out of 5 stars Great intro book March 4, 2012
By Ghost
Format:Paperback|Verified Purchase
I'm using this book in my independent study class, it's an excellent introductory book for self studies.

Pros:
1. Highly readable
2. There're ample example walk-throughs
3. Full solution at the back of the book
4. Contains the complete introduction to the subject
Cons:
1. Only contains a classical introduction and is mostly restricted to 3-d space, hard to generalize to higher dimensions.

I'm using this in conjunction with Wolfgang's intro to Differential Geometry(ISBN 978-0821839881), which provides a more modern view of the subject and is much more general.

Would definitely recommend to self learners as a first course in Differential Geometry.
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6 of 8 people found the following review helpful
4.0 out of 5 stars Very appropriate for self-study February 26, 2008
Format:Paperback
It's a very good book overall, especially if you like to spend more time reading on your own than in a classroom.
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5 of 7 people found the following review helpful
2.0 out of 5 stars Second Edition or Rough Draft? October 10, 2013
By Carlos
Format:Paperback|Verified Purchase
I got this book for a graduate level differential geometry class. The book has a typo almost every other page. Don't get me wrong, typos are generally not a big deal, however if they're in the middle of equations it is just incorrect and useless. I don't recommend this book to anyone. The "Second Edition" on the cover makes me laugh. I can only imagine how much worse the first one was.
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5.0 out of 5 stars A Wonderful Book March 18, 2014
Format:Paperback|Verified Purchase
I'm only reading sections of this book for the purpose of understanding some half-baked math in a physics book, but I can say that this is simply a lovely book: the proofs are clear, the diagrams are copious, and the book contains the worked solutions to hundreds of problems - it's excellent for self study. It's also a nice demonstration of what can be done using just some advanced calculus - this book is suitable for anyone with two years of calc/linear algebra.

The book DOES say clearly in the introduction what it's scope is: mostly differential geometry in low dimensions and with methods that do NOT generalize to higher dimensions - so if you're looking for something else this isn't the book you want.
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