Differential Geometry Class: Suggestions Welcome

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Discussion Overview

The discussion revolves around recommendations for online classes in differential geometry, particularly in the context of preparing for studies in General Relativity (GR). Participants share resources and personal experiences related to learning differential geometry.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks recommendations for online classes in differential geometry to build a foundation for studying GR.
  • Another participant suggests that @jedishrfu might have useful insights due to their familiarity with online video sources.
  • A participant shares specific resources, including the MIT Open Courseware course on differential geometry and a course by Prof Arezzo, noting the difficulty in finding suitable courses.
  • This participant also mentions their own background in differential geometry, referencing previous studies and books, and suggests a progression through different resources for a comprehensive understanding.
  • There are mentions of visual resources on YouTube that are appreciated for their brevity and interactive graphics.

Areas of Agreement / Disagreement

Participants generally agree on the difficulty of finding quality online courses in differential geometry and share various resources, but there is no consensus on a single best option or approach.

Contextual Notes

Some participants express uncertainty about their current knowledge and the effectiveness of the resources mentioned, indicating that their understanding may be outdated or incomplete.

Who May Find This Useful

Individuals interested in studying differential geometry, particularly those planning to delve into General Relativity, may find the shared resources and experiences beneficial.

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TL;DR
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.
 
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Many thanks for all the info.
 
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