## Mathematics
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>
5 years ago
* :scroll: [The Transcendence of Pi ](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf ) by Steve Mayer
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>
5 years ago
* :scroll: [Tilings ](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/tilings.pdf ) by Ardila
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>
5 years ago
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
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
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.
* :scroll: [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’
* :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
High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnor’
* :scroll: [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.
### 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 )
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
Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'
