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Calculus Is Deeply Irrational
You’re lying on a beautiful beach when you feel a tap on your shoulder, and suddenly you’re not at the beach at all — you’re in a classroom. The student who woke you looks apologe…
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An Overview of Cryptography
Free, evolving crypto tutorial since 1999!
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Common statistical tests are linear models
By Jonas Kristoffer Lindeløv ( blog , profile ). Last updated: 28 June, 2019 (See changelog ). Check out the Python version and the Twitter summary .
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Use perfect hashing, instead of binary search, for keyword lookup
We've been speculating for a long time that hash-based keyword lookup ought to be faster than binary search, but up to now we hadn't found a suitable tool for generating the hash function. Joerg Sonnenberger provided the inspiration, and sample code, to show us that rolling our own generator wasn't a ridiculous idea…
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The Paxos Algorithm, or How to Win a Turing Award
The lectures assume no prior knowledge of the Paxos consensus algorithm or of TLA+, the language in which the specifications are written. In fact, the lectures constitute a crash course on TLA+. If you're interested just in the algorithm, you will probably find the specs annoying and will try to read only the…
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Words that do Handstands
The other day I ordered a book on art history from Amazon… which reminded me of the movie Angels and Demons , which reminded me of ambigrams. Ambigrams are those stylized words that look the same when you turn them upside down. Here is the classic, by John Langdon .
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Outperforming everything with anything: Python? Sure, why not?
A 100 lines of Python code that substitute the compiler front-end for a specific computation. This shows that you don't need a “fast” compiling language to write efficient code. In fact, a compilation is only one of the multiple ways to achieve speed.
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Free and Open-Source Mathematics Textbooks
Mathematics, Teaching, & Technology
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A book from Alan Turing and a mysterious piece of paper
Sleuthing into the history of a 1930 book on quantum mechanics previously owned by Alan Turing and a lambda calculus note tucked inside.
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9999999999999999.0 – 9999999999999998.0
Note that some of the wrong answers can be fixed with various workarounds. For example Common–Lisp gives the correct answer for:
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Why Do Buses Bunch?
Created by Lewis Lehe (of Setosa and UC Berkeley Trans. Eng. ) with design and art by Dennys Hess . Thanks to Ian Johnson for good advice. Tools: d3 , Angular Material , Coffeescript , Browserify , Gulp and Five-Hour Energy Drink .
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A Gentle Introduction to Bayes’ Theorem for Machine Learning
Bayes Theorem provides a principled way for calculating a conditional probability. It is a deceptively simple calculation, although it can be used to easily calculate the conditional probability of events where intuition often fails. Although it is a powerful tool in the field of probability, Bayes Theorem is also…
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Queueing theory: The science of waiting in line
The math behind how people wait in line
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The Riemann Hypothesis
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Gamedev Tutorial: Trigonometry Basics – Sine and Cosine
[latexpage] 本文之中文翻譯在此 Overview Trigonometry is a very essential building block to a huge portion of game math. That's why I've chosen this topic for the first tutorial of my new Gamedev Tutorials series. Having a solid understanding of basic of trigonometry can go a long way for game development. It is used…
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Algorithm No One Knows About (2016)
Here’s a program roughly 0% of programmers know how to write: generate a list of random tweets, without duplication. You may think you know how to do this, but you almost assuredly don’…
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What Is a Manifold?
In machine learning, the term manifold is thrown around a lot—in fact, there’s even a branch of machine learning dealing with learning the structure of manifolds. Said branch is aptly named manifold learning . Inspired by fantastic visualizations of shapelet mining algorithms , this post aims to give a visual…
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It’s Time for Some Queueing Theory
Queueing theory is the scientific study of waiting in line. It can apply to familiar lines like those at the grocery store or bank but also to things like web s
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Calculating the mean of a list of numbers (2016)
You have a list of floating point numbers. No nasty tricks - these aren't NaN or Infinity, just normal "simple" floating point numbers.
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L-systems
Jordan Santell, focusing on open web engineering, immersive web, WebXR, WebGL, JavaScript, open source, open standards, and all things weird web.
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A Brief Guide to a Few Algebraic Structures
Occasional writings about Haskell.
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Pathfinding for Tower Defense
In a Tower Defense game, there are many enemies that are all headed to the same place. In many Tower Defense games, there is a predetermined path, or a small number of paths. In some, such as the classic Desktop Tower Defense [1] , you can place towers anywhere, and they act as obstacles that affect the paths taken by…
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Explaining Sex Rate Changes
According to the Post, polls say 28% of US men age 18-30 report not having sex in the last year, almost 3 times as many as a decade ago.
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Gaussian Processes, not quite for dummies
Before diving inFor a long time, I recall having this vague impression about Gaussian Processes (GPs) being able to magically define probability distributions over sets of functions, yet I procrastinated reading up about them for many many moons. However, as always, I’d like to think that this is not just due to my…
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Using spaced repetition systems to see through a piece of mathematics
By Michael Nielsen, January 2019
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Escher-Like Spiral Tilings
The artist M.C. Escher drew many lovely tilings, which he called “regular divisions of the plane”. He worked hard to ensure that his tilings were of lifelike animal forms such as birds and fish. He filled notebooks with hand-drawn sketches of tilings, many of which later found their way into his woodcuts. If you’d…
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Dungeon Generation in Diablo 1
Diablo1 is a classic 1996 hack and slash rogue-like. several fans took it upon themselves to reverse-engineer the source code. I began a week long deep dive into how exactly did lead developer, Dav…