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Suddenly HN has decided that they're not visual learners anymore. Too bad, Keenan Crane from CMU has the best video course series on Discrete Differential Geometry:

https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1...

https://www.cs.cmu.edu/~kmcrane/Projects/DDG

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Those are some awesome videos. You'll notice that by the end of the series, he's using advanced notation everywhere as well. And you'll notice the original PDF has lots of pictures too. The use of calculus notation is required to be precise about differential geometry. It is not some kind of elitism, it's just the most effective way to communicate abstract ideas without misunderstanding. I hit a wall in my math understanding until I was willing to embrace the symbols, rules and manipulations of good notation.

I'd go further and say that mathematical and physics notation is beautiful unto itself. The evolution of symbols used to transmit abstraction is incredible. They are way of exploring patterns which can then be refined and layered using proven notational magic. So cool.

This resonates much more with with than the above PDF that jumps right into the first definition.

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