Differential Geometry Class: Suggestions Welcome

In summary, the conversation is about a recommendation for a good online class for differential geometry. The person wants to study general relativity but needs a good background in differential geometry first. @jedishrfu is suggested as a potential source for recommendations. Some courses are mentioned, including one from MIT Open Courseware and one by Prof Arezzo. The person also mentions some visual courses on YouTube and their own experience with learning differential geometry. They suggest checking out a selection by Faculty of Khan and then the larger format course by Prof Arezzo, followed by the MIT course. The courses are said to be at the undergraduate level and the person recommends studying relevant books like Wheeler's and Flanders' after completing the courses.
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TL;DR Summary
On-Line class suggestions
Can anyone recommend a good on-line class for differential geometry? I'd like to start studying GR but want a good background in differential geometry before doing so. Many thanks.
 
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  • #2
Maybe @jedishrfu has some idea because he normally has a good overview of online video sources.
 
  • #3
This topic is much harder to find courses on as I’ve tried in the past. However, I did find the MIT Open Courseware course:

https://ocw.mit.edu/courses/mathematics/18-950-differential-geometry-fall-2008/

or this course by Prof Arezzo which looks pretty thorough:

and some more visual ones on YouTube which I like because of the relative shortness of the videos and the use of interactive graphics:



My differential Geometry knowledge is somewhat dated with many cobwebs. I learned pieces from an independent studies in General Relativity and in math using Wheeler‘s Gravitation and McConnell’s Dover book on the subject. More recently I looked at Flanders book on Differential Forms but had no time to really get into it.

Personally, I would check out the last selection by Faculty of Khan and then slog through the larger format Prof Arezzo for greater understanding and lastly the MIT one to complete your understanding. I believe they are all at the undergrad level so I guess after that one would tackle the relevant books like Wheelers and Flanders.
 
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  • #4
Many thanks for all the info.
 
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1. What is Differential Geometry?

Differential Geometry is a branch of mathematics that studies the properties of curves and surfaces in higher-dimensional spaces. It uses tools from calculus and linear algebra to understand the geometric properties of these objects.

2. What topics are typically covered in a Differential Geometry class?

A Differential Geometry class may cover topics such as curves and surfaces in 3-dimensional space, curvature and torsion, Gaussian and mean curvature, geodesics, and applications in physics and engineering.

3. What are some applications of Differential Geometry?

Differential Geometry has numerous applications in fields such as physics, engineering, computer graphics, and robotics. It is used to model and analyze the shape and movement of objects in space, and to solve optimization problems.

4. What are some useful resources for studying Differential Geometry?

Some useful resources for studying Differential Geometry include textbooks, online lectures and courses, and practice problems. It is also helpful to consult with a professor or join a study group to deepen understanding of the material.

5. What are some tips for succeeding in a Differential Geometry class?

To succeed in a Differential Geometry class, it is important to have a strong foundation in calculus and linear algebra. It is also helpful to practice solving problems and to ask questions when something is not clear. Additionally, staying organized and keeping up with the material will aid in understanding and retention of the concepts.

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