Differential Geometry of Curves and Surfaces

Rating:
Summary: Very Difficult
Review: Although some claim it is classic, don't expect it to be readable. The book's definitions cna be quite confusing, and it is often difficult to understand many of the definitions or problems without a great deal of effort. If you are using this book for a class, I would reccomend getting a more readable text for reference.

Rating:
Summary: Pretty good
Review: Excellent introduction in differential geometry. Beginning with simple and concrete cases, goes gradually into more abstracts idea of intrinsic geometry, and end up with totally abstract idea of abstract surfaces and Riemannian Manifolds. Full of motivations and examples but at the same time focus on the anylytic and mathematical aspects. You only need to know basic calculus and linear algebra so as to understand the text. Introductory knowledge in differential equations is preferrable but it is not a must. However, this book cost only about US$25 in Hong Kong.....

Rating:
Summary: excellent
Review: For the reader with a basic knowledge of the definition of tangent space on a manifold (chapter zero) this book is excellent. I find it one of the true masterpieces of pedagogy among the books I've read. It's a clear exposition of differential geometry from the mathematical standpoint. I think it goes well with hirsch's differential topology and it's always good to get a second perspective on Diff.G from the physics point of view, like Weinberg's Gravitation and Cosmology.

Rating:
Summary: Excellent introduction to differential geometry
Review: I found this book to be a good introduction to differential geometry for undergraduates. All concepts are clearly and concisely developed and explained well. Also, the details of advanced calculus and analysis required for the book are covered very well in appendices. My only reservation is that the problems can be very difficult at first. For someone interested in really exploring and learning differential geometry, however, this is not a problem.

Rating:
Summary: Excelent exposition !
Review: I used this book during my MsC in Math at University of Brasilia, Brazil. Manfredo gives a detailed exposition about the local and global properties of a surface and introduces the abstract surfaces at the end of the book. I really recommend this book for a first course in Differential Geometry and it gives a good knowledge to read the Riemannian Geometry(Manfredo).

Rating:
Summary: A good introductory book on Differential Geometry
Review: I used this book to study for the geometry qualifying exam at UC Santa Barbara for Masters and Ph.D. students. I found it easily accesible, concise, and self-contained.

Rating:
Summary: A good introductory book on Differential Geometry
Review: I used this book to study for the geometry qualifying exam at UC Santa Barbara for Masters and Ph.D. students. I found it easily accesible, concise, and self-contained.

Rating:
Summary: Very clear and concise geometry book suitable for coursework
Review: In a differential geometry course of three students, this text was used instead of the one we began the course with. This book was far and away more organized and paid attention to detail much better than most math books.

Rating:
Summary: A great introduction and surely a classic !!!
Review: Manfredo is a great teacher and a great geometer. In this book he follows Einstein's criteria "things must be presented in its simplest form, but not any simpler than that". It has great explanations and beautiful demonstrations. If you love math and geometry, buy it now!

Rating:
Summary: too wordy
Review: Many people say that this is an excellent book on elementary Differential Geometry,so I borrowed one.I read most of chapter1-4,but I do not find it clear enough.Maybe I have been confused by so many examples.It is too wordy for me.It can be more concise.I recommend the book of Klingenberg,which is used as my textbook.Klingenberg'book is a little dense and does not contain enough exercises.But your professor will give you some.