4.0 KiB
Mathematics
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📜 The Transcendence of pi by Steve Mayer
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[📜] Tilings by Ardila
Programmers are used to counting boring things. Why not count something more interesting for a change? This paper covers a broad swatch of the topic of 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
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. -
[📜] Conway's ZIP proof by George Francis and Jeffrey Weeks
This paper can be shown to college freshmen because
- it is pictorial
- it is about an object you might not have considered mathematical
- no calculus, crypto, ML, or pretentious notation
- it is short
- it is a classification proof: “How can it be that you know something about all possible
X, even thexϵXyou haven’t seen yet? ”
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[📜] packing of spheres by N. Sloane
- role of E8 & Leech lattice in optimal codes
- mathematically best compression was never used
- ikosahedron
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[📜] some underlying geometric notions
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.
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[📜] what is a young tableaux? by Alexander Yong
Young Tableau appear in many areas of mathematics. Beyond combinatoric problems, we also see them in representation theory, and the calculus of Grassmannians.
Another common topic is sorting "You do sorting all the time. Are there smart 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
Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'