elementary differential geometry pressley

#Elementary differential geometry pressley how to
#Elementary differential geometry pressley update

Congruence of Surfaces.Ĭhapter 7: Riemannian Geometry: Geometric Surfaces. Differentiable Functions and Tangent Vectors. Nowadays he's an old fogey who teaches at Colby College in Waterville, ME.Įuclidean Space. Gouvêa read parts of O'Neill's book way back when he was an undergraduate. But I do know that O'Neill's book is very nice, the sort of book that can make the right student learn to love the subject.įernando Q. I don't know which I prefer it depends on the day. His competitors (e.g., the books by do Carmo, Oprea, and Pressley) all prefer to avoid differential forms. O'Neill has remained alone in choosing this approach.

On the other hand, this is the language used in more advanced books, so learning it can be very useful to the student. This can get in the way of the geometry, as I learned when I tried to teach from this book. There is no doubt that this is the right language, but using it in an introductory book means quite a large amount of setup is needed right at the beginning of the course. the learning curve for differential geometry is unusually steep, even by math standards. As the author points out, it is instructive to do these calculations by hand once or twice, but once the matter is understood one should use technology.įor instructors looking for an undergraduate textbook, the most problematic aspect of this book will be O'Neill's decision to use the language of tangent vectors, differential forms, and covariant derivatives. Honestly, the text I most like for just starting in differential geometry is the one by Wolfgang Kuhnel, called 'Differential Geometry: curves - surfaces - manifolds.' 2nd.

#Elementary differential geometry pressley how to

Beyond that, the only real change is the addition of a very useful appendix showing how to use Mathematica or Maple to do the more important computations in elementary differential geometry. There are lots of corrections, and the exercises have been significantly improved. The changes to the text are fairly minimal. It's good to see it come back in a new edition. But it's still a beautiful book, well-written and displaying a deep understanding of the subject. And with old-fashioned artist-drawn illustrations. Forty years later, O'Neill has lots of competition, of course. There was simply no other book taking a modern approach to the material that could be used as an undergraduate text. The book has an attractive price point from Springer, and you can get it from for even cheaper.

#Elementary differential geometry pressley update

The first edition is from 2002, with the update published in 2010. At that point, it pretty much had the field to itself. It is time to return to the book reviews Our next book is Elementary Differential Geometry, 2nd Ed by Andrew Pressley. Barrett O'Neill's introduction to differential geometry was first published in 1966.