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The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
I’ve never been good at playing football 1 . I started playing again last year and I have scored more own goals than goals for my team. Also, I support the RCD Espanyol 2 , which has spent last season in the second division and has miraculously ascended to the first division last week. And to be honest, I only watch…
A year ago today I self-published “A Programmer’s Introduction to Mathematics” (PIM). In this short note I want to describe the success it’s had, summarize the complaints of some readers and the praise of others, and outline what’s next. Since publication PIM has sold over 11,000 copies. A rough chart showing the…
Probability theory might be the most useful area for programmers, but it is also a blurry field, difficult to learn right. You might check this book for details, and there is also an free, online draft version available. The Logic of Science
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…
This is part 11 of Categories for Programmers. Previously: Natural Transformations. See the Table of Contents. Introduction to Part II In the first part of the book I argued that both category theo…
Restate Some Basic Concepts and Math in Bayesian Filter
For twenty years, the fastest known algorithm to multiply two n-by-n matrices, due to Coppersmith and Winograd, took a leisurely O(n2.376) steps. Last year, though, in his PhD thesis, Andrew Stot…
I really like decision tables but they’ve fallen out of common knowledge. Let’s fix that. A decision table is a means of concisely representing branching and conditional computations. In the most basic form, you have some columns that represent the “inputs” as booleans and some columns that represent outputs and…
Can you use math to escape from, what seems like, an impossible prison escape problem based on coins and a chessboard?
Update - 05 Dec 2017: Google just announced that it will be commited to the development of a new released version of the S2 library, amazing news, repository can be found here. Google's S2 library is a real treasure, not only due to its capabilities for spatial indexing but also because it is a library that
Array and hash table are probably the most important data structures. Some programming languages such as Perl, Lua and Javascript, almost build the language core on top of the two data structures. …
When you resize, rotate, or in any way transform an image; or more generally when you resample some discrete signal, the software you are using must _interpolate_ between the discrete points to produce a result. Linear and cubic interpolation are easy to explain, but Lánczos interpolation, one of the most popular…
I wondered how GPT-3 might do on the following problem: given a partially-connected graph, find a path between two nodes, or determine that no path exists. I wrote some code to automate generating …
A remainder and a modulus look so very similar, but they are not the same thing and worse, are treated differently by different programming languages. Do you know how your language handles mod?
I hope everyone had a good weekend. I went on a hike. It was great. Statistics One of my great school regrets, next to “taking three years of business...
If there is one highly underrated concept in philosophy today, it is computation . Why is it so important? Because computationalism is t...
This paper appeared in Communications of the ACM in April 1960. It is the original paper on Lisp.
It’s fairly clear when one should buy a particular stock. One should buy stock when it is undervalued. What I have always wondered about is how much stock one should buy. A few months ago I stumbled upon the answer which is given by the Kelly criterion . It says that one should invest an amount to maximize one’s…
The python code that goes along with this blog post can be found at To evaluate the quality of a blue noise texture, you can analyze it in frequency space by taking a discrete Fourier transform. Wh…
For every n, there is a base b such that n! = b^n. The relation between n and b(n) is surprisingly close to linear.
For reasons beyond the scope of this entry, I have been investigating elliptical and ovoid shapes. The Wikipedia article for Moss’s egg has a link to a tutorial on Euclidean Eggs by Freyja Hreinsdóttir which (amongst other things) describes how to construct the “four point egg”. I think it is a nicer shape than Moss’s…
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…
Efficient elliptic curves tend not to have a prime order. This discusses the problems this causes, and the solutions.
A programming model for spatial canvases
In the early 1990s, they were merely visualization aids in the study of mathematics. Gradually, the complexity and artistry of the images becomes an end itself.
The logic behind Bézier Curves used in CSS animations and visual elements.
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"
