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53 lines
3.8 KiB
Markdown
53 lines
3.8 KiB
Markdown
## Mathematics
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* [:scroll:](transcendence-of-pi.pdf) [The Transcendence of pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer
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* [:scroll:] [Tilings](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/tilings.pdf) by Ardila
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This paper takes programmers out of the domain of what they are familair with counting, and into new terrain. The paper covers a broad swath of the topic of analysis of tiling, and related strategies.
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* [:scroll:] [From Dominoes to Hexagons](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/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](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/graph-isomorphism-and-representation-theory.pdf) by Daniel Litt
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Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem"). 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.
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This <10 page paper also uses `𝔰𝔩₂(ℂ)` that will be seen to be a simple mathematical object, which leads into an area of real mathematics—rep theory.
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* [:scroll:] [Conway's ZIP proof](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/conways-zip-proof.pdf) by George Francis and Jeffrey Weeks
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This paper is good for most knowledge levels because
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* it is pictorial
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* it is about an object you might not have considered mathematical
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* no calculus, crypto, ML, or tough notation
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* it is short
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* it is a classification proof: “How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet? ”
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* [:scroll:] [packing of spheres](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/packing-of-spheres.pdf) by N. Sloane
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* The role of E8 & Leech lattice in optimal codes
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* An understanding of how mathematically-best compression was never used
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* Ikosahedrons
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* [:scroll:] [some underlying geometric notions](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/some-underlying-geometric-notions.pdf)
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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.
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* [:scroll:] [what is a young tableaux?](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/what-is-a-young-tableau.pdf) by Alexander Yong
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Young Tableau appear in many areas of mathematics. Beyond combinatoric problems, we also see them in representation theory, and the calculus of Grassmannians.
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Another common topic is sorting "You do sorting all the time. Are there smart ways to organise sub-sorts?"
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### Topology
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* [:scroll:] [Topology of Numbers](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/topology-of-numbers--hatcher.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](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/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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* [:scroll:] [Elements of Algebraic Topology: Sheaves](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/elements-of-algebraic-topology-ch9-sheaves.pdf)
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Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology' |