Ebook Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
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Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
Ebook Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
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. Gouvêa, The Mathematical Association of America, May, 2010)
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From the Back Cover
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com Praise for the first edition: "The text is nicely illustrated, the definitions are well-motivated and the proofs are particularly well-written and student-friendly…this book would make an excellent text for an undergraduate course, but could also well be used for a reading course, or simply read for pleasure." Australian Mathematical Society Gazette "Excellent figures supplement a good account, sprinkled with illustrative examples." Times Higher Education Supplement
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Product details
Series: Springer Undergraduate Mathematics Series
Paperback: 474 pages
Publisher: Springer; 2nd ed. 2010 edition (March 18, 2010)
Language: English
ISBN-10: 184882890X
ISBN-13: 978-1848828902
Product Dimensions:
6.1 x 1.1 x 9.2 inches
Shipping Weight: 1.9 pounds (View shipping rates and policies)
Average Customer Review:
4.0 out of 5 stars
24 customer reviews
Amazon Best Sellers Rank:
#355,975 in Books (See Top 100 in Books)
I'm only reading sections of this book for the purpose of understanding some half-baked math in a physics book, but I can say that this is simply a lovely book: the proofs are clear, the diagrams are copious, and the book contains the worked solutions to hundreds of problems - it's excellent for self study. It's also a nice demonstration of what can be done using just some advanced calculus - this book is suitable for anyone with two years of calc/linear algebra.The book DOES say clearly in the introduction what it's scope is: mostly differential geometry in low dimensions and with methods that do NOT generalize to higher dimensions - so if you're looking for something else this isn't the book you want.
I've been looking for a decent book on differential geometry for years now. Most of the good ones are fairly pricey, or require the reader to have a deep knowledge of mathematics. This fits in neither category. You only need multi variable calculus, linear algebra, and some experience with reading/writing proofs. This book will also appeal to those who want to learn on their own, as every problem has a hint/solution in the back.
I think this book is a good introduction to differential geometry. The first five chapters are pretty good, after that it starts to go downhill. Chapter 6 on normal and geodesic curvature, is very heavy on linear algebra, and the geometry seems to be put off until the very end of the chapter. Chapter 7 is somewhat better about this. Chapter 8 is boring and I found the problems to be overly challenging simply because a lot of explicitly refer to results from exercises in chapter 5 and 6. I am still in the process of reading this book.
For a stand-alone course in differential geometry at the undergraduate level, this is one of the clearest and most accessible texts around, with perhaps its only rival being McCleary's "Geometry from a Differentiable Viewpoint." It's written in the spirit of Struik's classic, "Lectures on Classical Differential Geometry," and explains the classical material developed largely by Gauss. The caveat is that a student planning to later study Riemannian geometry will perhaps not be best served by such a book -- e.g., there's no mention of covariant derivatives, which -- as Riemannian connections on a differentiable manifold -- serve as the bedrock of Riemannian geometry. Such a student would be better served either by O'Neill's "Elementary Differential Geometry" or Oprea's "Differential Geometry and its Applications" (see in particular the last chapter). This is the difference between classical and modern treatments of differential geometry.
This is a great self-teaching guide for someone who is already comfortable with the calculus and matrix algebra.
I got this book for a graduate level differential geometry class. The book has a typo almost every other page. Don't get me wrong, typos are generally not a big deal, however if they're in the middle of equations it is just incorrect and useless. I don't recommend this book to anyone. The "Second Edition" on the cover makes me laugh. I can only imagine how much worse the first one was.
I'm using this book in my independent study class, it's an excellent introductory book for self studies.Pros:1. Highly readable2. There're ample example walk-throughs3. Full solution at the back of the book4. Contains the complete introduction to the subjectCons:1. Only contains a classical introduction and is mostly restricted to 3-d space, hard to generalize to higher dimensions.I'm using this in conjunction with Wolfgang's intro to Differential Geometry(ISBN 978-0821839881), which provides a more modern view of the subject and is much more general.Would definitely recommend to self learners as a first course in Differential Geometry.
I would not recommend this book for math majors. I used this book for a course in differential geometry which was not intended for math majors (so yes, it is sort of my fault), but thought I would mention this here just in case there are math students who are considering it. Like the author mentions, some of the methods he uses don't generalize and so they keep the requirements to a minimum and parts of the book cover topics that a math major would already know and not as rigorously. A math student should be able to tackle the classic in the genre by do Carmo. My professor often times used the proofs of do Carmo instead of the ones from Pressley. However, I suppose for non-math majors this is probably a very good book as it also includes solutions to every problem at the back. So its excellent for self-study!
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