Diagrammatic Tensor Notation from the Beginning

LukeD
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I've posted this in the Geometry & Topology section, but I believe it will get many more views here, so I'm posting a link

Pictures here:
https://www.physicsforums.com/showthread.php?t=407776

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I really liked Penrose's diagrammatic way of writing tensor algebra, so I spent a while learning the basic notation. Unfortunately, it took a very long time for me to learn this because there is so little info on it to begin with. I also didn't see much mention of how to use the notation for doing numerical computations.

So since I want to be able to use the notation for everything that I should be able to do with tensors, I figured that I'd start at the very beginning of algebra and use the notation. My plan is to write a little tutorial that teaches everything from how to write numbers, vectors & covectors to how to take integrals.

The notation for adding tensors is mine as far as I know, and I've changed some other notation here and there.

I have 14 pages done, but they are very rough. So far they are very basic ideas. Should I continue with this? Any suggestions for cleaning it up? I want to make it as short & simple as possible while still getting the point across.
 
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