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Creating mathematics Folder and adding transcendence of pi paper (#473) * Creating mathematics folder and adding transcedence-of-pi.pdf * adding README.md
7 years ago
## Mathematics
fix mathematics readme formatting
4 years ago
* :scroll: [The Transcendence of Pi](transcendence-of-pi.pdf) by Steve Mayer
Creating mathematics Folder and adding transcendence of pi paper (#473) * Creating mathematics folder and adding transcedence-of-pi.pdf * adding README.md
7 years ago
fix mathematics readme formatting
4 years ago
* :scroll: [Tilings](tilings.pdf) by Ardila
Creating mathematics Folder and adding transcendence of pi paper (#473) * Creating mathematics folder and adding transcedence-of-pi.pdf * adding README.md
7 years ago
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
The paper covers a broad swath of the topic on analysis of tiling, and related strategies.
fix mathematics readme formatting
4 years ago
* :scroll: [From Dominoes to Hexagons](from-dominoes-to-hexagons.pdf) by Thurston
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
A paper on the generalization of tilings across different base planes.
fix mathematics readme formatting
4 years ago
* :scroll: [Graph Isomorphism and Representation Theory](graph-isomorphism-and-representation-theory.pdf) by Daniel Litt
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
fix mathematics readme formatting
4 years ago
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.
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
fix mathematics readme formatting
4 years ago
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.
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
fix mathematics readme formatting
4 years ago
* [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
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
Discusses the role of E8 & Leech lattices in optimal codes for mathematically-ideal compression. Ikosahedrons, a tool in this investigation, are also presented.
fix mathematics readme formatting
4 years ago
* [Some Underlying Geometric Notions](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) by Hatcher
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra.
fix mathematics readme formatting
4 years ago
* [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.pdf) by Alexander Yong
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
fix mathematics readme formatting
4 years ago
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.
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
fix mathematics readme formatting
4 years ago
### Topology
* [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf) by hatcher
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
* [Applied Algebraic Topology and Sensor Networks](https://www.math.upenn.edu/~ghrist/preprints/ATSN.pdf) by Robert Ghrist
fix mathematics readme formatting
4 years ago
* :scroll: [Intro to Tropical Algebra Geometry](intro-to-tropical-algebraic-geometry.pdf)
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
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.
fix mathematics readme formatting
4 years ago
* [Elements of Algebraic Topology: Sheaves](https://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist
Math papers from original `isomorphisms` PR (#587) * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs 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. 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. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre 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. * Create see.machine.learning * tropical geometry 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. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org>
4 years ago
fix mathematics readme formatting
4 years ago
Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'