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The Mathematics of 2048: Optimal Play with Markov Decision Processes (2018)
Finding provably optimal strategies for 2048 using Markov Decision Processes
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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I simulated California housing and learned about simulators
Back in the early 2000s, XML was all the rage. An unusual evolution from HTML, which itself was an evolution (devolution?) from SGML, XML w...
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Understanding Quaternions
Quaternions are used to represent an orientation in 3D space. This article attempts to demystify the complexities of quaternions.
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Teaching Linear Algebra
In a recent Hacker News post I made reference to an interesting teaching experience I had in the mid-90s. This is a longer explanation of ...
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Damn Cool Algorithms: Levenshtein Automata
Posted by Nick Johnson | Filed under python , tech , coding , damn-cool-algorithms
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Think in math, write in code (2019)
Programmers love to discuss programming languages. We not only debate their technical merits and aesthetic qualities, but they become integrated into our personal identities, along with the values and traits that we associate with them. Some even defend a form of Linguistic Determinism that thinking is confined to…
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Using Fourier Transforms to Multiply Numbers
The purpose of this article is to show you step-by-step examples of how to use the Fourier transform algorithm to multiply two numbers. The primary advantage of using fourier transforms to multiply numbers is that you can use the asymptotically much faster 'Fast Fourier Transform algorithm', to achieve better…
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Best algorithms book I ever read
Best algorithms book I ever read I took a fair amount of time looking at data structures and algorithms while I was st...
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A Visual Exploration of Gaussian Processes
Consulting software engineer and research scientist. I build visualization systems for complex data and machine learning models.
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What Is Spacetime, Really?
On the 100th anniversary of Einstein’s Theory of Relativity, Stephen Wolfram discusses the nature of space and time, and fundamental theory of physics.
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Discovering errors in Donald Knuth's TAOCP
As Donald Knuth has just published Volume 4, Fascicle 7 of The Art of Computer Programming (TAOCP), on constraint satisfaction, I would like to provide…
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Probability-generating functions
I have long struggled with understanding what probability-generating functions are and how to intuit them. There were two pieces of the puzzle missing for me, and we’ll go through both in this article.
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Why are we even doing all this?
[This is a guest post by Rikab Gambhir. This blog post was initially written in a different file format and converted using AI. — T.] First, they came for the artists, and I did not speak out…
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US Army applying new areas of math
Many times on this blog I've argued that the difference between pure and applied math is motivation. As my graduate advisor used to say, “Applied mathematics is not a subject classification. It's an attitude.” Traditionally there was general agreement regarding what is pure math and what is applied. Number theory and…
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How to implement an algorithm from a scientific paper
This article is a short guide to implementing an algorithm from a scientific paper. I have implemented many complex algorithms from books and scientific publications, and this article sums up what I have learned while searching, reading, coding and debugging. This is obviously limited to publications in domains…
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Clojure Linear Algebra Refresher: Eigenvalues and Eigenvectors
I stumble upon eigenvectors and eigenvalues regularly when reading about machine learning topics. They seem to be important. They are not introduced in those...
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Minesweeper thermodynamics
You know how sometimes you start a game of Minesweeper and immediately get stuck?
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Matrices from a geometric perspective
Graphics is all about geometry. In particular, there are points that have a certain color, and the pattern of colors gives you a certain picture. You can change the way the points are distributed by applying certain transformations like translation (movement), rotation and scaling. While most people familiar with the…
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A new kind of fractal?
Experimenting with the "divisibility" of complex numbers, I stumbled across this thingy. It looks like a fractal. Although the formula does not do any iterations. It reminds me of something. But I dont know what. Doing a Google image search brings up a couple of galaxies :) This image shows the region from (-1/-1) to…
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An Introduction to the Lambda Calculus (2015)
;; Done Twice as a "Dojo" at Villiers Park on Thursday 19th March 2015 ;; To groups of about 15 ultra-clever teenagers who were thi...
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Foldable Words
Packing up the household for a recent move, I was delving into shoeboxes, photo albums, and file folders that had not been opened in decades. One of my discoveries, found in an envelope at the back of a file drawer, was the paper sleeve from a drinking straw, imprinted with a saccharine message:
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When Big O Fools You
Big O notation is a great tool. It allows one to quickly make smart choices among various data structures and algorithms. But sometimes a casualBig O analy...
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Formalising Mathematics: An Introduction
An introduction to the TCC course “Formalising Mathematics”