Customer Reviews

Elementary Differential Geometry

5 star:		(3)
4 star:		(5)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

Pressley's gives you a very comprehensible and down to earth introduction to differential geometry.
By avoiding the more modern and abstract generalizations of differential geometry to more than three dimensions you really feel that you grasp what the theorems and methods are about. In this way you are able to work your way quickly through the book and avoid getting stuck and loosing interest. Another plus is that the book contains lots of examples and fully worked answers to all exercises, which makes it perfect for self-study.
The downside is that the book is not as exhuastive as you perhaps would like, when you have looked at books like O'Neills and DoCarmos ... on the other hand, you only need to spend a fraction of the time to get through Pressleys.
I definitely think that this is a much better book that Struiks classical work (by being more structured and goal oriented) and an excellent introduction to further studies in differential and Riemann geometry.

I have purchased hundreds of technical books and really treasure the ones that seem to have been written in order to really convey the material rather than impress the reader with how smart the author is. This is such a book. The material is remarkably clear and the author's style strikes me as a notable example of the mathematical writing styles put forth in the articles comprising the text "How to Write Mathematics." For example, the material proceeds in a logical chain such that the reader is never confronted with a term or concept before it has been explained. The notation is defined meticulously and repeatedly so the reader is not forced to continually refer backwards through the text to remember the meaning of the symbols. This also is a boon for "grasshopper readers" who will use the text as a reference, as opposed to a linear reader. Symbols don't change meaning, are not overloaded, and seem to have been chosen for intuitive appeal. For example, a lower-case gamma denotes a parametric function for a curve and, to me, the shape of the gamma suggests the sorts of curves being discussed. In my experience, this book is best in class.

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.

If you want a very general introduction of Differential Geometry, this is the book to start. Very nicely written text. Understandable examples. Broad coverage of materials . Explains space curves and surface properties with amazing quality. Recommended as a beginners level introduction

It's a very good book overall, especially if you like to spend more time reading on your own than in a classroom.

After trying several others, I found this book the best for individual study. The worked out solutions to all exercises gives you a good way to check your understanding. The writing is clear and the book has adequate illustrations to help you see what's going on.

I also liked presentation in Banchoff's book, Differential Geometry of Curves and Surfaces, but it has no answers or solutions to the exercises.

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!

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.

I am using this book for a 2 semester Differential Geometry course at my university. The school used to use Do Carmo, but apparently the book was too advanced for the undergraduate level, so this semester they decided to switch over to give this one a test and see how it worked out. This book is not bad. It is basically Do Carmo rehashed for the not so mathematically mature. In all seriousness, the book even follows almost the exact same flow as Do Carmo, the topics are just presented with less rigor. The exercises are rather tedious at the end of each chapter, and in my opinion they don't really help to enhance the subject matter.

On the other hand, if you fall in the category that most of the math majors at my university fall in (i.e. the category of people who really don't care, they just want to get an A and graduate, and don't care about mathematics), then you'll love this book. Why? Because the solution to every single problem is at the end of the book. In my opinion this is a huge flaw. It would be great if everyone were honest and everybody was genuinely interested in the learning Differential Geometry, but that isn't the case. So 90% of my class simply copies the answers out of the back of the book and hands it in to get a 100 on the homework assignments. Pretty sad if you ask me. The book is almost there. Without full solutions to every problem, this book would get 5 stars. But those students who simply turn to the back of the book 15 seconds after looking at the problem statement will learn nothing from this book, so I have to knock it down 2 stars. After all, what good is a book if it doesn't serve it's intended purpose. Perhaps some people would rate a book by "how easy is it to get an A in the class if this is the textbook", in which case they would probably rate this book 5 stars.

Differential Geometry is a hard subject. It's _supposed_ to be hard. We're not talking about taking the reciprocal of a fraction here, it's Differential Geometry. You're _supposed_ to think about these problems for a long time. So if you're a professor considering this book for a course I would recommend against it. The text is good, but the students won't learn anything from it. I've suggested to my professor that perhaps it would be good to not assign problems from the text, but rather get problems from other textbooks where students can't look at the answers.

In my opinion that is the only flaw with this book. Otherwise I think it's a great introduction, and about as elementary as you can really make the subject. If another book was too hard, then this is the one for you.

Also, if you're interested in this book for self study it's a good choice since obviously you're genuinely interested in the subject matter and won't be tempted to look at the answer at the first opportunity.

The book starts ok, but very quickly deteriorates into the classical boring math style of theorem-proof. There are a million books on the subject matter, and I don't see the need of another one which is pretty much identical. It is not a bad book, but has absolutely no added value - just pick any of the differential geometry books out there, and they will be the exact same thing. Why do they bother writing the same book over and over??