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May
1
revised Why is there a connection between enumerative geometry and nonlinear waves?
corrected ODE and alternative formula for g(z)
Apr
27
comment In “splendid isolation”
The arxiv paper is "Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details" by Aitchison, MacManus, and Snyder (pg. 4-5).
Apr
27
comment Should the formula for the inverse of a 2x2 matrix be obvious?
The geometry associated with Poloni's answer makes the algebra transparent, is easy to remember, and is suitable for introductory lessons on matrices and vectors in linear algebra.
Apr
25
comment Should the formula for the inverse of a 2x2 matrix be obvious?
I.e., an orientation and scaling giving unity for the inner products of the first (second) column of the inverse and first (second) row of A.
Apr
23
comment Should the formula for the inverse of a 2x2 matrix be obvious?
Geometrically, the off-diagonal elements of the resulting identity matrix being zero translates into the first column of the inverse matrix being orthogonal to the second row of the matrix to be inverted (A) and likewise for the second column of the inverse and the first row of the matrix A. Overall signs are determined by correct orientation of the orthognal vectors to give a normalization by the signed area (determinant) to unity.
Apr
19
revised A question about summation formula involving binomial coefficient
Corrected Tex
Apr
19
revised A question about summation formula involving binomial coefficient
Added a relation
Apr
16
answered A question about summation formula involving binomial coefficient
Apr
13
revised Why is there a connection between enumerative geometry and nonlinear waves?
Corrected notation
Apr
13
awarded  Necromancer
Mar
25
awarded  Nice Answer
Mar
19
comment Parodies of abstruse mathematical writing
Yet (in another universe), Walter Pitts notified Russell of several mistakes in the Principia (when Pitts was 12!). nautil.us/issue/21/information/…
Mar
17
comment Parodies of abstruse mathematical writing
Many of the examples here are cerebral. You smirk if anyone is around just so they understand you get the inside joke, but the Hitler parody is visceral, with the roles of authority reversed between the student and teachers, and had me ROTFL. I think disenchanted students can relate more to it than the insider jokes that are intended more to embarrass the pretentious than as a self-parody.
Mar
17
comment Parodies of abstruse mathematical writing
@LSpice "Hence" following a question!? Furthermore, the OP stipulates the source be a knowledgeable mathematician (= a random sentence generator? Maybe).
Mar
17
comment Parodies of abstruse mathematical writing
I suppose this is highly upvoted more for the examples at Eldredge's website than the grammatically incoherent example here.
Mar
14
comment Parodies of abstruse mathematical writing
Simplest example to illustrate Todd's "just about all": Hitler Learns Topology on YouTube.
Mar
10
awarded  Popular Question
Feb
23
comment Intuition for Integral Transforms
Convolution integral reps exist for the appropriate integration ops and the derivative acting on suitable functions for the Fourier, Laplace, and Mellin transforms. Applying the associated convolution theorems gives products in the reciprocal space. The extremely simple derivations of these convolution theorems provide an accurate and intuitive pic of the separability into products in the reciprocal space as largely based on the simple group properties $e^{-p(x+y)} = e^{-px}e^{-py}$ and $(x/y)^{s-1} = x^{s-1}y^{1-s}$. The transforms of the Heaviside step fct are required for int ops.
Feb
20
comment What is a cumulant really?
A great introduction to both classical and free cumulants is "Three lectures on free probability" by Novak and LaCroix arxiv.org/abs/1205.2097.
Feb
20
comment Relationship between R-transform and free convolution of random matrices?
For an overview of these topics, see "Three lectures in free probability" by Novak and LaCroix arxiv.org/abs/1205.2097