ZerusMaximus / is on Nostr

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Last Notes

2024-12-14 03:11:01

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@nprofile…3yjd any Christmas thoughts on functional analysis, particularly Sobolev spaces, Hilbert, Banach spaces, L2 spaces, and others? The visual/geometric idea of a finite tuple of numbers representing a basis vector, being similar to a discrete approximation of a squiggly line on some hyperplane, helped me with the idea that if we increase the number of interceptions, the quality of approximation, we get closer to a continuous squiggly line, in the limit, a function. Functions as basis. That may sound basic, obvious, even silly, but that was a geometric intuition somehow, that helped me grasp it. I wished more textbooks spent more time on visual, geometric, even physical (world, and physics, application), rather than just notation. The work of Tristan Needham is an example of visually rich advanced mathematics textbooks that provide many viewpoints for the reader to relate concepts, and develop a firm understanding. Anyway, I digress. Thank you for your exposes, they're very interesting to read.