Posts

• Wed 20 January 2021 - The Laplacian Quadratic Form Is an Edge-Energy Sum [mathematics] [spectral graph theory] [random walks] [electrical networks] - updated: Tue 11 June 2024
• Tue 04 June 2024 - The Euclidean Algorithm Writes a Rational as a Continued Fraction [mathematics] [continued fractions] [Diophantine approximation] [Pell equations]
• Fri 05 January 2024 - Rooted-Tree Subtree Sizes Obey a Bottom-Up Recurrence [mathematics] [trees] [graph distance] [structural graph theory] - updated: Thu 23 May 2024
• Mon 20 May 2024 - Jordan Form Separates Eigenvalues from Nilpotent Drift [mathematics] [eigenvalues] [canonical forms] [minimal polynomials]
• Tue 23 August 2022 - Backward Euler Is A-Stable on the Left Half-Plane [mathematics] [ordinary differential equations] [Runge--Kutta methods] [stability] - updated: Tue 16 April 2024
• Fri 29 March 2024 - The First-Moment Method Deletes All Bad Outcomes [mathematics] [extremal combinatorics] [probabilistic method] [Ramsey theory]
• Wed 28 February 2024 - An Adjunction Is a Natural Hom-Set Bijection [mathematics] [category theory] [functors] [adjunctions]
• Tue 27 February 2024 - A Prime Is a Sum of Two Squares Exactly in the Split Case [mathematics] [quadratic residues] [quadratic reciprocity] [sums of squares]
• Wed 31 January 2024 - Hoeffding Gives Subgaussian Tails for Bounded Sums [mathematics] [concentration inequalities] [tail bounds] [martingales]
• Mon 09 March 2015 - Multiplicative Order Divides Every Valid Exponent [mathematics] [congruences] [multiplicative order] [primitive roots] - updated: Mon 29 January 2024
• Fri 26 January 2024 - A DFS Tree Edge Is a Bridge When No Back Edge Escapes [mathematics] [connectivity] [bridges] [Menger theorem]
• Tue 09 February 2021 - Linear-Programming Duality Prices Every Constraint [mathematics] [polynomial algorithms] [optimization] [duality] - updated: Mon 15 January 2024
• Fri 12 January 2024 - The Killing Form Takes a Trace of Two Adjoint Maps [mathematics] [Lie algebras] [brackets] [matrix groups]
• Fri 12 May 2017 - Independence Factorizes Every Joint Event [mathematics] [conditional probability] [random variables] [distributions] - updated: Wed 13 December 2023
• Sat 18 May 2019 - The Picard Group Splits Divisors by Degree [mathematics] [algebraic curves] [divisors] [Riemann--Roch] - updated: Tue 21 November 2023
• Sat 18 June 2022 - Hilbert's Basis Theorem Adds One Polynomial Variable [mathematics] [Noetherian rings] [finiteness] [ideals] - updated: Mon 13 November 2023
• Thu 02 November 2023 - Maschke Averaging Produces an Invariant Projection [mathematics] [representation theory] [characters] [group algebras]
• Mon 23 October 2023 - Newton's Method Is Tangent-Line Root Finding [mathematics] [numerical analysis] [root finding] [interpolation]
• Thu 19 October 2023 - Optional Stopping Preserves Expectation under Safe Hypotheses [mathematics] [martingales] [branching processes] [optional stopping]
• Thu 14 September 2023 - Cyclotomic Polynomials Have Abelian Galois Groups [mathematics] [polynomials] [discriminants] [Galois groups]