2.7 KiB
Mathematics
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📜 The Transcendence of Pi by Steve Mayer
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📜 Tilings by Ardila
The paper covers a broad swath of the topic on analysis of tiling, and related strategies.
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📜 From Dominoes to Hexagons by Thurston
A paper on the generalization of tilings across different base planes.
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📜 Graph Isomorphism and Representation Theory 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. -
Conway's ZIP proof 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 thexϵXyou 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 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.
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Some Underlying Geometric Notions by Hatcher
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? 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
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Topology of Numbers by hatcher
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Applied Algebraic Topology and Sensor Networks by Robert Ghrist
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📜 Intro to Tropical Algebra 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.
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Elements of Algebraic Topology: Sheaves by Ghrist
Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'