Diagrammatic Tensor Notation from the Beginning

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SUMMARY

The discussion centers on the development of a tutorial for Penrose's diagrammatic tensor notation, which the author finds lacking in available resources. The author has created 14 pages of rough content covering fundamental concepts such as numbers, vectors, covectors, and integrals. They seek feedback on whether to continue refining this tutorial and how to improve its clarity and conciseness. The author's unique approach to tensor addition notation is also highlighted.

PREREQUISITES
  • Understanding of basic tensor algebra concepts
  • Familiarity with Penrose's diagrammatic notation
  • Knowledge of numerical computation techniques
  • Basic skills in writing and structuring educational content
NEXT STEPS
  • Research Penrose's diagrammatic notation in detail
  • Explore numerical computation methods for tensor operations
  • Study effective tutorial writing techniques
  • Examine existing resources on tensor algebra for reference
USEFUL FOR

Students and educators in mathematics and physics, particularly those interested in tensor algebra and diagrammatic notation. This discussion is also beneficial for content creators developing educational materials in these fields.

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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