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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
Feb
17
answered Books about history of recent mathematics
Feb
17
answered Insightful books about elementary mathematics
Feb
14
revised effective teaching
New link
Feb
12
comment Geometric interpretation of the half-derivative?
You can relate locality vs. non-locality to simple poles vs. branch cuts in the appropriate complex-contour/convolution integral reps for fractional differintegro ops of this type. The regular derivatives can also be evaluated with a nonlocal Cauchy contour integral, as well, with no singularity in the gamma fct.
Jan
31
comment Compositional inversion and generating functions in algebraic geometry
There is an intriguing tale told by He and Jejalla in "Modular matrix models" interweaving the compositional inversion of generating series as in free probability theory, matrix models, gauge field theory, Calabi-Yau geometry, the Klein modular invariant j-function, and some monstrous moonshine.
Jan
29
comment Cavalieri's principle and inversion of the Vandermonde matrix
See Roy Smith's mathoverflow.net/questions/28268/do-you-read-the-masters/…
Jan
26
comment Inversion, Koszul duality, combinatorics and geometry
Moderators, community wiki?
Jan
26
asked Inversion, Koszul duality, combinatorics and geometry
Jan
23
comment What is a good introduction to cluster algebras from surfaces?
I'll leave it open, if you don't mind, to encourage someone to find another good paper.
Jan
23
comment Why complete symmetric polynomials and elementary symmetric polynomials are dual to each other?
Thanks, but I'm simply looking for how the concept of Koszulness could inform me of the combinatorics/geometry of the reciprocal identity (as in, say, OEIS A133314). These inverse relations (multiplicative, compositional, umbral compositional) always seem to contain a lot of underlying combinatorics and often geometry.