Heinrich Hartmann — Mathematics
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% CHAPTER 1: DIFFERENTIAL DUALITY
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% CHAPTER 2: DISCRETE DUALITY
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% CHAPTER 3: ULTRA CALCULUS
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$$
Mathematical writings by Heinrich Hartmann. All sources available on GitHub.
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Publications
-
Discrete and Differential Calculus (2026) · DOI · pdf · GitHub · Zenodo
The four functors of higher-order calculus: \(D^+, D_+, \Delta^+, \Delta_+\) -
Discrete Faà di Bruno — Simulation Source Code (2026) · GitHub · Web
Python tooling to compute and validating discrete Faà di Bruno formulas. -
Discrete Faà di Bruno via Möbius Inversion (2026) · DOI · pdf · GitHub · arXiv · Zenodo
A new discrete, closed-form Faà di Bruno formula. -
Faà di Bruno is Taylor Composition (2026) · DOI · pdf · GitHub · arXiv · Zenodo
We approach Faà di Bruno from the Taylor composition standpoint and derive all common forms in a short, self-contained article. -
A Unified Polynomial Approximation Scheme for Classical Function Spaces (2026) · DOI · pdf · GitHub · Zenodo
We prove density results for polynomials in continuous, \(L^p\), \(C^k\), and Sobolev spaces. -
Fundamental Theorem of Algebra (2025) · DOI · pdf · GitHub · Zenodo
A short deformation argument. -
The Cayley-Hamilton Theorem (2025) · DOI · pdf · GitHub · Zenodo
A short rigidity argument.