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49 lines
2.7 KiB
Markdown
49 lines
2.7 KiB
Markdown
## Mathematics
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* :scroll: [The Transcendence of Pi](transcendence-of-pi.pdf) by Steve Mayer
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* :scroll: [Tilings](tilings.pdf) by Ardila
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The paper covers a broad swath of the topic on analysis of tiling, and related strategies.
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* :scroll: [From Dominoes to Hexagons](from-dominoes-to-hexagons.pdf) by Thurston
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A paper on the generalization of tilings across different base planes.
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* :scroll: [Graph Isomorphism and Representation Theory](graph-isomorphism-and-representation-theory.pdf) by Daniel Litt
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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.
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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.
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* [Conway's ZIP proof](https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf) by George Francis and Jeffrey Weeks
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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.
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* [Packing of Spheres](http://neilsloane.com/doc/Me109.pdf) by N. Sloane
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Discusses the role of E8 & Leech lattices in optimal codes for mathematically-ideal compression. Ikosahedrons, a tool in this investigation, are also presented.
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* [Some Underlying Geometric Notions](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) by Hatcher
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High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra.
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* [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.pdf) by Alexander Yong
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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.
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### Topology
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* [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf) by hatcher
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* [Applied Algebraic Topology and Sensor Networks](https://www.math.upenn.edu/~ghrist/preprints/ATSN.pdf) by Robert Ghrist
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* :scroll: [Intro to Tropical Algebra Geometry](intro-to-tropical-algebraic-geometry.pdf)
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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.
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* [Elements of Algebraic Topology: Sheaves](https://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist
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Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'
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