A Differential Geometry Class: Suggestions Welcome

TyP
Messages
2
Reaction score
1
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.
 
Physics news on Phys.org
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.
 
In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
So, to calculate a proper time of a worldline in SR using an inertial frame is quite easy. But I struggled a bit using a "rotating frame metric" and now I'm not sure whether I'll do it right. Couls someone point me in the right direction? "What have you tried?" Well, trying to help truly absolute layppl with some variation of a "Circular Twin Paradox" not using an inertial frame of reference for whatevere reason. I thought it would be a bit of a challenge so I made a derivation or...
I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
Back
Top