31
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 70 posts.
32
33
Bloom Filters by example
A Bloom filter is a data structure designed to tell you, rapidly and memory-efficiently, whether an element is present in a set.
34
I hate the Pumping Lemma
I hate the Pumping Lemma for regular languages. It’s a complicated way to express an idea that is fundamentally very simple, and it isn’t even a very good way to prove that a language is not regula…
35
Exact numeric nth derivatives
Automatic differentiation is a well-studied technique for computing exact numeric derivatives. Dan Piponi has a great introduction on the subject , but to give you an overview, the idea is that you introduce an algebraic symbol such that but . Formulas involving are called dual numbers (e.g., , ) in much the same way…
36
The Fallacy of Cracking Contests (1998)
In this issue: The Fallacy of Cracking Contests How to Recognize Plaintext News The Doghouse: Iomega Zip Disks Counterpane Systems News Final Report from the Commerce Department Technical Advisory Committee on Key Recovery Comments From Readers About "CRYPTO-GRAM"
37
38
Shakespeare.txt.jpg: A JPEG compression experiment
Experimenting with JPEG compressing text.
39
40
41
The keys to the keydom
Your security and privacy on the Internet (to the extent that such quaint notions still have meaning) depend on the difficulty of factoring certain large numbers. For example, take this 1,024-bit integer:
42
43
44
Principal Component Analysis for Dummies
(I recently wrote a new post that you may also find interesting called Principal Component Analysis 4 Philosophers) Having been in the social sciences for a couple of weeks it seems like a large am…
45
A back-projection algorithm to extract 3D volume from shadows
If you'd rather read python than english you can go straight to the code on github: https://github.com/jminardi/volume-from-shadow
46
Probability Theory — A Primer
It is a wonder that we have yet to officially write about probability theory on this blog. Probability theory underlies a huge portion of artificial intelligence, machine learning, and statistics, and a number of our future posts will rely on the ideas and terminology we lay out in this post. Our first formal theory…
47
48
How to make fake data look meaningful
If you are trying to trick somebody with your data, never share the raw data; only share the conclusions. Bonus points if you can’t share the data because it is somehow priviledged or a trade secret. The last thing you want is to allow other people to evaluate your analysis and possibly challenge your conclusions.
49
What is algebra?
NOVEMBER 20, 2011. We hear a lot about the importance that all children master algebra before they graduate from high school. But what exactly is algebra, and is it really as important as everyone …
50
Gödel, Turing and Cantor: The Math
This is mathematical section of the parent essay Gödel Incompleteness for Startups Gödel Numbering A formal system is just a collection of axioms and rules. Just like we did before we can record ax…
51
52
Feynman vs. The Abacus
A Japanese man came into the restaurant. I had seen him before, wandering around; he was trying to sell abacuses. He started to talk to the waiters, and challenged them: He said he could add numbers faster than any of them could do.
53
Elsevier journals: has anything changed?
Greg Martin, a number theorist at UBC (the University of British Columbia in Vancouver) doesn’t think so, so he has decided to resign from the editorial board of Elsevier’s Journal of N…
54
Ten Signs a Claimed Mathematical Breakthrough is Wrong
Yesterday several people asked my opinion of a preprint claiming to solve the Graph Isomorphism problem in deterministic polynomial time. I responded: If I read all such papers, then I wouldn’t hav…
55
Let's Play Ancient Greek Geometry
Today I’m releasing Let’s Play: Ancient Greek Geometry . It’s a Compass and Straightedge tool/puzzle game written in JavaScript. I’ve always thought Geometric Construction felt like a puzzle, so to me this pairing was quite natural. Compass and Straight edge is a technique for constructing shapes out of circles…
56
How to escape a monster (using calculus)
You are sitting in a rowing boat in the middle of a circular lake. How do you escape from a smart monster on the shore who can run four times faster than you can row?
57
The Median-of-Medians Algorithm
In this post, we consider the problem of selecting the \(i\)-th smallest element from an unsorted list of \(n\) elements. Somewhat surprisingly, there is an algorithm that solves this problem in linea
58
Understanding the FFT Algorithm
The Fast Fourier Transform (FFT) is one of the most important algorithms in signal processing and data analysis. I've used it for years, but having no formal computer science background, It occurred to me this week that I've never thought to ask how the FFT computes the discrete Fourier transform so quickly. I dusted…
59
Modelling a Basic Income with Python and Monte Carlo Simulation
Basic Income is a popular policy floating around the internet lately. The idea consists of declaring that the government will pay each living adult a fixed amount of money every month - an amount comparable to a minimum wage job. This policy would then replace all current welfare programs - welfare, unemployment …
60
