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Introduction to Calculus with Derivatives
Aditya Bhargava's personal blog.
New
The latest blog posts to take off on Hacker News. 2,851 posts.
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Prediction Markets: When Do They Work?
Epistemic Status: Resident Expert I’m a little late on this, which was an old promise to Robin Hanson (not that he asked for it). I was motivated to deal with this again by the launch of Augu…
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Limits on Matrix Multiplication
Can 2.3728639 be best? Personal site; note puzzles Josh Alman is a graduate student at a technical school in the Boston area. He is working on matrix multiplication, among other problems in complex…
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Pseudo-bandlimited pixel art filtering in 3D: A mathematical derivation
Recently, I’ve been playing Octopath Traveler, and I’m very disappointed with the poor texture filtering seen in this game. It is PS1-level, with severe shimmering artifacts, which ruins the nice pixel art. Tastefully merging retro pixel art with 3D environment is a very cool aesthetic to me, so I want it to look…
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Mod and remainder are not the same
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?
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A study of musical scales (2017)
PREFACE. This essay was written in 2009. Since then, a few errata have been corrected and I embedded the youtube videos, but there have been no substantial additions. I think it still holds up fairly well, but if I were to rewrite it today, I would change some things. My main regret is using the criteria of maximum…
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A Nerd’s Way to Walk Up the Stairs (2011)
Mathematics, applications of mathematics to life in general, and my life as a mathematician.
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The Math Required for Machine Learning
For the past year, I’ve been working on implementing well known model architectures and building web applications, so I have a fair amount…
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Modern SAT solvers: fast, neat and underused – part 2
The previous post in this series was a quick introduction to the world of SAT and SAT solvers. In this post, we will convert a harder real-world problem, namely _master-key system_, into SAT and explore some of the more advanced techniques used to efficiently convert problems to SAT.
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Introduction to A* (1997)
Movement for a single object seems easy. Pathfinding is complex. Why bother with pathfinding? Consider the following situation:
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Markov Chains Explained Visually (2014)
Markov chains, named after Andrey Markov , are mathematical systems that hop from one "state" (a situation or set of values) to another. For example, if you made a Markov chain model of a baby's behavior, you might include "playing," "eating", "sleeping," and "crying" as states, which together with other behaviors…
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The Superinvestors of Graham-and-Doddsville (1984)
Columbia Business School. For over 100 years, we’ve helped develop leaders who create value for business and society at large.
1727
MIT mathematicians solve age-old spaghetti mystery
Researchers have long have puzzled over why it’s so hard to break a piece of dry spaghetti into only two pieces. A new MIT study follows up on the musings of physicist Richard Feynman, showing how and why it can be done.
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LaTeX TikZ for Cryptographers
LaTeX Code for Cryptographic Images.
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Dijkstra's in Disguise
You can find a PDF version of this blog post here . A weighted graph is a data structure consisting of some vertices and edges, and each...
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1/0 = 0
Disclaimer 2024-12-02 Since this rant is going viral again (again (again)), some disclaimers: I wrote this six years ago to “”“win”“” an ugly Twitter fight. I’m glad I anonymized the inciting tweet and hope I’m the only person still getting grief over this. The core interesting bit— why it’s mathematically valid to…
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Generating random points inside a sphere
Visualization of different methods of generating random points inside a sphere
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Modern SAT solvers: fast, neat and underused
Before I started doing research, I saw SAT solvers as academically interesting but without practical uses ouside of other academic applications. I've since then changed my mind, and I want to change yours, because modern SAT solvers are neat, fast and almost criminally underused by the industry.
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Life lessons from differential equations (2015)
Some problems simply have no solution. Some problems have no simple solution. Some problems have many solutions. ...
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How to explain infinity to kids
From the highly eclectic blog of Mark Dominus
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Learning Math for Machine Learning
Vincent Chen is a student at Stanford University studying Computer Science. He is also a Research Assistant at the Stanford AI Lab. -------------------------------------------------------------------------------- It’s not entirely clear what level of mathematics is necessary to get started in machine learning…
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Prospecting for Hash Functions
Update 2022 : TheIronBorn has found even better permutations using a smarter technique. That thread completely eclipses my efforts in this article.
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Gamifying propositional logic: QED, an interactive textbook
About six years ago on this blog, I started thinking about trying to make a web-based game based around high-school algebra, and ended up using Scratch to write a short but playable puzzle game in …
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Thoughts On Machine Learning Accuracy
This blog shares some brief thoughts on machine learning accuracy and bias. Let’s start with some comments about a recent ACLU blog in which they ran a facial recognition trial. Using Rekognition, the ACLU built a face database using 25,000 publicly available arrest photos and then performed facial similarity searches…