Intro books on Differential Geometry?

In summary, the conversation is about finding a suitable book for self-study on introductory Differential Geometry. The person is looking for a book that is not too difficult and mentions their background in Linear Algebra, calculus, and basic vector calculus. They mention that their university recommends "Elementary Differential Geometry" by A. Pressley as a supplement to their course notes, but there are mixed reviews about its difficulty level. They ask if this is a good book for self-study or if there are better alternatives. They are advised to search for discussions about this topic on online forums and mention that they have already started doing so. They also mention budget constraints and ask for opinions on the affordability of Pressley's book.
  • #1
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I want a book on introductory Diff. Geometry for self study, but I don't know which book will be suitable for me, and not on a too high level. I know Linear Algebra, single & multi variablecalculus, basic vector calculus and very little about ODE's and PDE's.

At the Diff. Geometry course page (of the math department of my university) they recommened as a supplment to their own notes Elementary Differential Geometry by A. Pressley. But they mention that the level of Pressley is a little more difficult than their own notes. But when I read reviews about this book, it seems like this book is suitable for self study and easey to understand.
So is this a good material for self study and on the subject of diff. geometry, or maybe someone knows a better material for this subject?
 
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  • #2
There are tons of threads in PF on this very topic. Please search the Book Reviews and Tensor and Diff. Geom. forums. I think there was one active last week.
 
  • #3
neutrino said:
There are tons of threads in PF on this very topic. Please search the Book Reviews and Tensor and Diff. Geom. forums. I think there was one active last week.

I was actually just doing that.
Since I'm a poor student I mentioned Pressley because it's not too expensive :rolleyes:. I tried seaching about that book here, but can't seem to find anything about it. Maybe someone one knows alittle about this book and can tell wether it's worth buying?
 

1. What is Differential Geometry?

Differential Geometry is a branch of mathematics that deals with studying the properties of smooth curves and surfaces in different dimensions. It combines the concepts of differential calculus, linear algebra, and topology to analyze the geometric structures of objects and spaces.

2. What are the applications of Differential Geometry?

Differential Geometry has various applications in many fields, including physics, engineering, computer graphics, and robotics. It is used to describe the shape of objects in space, analyze the motion of objects, and solve optimization problems.

3. What are the prerequisites for studying Differential Geometry?

A strong understanding of multivariable calculus, linear algebra, and topology is necessary to study Differential Geometry. Familiarity with topics such as vector calculus, matrices, and topological spaces is essential for a thorough understanding of the subject.

4. How is Differential Geometry different from Euclidean Geometry?

Differential Geometry focuses on studying curved spaces and objects, while Euclidean Geometry deals with flat, two-dimensional spaces. Differential Geometry also uses tools and concepts from calculus and linear algebra, while Euclidean Geometry is primarily based on axiomatic systems.

5. What topics are covered in an Intro book on Differential Geometry?

An Intro book on Differential Geometry typically covers topics such as curves and surfaces, tangent spaces and vector fields, curvature and geodesics, and the fundamental forms of surfaces. It may also include applications of Differential Geometry, such as in physics and engineering.

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