Posts

• Tue 07 December 2021 - Cauchy's Integral Formula Reconstructs Interior Values [mathematics] [complex analysis] [contour integration] [residues] - updated: Wed 26 February 2025
• Tue 17 January 2023 - Kähler Differentials Represent Derivations [mathematics] [sheaves] [quasi-coherent sheaves] [differentials] - updated: Thu 20 February 2025
• Wed 19 February 2025 - A Short Exact Sequence of Complexes Produces a Long Exact Sequence [mathematics] [homology] [chain complexes] [exact sequences]
• Sat 19 November 2016 - Least Squares Projects b onto the Column Space [mathematics] [matrix factorizations] [least squares] [positive matrices] - updated: Sun 02 February 2025
• Sun 12 January 2025 - Normalization Repairs Missing Integral Functions [mathematics] [integral extensions] [normalization] [spectra]
• Sun 12 January 2025 - The Summatory Möbius Function Measures Cancellation [mathematics] [analytic number theory] [zeta functions] [Dirichlet characters]
• Sat 04 January 2025 - Kullback--Leibler Divergence Is Nonnegative [mathematics] [stochastic processes] [order statistics] [information theory]
• Sat 14 January 2023 - The Spectral Theorem Diagonalizes Self-Adjoint Operators [mathematics] [inner products] [spectral theorem] [quadratic forms] - updated: Wed 04 December 2024
• Sun 24 November 2024 - Galois Correspondence Reverses Inclusion [mathematics] [splitting fields] [separability] [Galois theory]
• Fri 24 April 2020 - Bellman--Ford Detects Reachable Negative Cycles [mathematics] [paths] [network flows] [matchings] - updated: Wed 20 November 2024
• Wed 20 November 2024 - Gauss's Lemma Counts Sign Crossings [mathematics] [quadratic residues] [quadratic reciprocity] [sums of squares]
• Wed 13 November 2024 - Annihilators Reverse Inclusion [mathematics] [vector spaces] [linear maps] [dual spaces]
• Sat 28 September 2024 - Turán's Theorem Maximizes Edges without a Clique [mathematics] [extremal combinatorics] [probabilistic method] [Ramsey theory]
• Tue 31 May 2016 - Integral Elements Form a Subring [mathematics] [integral extensions] [normalization] [spectra] - updated: Mon 23 September 2024
• Mon 16 September 2024 - The Dirac Delta Is a Distribution, Not an Ordinary Function [mathematics] [special functions] [asymptotic analysis] [distributions]
• Sat 02 April 2016 - K5 and K3,3 Violate Planar Density in Different Ways [mathematics] [planar graphs] [coloring] [duality] - updated: Sun 15 September 2024
• Tue 28 February 2023 - Planar Duality Exchanges Cycles and Cuts [mathematics] [planar graphs] [coloring] [duality] - updated: Wed 28 August 2024
• Sat 23 December 2023 - Dirichlet L-Functions Twist the Zeta Function [mathematics] [analytic number theory] [zeta functions] [Dirichlet characters] - updated: Fri 12 July 2024
• Wed 10 July 2024 - Lagrange Inversion Extracts Coefficients from Recursive Series [mathematics] [generating functions] [recurrences] [Lagrange inversion]
• Tue 30 August 2022 - The Legendre Family Displays a One-Parameter Moduli Coordinate [mathematics] [elliptic curves] [isogenies] [moduli] - updated: Tue 11 June 2024