From 172cf3834237f49a31251f4a08f6c6fc483830d3 Mon Sep 17 00:00:00 2001 From: Sean Broderick Date: Wed, 25 Dec 2019 23:59:05 -0500 Subject: [PATCH] fix mathematics readme formatting --- mathematics/README.md | 39 +++++++++++++++++++++------------------ 1 file changed, 21 insertions(+), 18 deletions(-) diff --git a/mathematics/README.md b/mathematics/README.md index 3030830..2702b20 100644 --- a/mathematics/README.md +++ b/mathematics/README.md @@ -1,45 +1,48 @@ ## Mathematics -* :scroll: [The Transcendence of Pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer +* :scroll: [The Transcendence of Pi](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 +* :scroll: [Tilings](tilings.pdf) by Ardila The paper covers a broad swath of the topic on 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 +* :scroll: [From Dominoes to Hexagons](from-dominoes-to-hexagons.pdf) by Thurston A paper on the generalization of tilings across different base planes. -* :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 +* :scroll: [Graph Isomorphism and Representation Theory](graph-isomorphism-and-representation-theory.pdf) by Daniel Litt - The *graph isomorphism problem* shows how to construct graphs using a simple building-block ("basis"). The same method applies to finding different building blocks to construct the same things. This technique can be applied to file systems, greplin, trees, virtual DOM, etc. - - A short paper, it also shows how to use `𝔰𝔩₂(ℂ)` as a simple mathematical object that leads into the area of real mathematics—represention theory. + The *graph isomorphism problem* shows how to construct graphs using a simple building-block ("basis"). The same method applies to finding different building blocks to construct the same things. This technique can be applied to file systems, greplin, trees, virtual DOM, etc. -* :scroll: [Conway's ZIP proof](https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf) by George Francis and Jeffrey Weeks + A short paper, it also shows how to use `𝔰𝔩₂(ℂ)` as a simple mathematical object that leads into the area of real mathematics—represention theory. - This paper presents a classification proof: "How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?" The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels. +* [Conway's ZIP proof](https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf) by George Francis and Jeffrey Weeks + + This paper presents a classification proof: "How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?" The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels. + +* [Packing of Spheres](http://neilsloane.com/doc/Me109.pdf) by N. Sloane -* :scroll: [Packing of Spheres](http://neilsloane.com/doc/Me109.pdf) by N. Sloane Discusses the role of E8 & Leech lattices in optimal codes for mathematically-ideal compression. Ikosahedrons, a tool in this investigation, are also presented. -* :scroll: [Some Underlying Geometric Notions](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) by Hatcher +* [Some Underlying Geometric Notions](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) by Hatcher High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra. -* :scroll: [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.pdf) by Alexander Yong +* [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.pdf) by Alexander Yong - Young Tableau appear in combinatoric problems, representation theory, and the calculus of Grassmannians. Another common topic is sorting, and smarter ways to organise sub-sorts. + Young Tableau appear in combinatoric problems, representation theory, and the calculus of Grassmannians. Another common topic is sorting, and smarter ways to organise sub-sorts. +### Topology + +* [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf) by hatcher -### Topology -* :scroll: [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf) by hatcher * [Applied Algebraic Topology and Sensor Networks](https://www.math.upenn.edu/~ghrist/preprints/ATSN.pdf) by Robert Ghrist -* :scroll: [Intro to Tropical Algebra Geometry](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/intro-to-tropical-algebraic-geometry.pdf) + +* :scroll: [Intro to Tropical Algebra Geometry](intro-to-tropical-algebraic-geometry.pdf) Recently there have been some papers posted about tropical geometry of neural nets. Tropical is also said to be derived from CS. This is a good introduction. -* :scroll: [Elements of Algebraic Topology: Sheaves](https://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist +* [Elements of Algebraic Topology: Sheaves](https://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist - Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology' \ No newline at end of file + Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'