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Rating: ![5 stars](http://www.reviewfocus.com/images/stars-5-0.gif) Summary: A Perfect Introduction Review: A Must !!! After reviewing a few dozen books in the subject, this is without any doubt one of the best. It it written with rare clarity, and gives enough motivation and examples to understand the more abstract and difficult aspects of the field. The book is intended for advanced undergraduate (with good understanding of linear algebra and calculus III) and should be read prior to an abstract course in differential geometry (such as is covered in the books of Warner and Hicks).
Rating: ![5 stars](http://www.reviewfocus.com/images/stars-5-0.gif) Summary: A Perfect Introduction Review: A Must !!! After reviewing a few dozen books in the subject, this is without any doubt one of the best. It it written with rare clarity, and gives enough motivation and examples to understand the more abstract and difficult aspects of the field. The book is intended for advanced undergraduate (with good understanding of linear algebra and calculus III) and should be read prior to an abstract course in differential geometry (such as is covered in the books of Warner and Hicks).
Rating: ![5 stars](http://www.reviewfocus.com/images/stars-5-0.gif) Summary: Took the class and the book Review: I had the class from Prof. Parker ~20 years ago. (BS Mathematics 83 from SIU) It was a wonderful class and this is a wonderful book. I still have my signed! copy. I am now a professor of EE and a large research university and this is still a subject that I love. Credit that to the Book and Prof. Parker.
Rating: ![5 stars](http://www.reviewfocus.com/images/stars-5-0.gif) Summary: Took the class and the book Review: I had the class from Prof. Parker ~20 years ago. (BS Mathematics 83 from SIU) It was a wonderful class and this is a wonderful book. I still have my signed! copy. I am now a professor of EE and a large research university and this is still a subject that I love. Credit that to the Book and Prof. Parker.
Rating: ![5 stars](http://www.reviewfocus.com/images/stars-5-0.gif) Summary: A solid introduction Review: It is hard to disagree with the idea that one must pursue the learning of mathematics in way that might be at odds with its axiomatic structure. One can pursue the study of differentiable manifolds without ever looking at a book on classical differential geometry, but it is doubtful that one could appreciate the underlying ideas if such a strategy were taken. Some background in linear algebra, topology, and vector calculus would allow one to understand the abstract definition of a differentiable manifold. However, to push forward the frontiers of the subject, or to apply it, one must have a solid understanding of its underlying intuition. Thus a study of classical differential geometry is warranted for someone who wants to do original research in the area as well as use it in applications, which are very extensive. Differential geometry is pervasive in physics and engineering, and has made its presence known in areas such as computer graphics and robotics. In this regard, the authors of this book have given students a fine book, and they emphasize right at the beginning that an undergraduate introduction to differential geometry is necessary in today's curriculum, and that such a course can be given for students with a background in calculus and linear algebra. They also do not hesitate to use diagrams, without sacrificing mathematical rigour. Too often books in differential geometry omit the use of diagrams, holding to the opinion that to do so would be a detriment to mathematical rigour. Much is to be gained by the reading and studying of this book, and after finishing it one will be on the right track to begin a study of modern differential geometry.
Rating: ![3 stars](http://www.reviewfocus.com/images/stars-3-0.gif) Summary: Another Differential Geometry Book - So So Review: This book I also purchased as a resource for studying differential geometry. It's a little bit better than the one by Thorpe, but not by much. The text is dedicated to the 'hard-core' mathematical, and even they would have to have some experience/guidance in this subject. I'm a self-learning type of guy, with an MS in physics. Too many questions arise to justify this book for the self-learner. There are problems, and a FEW examples.
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