Where can I find free or affordable resources for learning Reimann Geometry?

In summary, the speaker is asking for recommendations for free or cheap resources to learn the fundamentals of Reimann Geometry. They express a strong interest in higher dimensional mathematics and are open to applications as well. Another person suggests a list of books to check out, including Do Carmo's text on curves and surfaces and Marcel Berger's A Panoramic View of Riemannian Geometry for a deeper understanding of Riemannian curvature. The speaker expresses gratitude for the recommendations and plans to look into them.
  • #1
mepcotterell
21
0
Can anyone please forward me to some free or cheap resources for learning the fubdamentals of Reimann Geometry? I am very interested in the prospects of higher dimensional mathematics and would very much like to, at the very least, be able to understand the fundmentals and maybe even some applications. Any and all help is appreciated.
 
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  • #3
Thank you very much. This will help me a lot.
 
  • #4
You're welcome. :)
 
  • #5
neutrino said:

It's not a bad list. But always remember that with free books one always what one pays for.

A nice nuts-and-bolts introduction to 1 and 2-diml. Riemannian geometry can be found in Do Carmo's text on curves and surfaces. His text _Riemannian Geometry_ is the best introduction to Riemannian geometry proper out there.

Also, you might try looking at the first few chapters of Marcel Berger's A Panoramic View of Riemannian Geometry. In there he gives the best interpretation of Riemannian curvature and sectional curvature I've ever seen.
 
  • #6
Thanks Doodle Bob. I'll certainly look into those texts as well. A quick search for Do Carmo yields impressive commentary on his works. I look forward to reading it.
 

1. What is Reimann Geometry?

Reimann Geometry is a branch of mathematics that deals with the study of curved surfaces and spaces. It was developed by German mathematician Bernhard Riemann in the 19th century and has since been used in fields such as physics, engineering, and computer graphics.

2. How is Reimann Geometry different from Euclidean Geometry?

While Euclidean Geometry deals with flat, two-dimensional spaces, Reimann Geometry deals with curved, multi-dimensional spaces. It also takes into account the curvature of these spaces, which is not considered in Euclidean Geometry.

3. What are some practical applications of Reimann Geometry?

Reimann Geometry has many practical applications, including in the fields of general relativity, cosmology, and differential geometry. It is also used in computer graphics and mapping systems.

4. What are some common resources for learning Reimann Geometry?

There are many resources available for learning Reimann Geometry, including textbooks, online courses, and video lectures. Some popular textbooks include "Riemannian Geometry" by Manfredo P. Do Carmo and "Differential Geometry: Connections, Curvature, and Characteristic Classes" by Loring W. Tu.

5. Is Reimann Geometry difficult to understand?

Reimann Geometry can be a challenging subject, as it involves abstract concepts and advanced mathematical concepts. However, with dedication and practice, it can be understood by anyone with a strong foundation in mathematics and a willingness to learn.

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