Is Lang's Book on Differential Geometry Suitable for Beginners?

In summary, the conversation started with someone asking for recommendations on a textbook for learning differential geometry, specifically with worked examples. Some suggestions were made, including "Fundamentals of Differential Geometry" by Serge Lang, "A Comprehensive Introduction to Differential Geometry" by Michael Spivak, "The Geometry of Physics" by T. Frankel, and "Differential Geometry of Curves and Surfaces" by Do Carmo. However, there was some disagreement and hostility towards the suggestion of starting with Lang's book. It was also mentioned that the original poster may have been trolling.
  • #36
Like in the other thread I recommend to toe dippers with "some" calculus and linear algebra and an interest in physical stuffs Curvature in Mathematics and Physics by Shlomo Sternberg. To the sentimentalist who think three dimensions is more than enough try differential Geometry Of Three Dimensions by C.E. Weatherburn.
 
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  • #37
tade said:
Sometimes I think the people replying are just trying to show off and "overkill" instead of actually helping the OP.
In the guy's defense, I didn't feel like I understood differential geometry at all until I borrowed a copy of volume 1 of Spivak's introduction. It opens by defining a manifold as a metric space rather than the more general topological space, but other than that it was fantastic. Plus, I like the way Spivak writes. I don't know about anyone else, but it often reads like he's talking to you rather than attempting to talk around your perceived skill level. I appreciate this.

That being said, Spivak doesn't hold much back either. :tongue:
 
  • #38
Spivak isn't a problem. Lots of people use Spivak for a first exposition to differential topology. Only Gauss, Riemann, or Weyl would use Lang as an intro to the subject.
 
  • #39
^I don't see any problem looking at Lang (or Kobayashi and Nomizu) early on. It does not cause your face to melt. Lang is one of the few books with infinite dimensional flavor, and as is often the case with Lang, he presents things as they are best understood instead of easiest understood. Still most people would like to also read a more gentle book. Spivak is pretty chatty which others dislike, but I consider it a strength. I dislike the typeset though and if I recall correctly it is unchanged in the third edition.
 
  • #40
The issue I have with Lang is it has no exercises. Otherwise I think it would be a reasonable choice for a dedicated student.
 
  • #41
lurflurf said:
^I don't see any problem looking at Lang (or Kobayashi and Nomizu) early on. It does not cause your face to melt. Lang is one of the few books with infinite dimensional flavor, and as is often the case with Lang, he presents things as they are best understood instead of easiest understood. Still most people would like to also read a more gentle book. Spivak is pretty chatty which others dislike, but I consider it a strength. I dislike the typeset though and if I recall correctly it is unchanged in the third edition.

deluks917 said:
The issue I have with Lang is it has no exercises. Otherwise I think it would be a reasonable choice for a dedicated student.

Man, even my old differential geometry professor said that he looked at Lang and didn't understand much of it because it was so horrible written. And this is a guy who knows differential geometry inside out.
 
<h2>1. What is differential geometry?</h2><p>Differential geometry is a branch of mathematics that studies the properties of curves and surfaces using the tools of calculus and linear algebra. It is used in many fields, including physics, engineering, and computer graphics.</p><h2>2. What is the purpose of a book on differential geometry?</h2><p>A book on differential geometry serves as a comprehensive guide to the subject, providing an in-depth understanding of the fundamental concepts and techniques used in this field. It also serves as a reference for researchers and practitioners in related fields.</p><h2>3. What are some applications of differential geometry?</h2><p>Differential geometry has many applications in various fields, including physics, engineering, computer graphics, and robotics. It is used to study the shape of objects, the motion of particles and fluids, and the behavior of light and sound waves.</p><h2>4. Is a strong background in mathematics necessary to understand a book on differential geometry?</h2><p>Yes, a strong foundation in mathematics, particularly in calculus and linear algebra, is necessary to fully understand a book on differential geometry. However, many introductory books on the subject provide explanations and examples that can be understood by readers with a basic understanding of these mathematical concepts.</p><h2>5. Are there any recommended prerequisites for reading a book on differential geometry?</h2><p>A solid understanding of calculus, linear algebra, and multivariable calculus is recommended before delving into a book on differential geometry. Some familiarity with abstract algebra, topology, and differential equations may also be helpful.</p>

1. What is differential geometry?

Differential geometry is a branch of mathematics that studies the properties of curves and surfaces using the tools of calculus and linear algebra. It is used in many fields, including physics, engineering, and computer graphics.

2. What is the purpose of a book on differential geometry?

A book on differential geometry serves as a comprehensive guide to the subject, providing an in-depth understanding of the fundamental concepts and techniques used in this field. It also serves as a reference for researchers and practitioners in related fields.

3. What are some applications of differential geometry?

Differential geometry has many applications in various fields, including physics, engineering, computer graphics, and robotics. It is used to study the shape of objects, the motion of particles and fluids, and the behavior of light and sound waves.

4. Is a strong background in mathematics necessary to understand a book on differential geometry?

Yes, a strong foundation in mathematics, particularly in calculus and linear algebra, is necessary to fully understand a book on differential geometry. However, many introductory books on the subject provide explanations and examples that can be understood by readers with a basic understanding of these mathematical concepts.

5. Are there any recommended prerequisites for reading a book on differential geometry?

A solid understanding of calculus, linear algebra, and multivariable calculus is recommended before delving into a book on differential geometry. Some familiarity with abstract algebra, topology, and differential equations may also be helpful.

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