Differential Geometry of Curves and Surfaces

Rating:
Summary: Outdated classic in the field
Review: While many consider this text the classic in the field, I think that it's time to find something a bit more modern. do Carmo often skips steps in his proofs or examples that he deems "obvious" but that my professor even had to spend a good deal of time trying to figure out how to bridge the gap. The writing style and terminology are beginning to show their age, and the exercises are particularly incomprehensible. Also, the few examples that are actually included don't give any insight into doing the exercises, which seem to be written primarily as a way for do Carmo to include topics that he couldn't squeeze into the body of the text. The hints in the back of the book are often too vague to provide any useful insight into solving the problem, especially for someone not familiar with geometry. Hope that you don't have to use this text for a first course in differential geometry, and if you do, hope that the professor writes his/her own exercises.