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Dear all, next year, I will probably teach a one-semester course of Differential Geomtry of curves and surfaces. Its content must be something along the lines of the first four chapters of Do Carmo's famous book and my plan is indeed to follow it.

But I would like to know some other, more modern, references. Particularly some including material for Matlab or Maple. I'm already aware of the book of John Oprea: any other references?

I would also be greatful to know about some links to webpages with this subject.

Any hints, ideas, references, suggestions... are welcome. Thank you in advance.

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See also: mathoverflow.net/questions/7834/… –  Jesse Madnick Jan 18 '11 at 18:35
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Richard Palais has been working on interactive software for such courses: vmm.math.uci.edu/3D-XplorMath –  Ryan Budney Jan 18 '11 at 18:35

5 Answers 5

If you can use Mathematica, see Modern Differential Geometry of Curves and Surfaces with Mathematica.

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The book by Kuhnel is a good introduction. I am sitting through an introductory differential geometry class at Stanford which is being taught by Richard Schoen and he follows this book. The first four chapters will be a good introduction to differential geometry and the rest concentrates on Riemannian geometry. I have read the first three chapters so far and the book so far seems to be complete and concise. You can look up some reviews of the book on Amazon.

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My favorite is Andrew Pressley's "Elementary Differential Geometry." The material in it is very standard, yet the treatment is more modern than do Carmo's. However, I don't think there's much in the way of material for MatLab or Maple...

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I like the book Differential Geometry of Curves and Surfaces by Toponogov.

Besides its conciseness, it is well written and has some cool results on geodesic triangles which don't appear on Manfredo´s book.

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Another good book is the one of Barrett O'Neil,titled" Elementary Differential Geometry".I think it's at the same level as the Do Carmo's book but it makes a different approach.

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