Quantum Multivariable Calculus

This is a first of a few videos about an approach to calculus which is rooted both in Riemannian geometry and probability theory. The exterior derivative will be a bounded operator and a smoothed out version of the usual derivative. In this first video, I look at a few approaches for calculus with a bounded derivative. Pictures were taken on Thursday when running along the battle road in Lexington on Thursday. Some links: https://people.math.harvard.edu/~knill/thesis. My Thesis from 1993 https://people.math.harvard.edu/~knill/preprints/feldman.pdf Cohomology of abelian group actions https://people.math.harvard.edu/~knill/various/quantumcalc An approach from 2006-2007 https://arxiv.org/abs/1306.2166 Dirac operator of a graph. (2013) https://people.math.harvard.edu/~knill/pedagogy/pechakucha Pecha Kucha about quantum calc https://people.math.harvard.edu/~knill/teaching/math1a_2011 Math 1a, 2011 https://people.math.harvard.edu/~knill/teaching/math1a2024 Math 1a. 2024 https://people.math.harvard.edu/~knill/teaching/summer2025/exhibits/discretestokes 21a Summer 25 https://people.math.harvard.edu/~knill/teaching/summer2025/handouts/00-quantum.pdf 21a 2050