Graduate Differential Geometry Class: Suggestions Welcome

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SUMMARY

The discussion centers on recommendations for online classes in differential geometry, essential for studying General Relativity (GR). Key resources mentioned include the MIT Open Courseware course (18.950 Differential Geometry, Fall 2008) and a thorough course by Professor Arezzo. Additionally, visual resources from Khan Academy and YouTube are suggested for their engaging content. The conversation highlights the importance of foundational knowledge in differential geometry before advancing to GR studies.

PREREQUISITES
  • Understanding of General Relativity (GR)
  • Familiarity with differential forms
  • Basic knowledge of mathematical concepts from Wheeler's "Gravitation"
  • Exposure to MIT Open Courseware materials
NEXT STEPS
  • Explore the MIT Open Courseware course on Differential Geometry
  • Study Professor Arezzo's course for a comprehensive understanding
  • Review Khan Academy's visual resources on differential geometry
  • Read Wheeler's "Gravitation" and Flanders' book on Differential Forms for deeper insights
USEFUL FOR

Students and educators in mathematics, physicists preparing for General Relativity, and anyone seeking to strengthen their understanding of differential geometry.

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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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Maybe @jedishrfu has some idea because he normally has a good overview of online video sources.
 
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.
 
Many thanks for all the info.
 

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