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Differential Geometry of Curves and Surfaces

3.5 out of 5 stars 2 customer reviews
ISBN-13: 978-1568814568
ISBN-10: 1568814569
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Editorial Reviews


… a complete guide for the study of classical theory of curves and surfaces and is intended as a textbook for a one-semester course for undergraduates … The main advantages of the book are the careful introduction of the concepts, the good choice of the exercises, and the interactive computer graphics, which make the text well-suited for self-study. …The access to online computer graphics applets that illustrate many concepts and theorems presented in the text provides the readers with an interesting and visually stimulating study of classical differential geometry. … I strongly recommend [this book and Differential Geometry of Manifolds] to anyone wishing to enter into the beautiful world of the differential geometry.
―Velichka Milousheva, Journal of Geometry and Symmetry in Physics, 2012

Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book … Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
L’Enseignement Mathématique (2) 57 (2011)

… an intuitive and visual introduction to the subject is beneficial in an undergraduate course. This attitude is reflected in the text. The authors spent quite some time on motivating particular concepts and discuss simple but instructive examples. At the same time, they do not neglect rigour and precision. … As a distinguishing feature to other textbooks, there is an accompanying web page containing numerous interactive Java applets. … The applets are well-suited for use in classroom teaching or as an aid to self-study.
―Hans-Peter Schröcker, Zentralblatt MATH 1200

Coming from intuitive considerations to precise definitions the authors have written a very readable book. Every section contains many examples, problems and figures visualizing geometric properties. The understanding of geometric phenomena is supported by a number of available Java applets. This special feature distinguishes the textbook from others and makes it recommendable for self studies too. … highly recommendable …
―F. Manhart, International Mathematical News, August 2011

… the authors succeeded in making this modern view of differential geometry of curves and surfaces an approachable subject for advanced undergraduates.
―Andrew Bucki, Mathematical Reviews, Issue 2011h

… an essential addition to academic library Mathematical Studies instructional reference collections, as well as an ideal classroom textbook.
Midwest Book Review, May 2011

About the Author

Thomas F. Banchoff is a geometer and has been a professor at Brown University since 1967. Banchoff was president of the MAA from 1999-2000. He is published widely and known to a broad audience as editor and commentator on Abbotts Flatland. He has been the recipient of such awards as the MAA National Award for Distinguished College or University Teaching of Mathematics and most recently the 2007 Teaching with Technology Award.

Stephen Lovett is an associate professor of mathematics at Wheaton College in Illinois. Lovett has also taught at Eastern Nazarene College and has taught introductory courses on differential geometry for many years. Lovett has traveled extensively and has given many talks over the past several years on differential and algebraic geometry, as well as cryptography.


Product Details

  • Hardcover: 352 pages
  • Publisher: A K Peters/CRC Press (March 1, 2010)
  • Language: English
  • ISBN-10: 1568814569
  • ISBN-13: 978-1568814568
  • Product Dimensions: 9.3 x 7.6 x 0.9 inches
  • Shipping Weight: 1.4 pounds
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #581,209 in Books (See Top 100 in Books)

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Top Customer Reviews

By Danny on May 3, 2012
Format: Hardcover Verified Purchase
After finishing the course in differential geometry with this book, it is ok.
First of all, I know this is a first edition book so there are errors. But some of the errors are pretty big. Especially when you get to the second fundamental form, there is a huge error that makes the proofs very confusing, which is strange since the author should have picked up on it. But oh well.
The exercises are fun and sometimes challenging. the explanation are fair and sometimes very vague. They could have been better but the author expects you to fill in alot of the detail. and sometimes pretty much every everything. and many proofs are omitted.

The notation.
The notation can be difficult to follow but after a while it becomes understandable but still annoying. They should work on their notation for the next edition.
For self study.
It may be difficult for self study because a lot of detail is left out. you would be learning differential geometry with a lot of black boxes, lol. But I mean if you have a strong topology background, multivariable calculus, linear algebra, and some differential geometry you should be fine. But doing the exercises may be quite frustrating unless you know for sure you did them right since there is no answers to the quesetions. Which by all means not such a bad thing. i mean it is very fun to just think about the questions and take a pick at them. I mean if you doubt yourself you can always see a professor at your university to assist you.

the applets
not all that impressive but it helps you see what you been learning.

This is an ok book. It is not the best. If you want a good differential geometry book for self study you should go look for another one. If you want something to do, buy this used for the exercises. It is very fun! well they are very fun to do! They vary from computational, to proofs. Well just those two. thats all there is.
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Format: Hardcover Verified Purchase
I liked the presentation of the material in the book. In fact, after 4 others, I found this one the easiest to understand. There are java applets on the web-site but not enough illustrations in the book. The applets are dynamic animations and can show things that would be difficult in fixed illustrations. In the book there are many (sometimes 2 or 3 per page.) small computer icons to tell you to go to the web-site, but I would have liked a screen-shot or illustration in the book so you can read it without sitting at the computer. My other disappointment is there are no answers or solutions to the any exercises.
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