Posts

• Mon 26 June 2023 - The Wedge Product Is Alternating Multiplication of Forms [mathematics] [smooth manifolds] [tangent spaces] [differential forms] - updated: Thu 14 September 2023
• Mon 18 May 2015 - The Tower Formula Multiplies Extension Degrees [mathematics] [field extensions] [minimal polynomials] [degrees] - updated: Sun 10 September 2023
• Sat 09 September 2023 - Naturality Is a Family of Commuting Squares [mathematics] [category theory] [functors] [adjunctions]
• Sat 20 August 2022 - Direct Sums Are Unique Coordinate Decompositions [mathematics] [vector spaces] [linear maps] [dual spaces] - updated: Mon 28 August 2023
• Mon 21 September 2015 - Hamilton's Equations Come from Contracting dH with omega [mathematics] [symplectic geometry] [Hamiltonian systems] [Morse theory] - updated: Wed 23 August 2023
• Mon 31 August 2015 - A Durfee Square Decomposes a Partition into Three Pieces [mathematics] [integer partitions] [Young tableaux] [q-analogues] - updated: Sun 13 August 2023
• Mon 17 July 2023 - The Jacobi Identity Is a Cyclic Cancellation Law [mathematics] [Lie algebras] [brackets] [matrix groups]
• Tue 27 June 2023 - Simple Random Walk Is Reversible with Degree Weights [mathematics] [spectral graph theory] [random walks] [electrical networks]
• Mon 01 November 2021 - Riesz Representation Identifies Hilbert-Space Functionals [mathematics] [functional analysis] [Banach spaces] [operator theory] - updated: Sat 24 June 2023
• Tue 20 June 2023 - Lower Ramification Groups Measure How Nearly Automorphisms Fix Integers [mathematics] [infinite Galois theory] [local fields] [ramification]
• Tue 23 May 2023 - Every Nontrivial Tree Has at Least Two Leaves [mathematics] [trees] [graph distance] [structural graph theory]
• Wed 18 May 2022 - A Noetherian Ring Need Not Be Artinian [mathematics] [Noetherian rings] [finiteness] [ideals] - updated: Wed 17 May 2023
• Tue 31 May 2016 - Effective Resistance Is a Laplacian Pseudoinverse Distance [mathematics] [spectral graph theory] [random walks] [electrical networks] - updated: Sun 07 May 2023
• Fri 05 January 2018 - Möbius Inversion Extracts Primitive Necklaces [mathematics] [Polya enumeration] [combinatorial species] [symmetry] - updated: Sun 30 April 2023
• Mon 10 April 2023 - Character Inner Products Count Multiplicities [mathematics] [representation theory] [characters] [group algebras]
• Tue 04 April 2023 - The Supplementary Laws Handle Minus One and Two [mathematics] [quadratic residues] [quadratic reciprocity] [sums of squares]
• Sun 19 September 2021 - Order Ideals Form a Distributive Lattice [mathematics] [posets] [Mobius functions] [extremal set theory] - updated: Sun 02 April 2023
• Sun 26 March 2023 - The Discriminant Changes by the Sign of a Root Permutation [mathematics] [polynomials] [discriminants] [Galois groups]
• Sun 19 March 2023 - Conjugacy Classes in S_n Are Indexed by Partitions [mathematics] [permutation groups] [group actions] [conjugacy]
• Tue 28 February 2023 - Algebraic Elements Form a Field [mathematics] [field extensions] [minimal polynomials] [degrees]