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Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition Hardcover – December 29, 1997

ISBN-13: 978-0849371646 ISBN-10: 0849371643 Edition: 2nd

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Product Details

  • Series: Textbooks in Mathematics
  • Hardcover: 1088 pages
  • Publisher: CRC Press; 2nd edition (December 29, 1997)
  • Language: English
  • ISBN-10: 0849371643
  • ISBN-13: 978-0849371646
  • Product Dimensions: 10.3 x 7.3 x 2.5 inches
  • Shipping Weight: 4.6 pounds
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #2,460,430 in Books (See Top 100 in Books)

Editorial Reviews

Review

"I wish that I would have used this book as my introduction to differential geometry instead of the here-unnamed horror-flick-of-a-book required by my early professors on the subjectIn the high-turnover of textbooks this much improved 2nd edition is truly deserving of the title and furthermore acts as an excellent tribute to its author." - The Mathematica Journal, Vol. 7 No. 2, 1998 "More than any other text I am aware of, Gray integrates computing into the materialGray's Mathematica programs offer new and fascinating ways to present material. With an appropriate selection of material the first edition and, even better, the present second edition, may provide an excellent background for a course on the subjectsecond edition provides considerable extensions of the subjectsauthor's acknowledgements show that comments from a lot of well-known geometers have lead to an improvement of the book." --Bernd Wegner, Zentralblatt MATH, Vol. 942

About the Author

Gray; Alfred University of Maryland, College Park, USA,

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Customer Reviews

3.6 out of 5 stars
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Most Helpful Customer Reviews

18 of 18 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on May 7, 2002
Format: Hardcover
The visualization of complicated geometrical objects
is now routine thanks to the excellent software that
has been developed over the past two decades. Now
students and professionals can have a better
appreciation of the geometrical properties of these
objects thanks to these software packages. In this
book the author has done a great job of doing this,
having chosen one of the best tools for this purpose:
Mathematica. The book is a hefty one, totaling almost
1100 pages, but its perusal is worth the effort for
those who want a more intuitive appreciation behind
the concepts of differential geometry. Physicists in
particular, who usually need a pictorial approach to
complement the learning of a subject, should really
enjoy this book. It could definitely be used as a
textbook in a beginning course in differential
geometry since there are problems at the end of each
chapter and most of the results in the book are proven
with the required mathematical rigor, I.e. this book
is not just code and pictures, and a substantial
portion of it is devoted to definitions and rigorous
proofs. This is especially true for the discussion on
differentiable manifolds and Riemannian geometry. The
author also includes a brief biography of the
mathematicians who have been involved in differential
geometry at various places in the book. The
Mathematica code in the book though can be revised to
make it look more like standard mathematical notation,
thanks to the new features of Mathematica that have
appeared since this book was published (1997).
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18 of 21 people found the following review helpful By A Customer on December 8, 1999
Format: Hardcover
Using this book might help you learn Mathematica, but if your goal is to learn differential geometry, please try something else. The Mathematica learner can benefit from the numerous useful examples and exercises in the book. In most programming books, the examples provided are trivial and usually do nothing useful, and this can make reading the book extremely boring. By using "Modern Differential Geometry of Curves and Surfaces with Mathematica"as a companion to a standard book on Mathematica, you can find a way out of this boredom. But the book essentially lacks the qualities of a text on pure mathematics. In some cases it lacks mathematical rigor, and even sometimes the definitions and their usage are inconsistent (see pages 159-161 for instance.) The proofs are also usually nothing but simple manipulations of formulae, the type that we have encountered mostly in high school. And when complicated mathematical reasoning becomes necessary, the author simply tries to avoid it. To summarize, if I were to pick a title for this book, I would chose "Fun with Mathematica through Differential Geometry."
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6 of 6 people found the following review helpful By angelos Vorvolakos on December 10, 1999
Format: Hardcover
I would recommend this book to anyone that needs an intuitive introduction to the subject that is complete in many ways and that provides visualization and examples using mathematica when needed. Before purchasing this I was expecting the treatment to be 'informal' and using mathematica rather than mathematical rigour to introduce concepts and results. This is not the case however. In my opinion the author has struck the right balance between a formal maths treatment and the abilities provided by mathematica to make the book easier to read and coprehend.
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7 of 8 people found the following review helpful By A Customer on January 24, 2000
Format: Hardcover
I strongly disagree with the reviewer at the bottom of this page. Having taken a differential geometry course last year using do Carmo's book (also excellent) I came to appreciate the intuition that this book lends to the reader. Also, this book makes greater use of elementary linear algebra than is common in some more standard texts, for example in defining the second fundamental form in terms of the Shape Operator. For students wanting to compliment their course notes or standard text with a book which will thoroughly explain both the fundamentals and isolated topics, this book is highly recommended.
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