papers-we-love_papers-we-love/mathematics/README.md
2019-12-25 23:59:05 -05:00

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Mathematics

  • 📜 The Transcendence of Pi by Steve Mayer

  • 📜 Tilings by Ardila

    The paper covers a broad swath of the topic on analysis of tiling, and related strategies.

  • 📜 From Dominoes to Hexagons by Thurston

    A paper on the generalization of tilings across different base planes.

  • 📜 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() 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 the xϵX you havent 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.

  • Some Underlying Geometric Notions by Hatcher

    High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnors exceptional fibre, and algebra.

  • 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