From 083cbbaf9899a10d8f9848f073ee1ed802ebff26 Mon Sep 17 00:00:00 2001 From: ZJ Date: Thu, 28 Nov 2019 23:32:39 -0500 Subject: [PATCH] fixed crappy explanations --- mathematics/README.md | 18 ++++++++---------- 1 file changed, 8 insertions(+), 10 deletions(-) diff --git a/mathematics/README.md b/mathematics/README.md index 57ab7a7..a2c11ef 100644 --- a/mathematics/README.md +++ b/mathematics/README.md @@ -3,7 +3,7 @@ * [:scroll:](transcendence-of-pi.pdf) [The Transcendence of pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer * [:scroll:] [Tilings](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/tilings.pdf) by Ardila - Programmers are used to counting boring things. Why not count something more interesting for a change? This paper covers a broad swatch of the topic of analysis of tiling, and related strategies. + This paper takes programmers out of the domain of what they are familair with counting, and into new terrain. The paper covers a broad swath of the topic of analysis of tiling, and related strategies. * [:scroll:] [From Dominoes to Hexagons](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/from-dominoes-to-hexagons.pdf) by Thurston @@ -11,30 +11,28 @@ * [:scroll:] [graph isomorphism and representation theory](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/graph-isomorphism-and-representation-theory.pdf) by Daniel Litt - Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem" (who cares) ). But have you ever tried to construct a simpler building-block (basis) with which graphs could be built? Or at least a different building block to build the same old things. + Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem"). But have you ever tried to construct a simpler building-block (basis) with which graphs could be built? Or at least a different building block to build the same old things. - This <10-page paper also uses `𝔰𝔩₂(ℂ)`, a simple mathematical object you haven’t heard of, but which is a nice lead-in to an area of real mathematics—rep theory—that (1) contains actual insights (1a) that you aren’t using (2) is simple (3) isn’t pretentious. + This <10 page paper also uses `𝔰𝔩₂(ℂ)` that will be seen to be a simple mathematical object, which leads into an area of real mathematics—rep theory. * [:scroll:] [Conway's ZIP proof](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/conways-zip-proof.pdf) by George Francis and Jeffrey Weeks - This paper can be shown to college freshmen because + This paper is good for most knowledge levels because * it is pictorial * it is about an object you might not have considered mathematical - * no calculus, crypto, ML, or pretentious notation + * no calculus, crypto, ML, or tough notation * it is short * it is a classification proof: “How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?” * [:scroll:] [packing of spheres](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/packing-of-spheres.pdf) by N. Sloane - * role of E8 & Leech lattice in optimal codes - * mathematically best compression was never used - * ikosahedron + * The role of E8 & Leech lattice in optimal codes + * An understanding of how mathematically-best compression was never used + * Ikosahedrons * [:scroll:] [some underlying geometric notions](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/some-underlying-geometric-notions.pdf) This is a higher-level paper, but still a survey (so more readable). It ties together disparate areas like Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra. - It has pictures and you’ll get a better sense of what mathematics is like from skimming it. - * [:scroll:] [what is a young tableaux?](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/what-is-a-young-tableau.pdf) by Alexander Yong Young Tableau appear in many areas of mathematics. Beyond combinatoric problems, we also see them in representation theory, and the calculus of Grassmannians.