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Random Solutions are Often Good Enough
Sometimes taking the easy way out isn’t nearly as bad as it might seem! posted Thursday February 13th, 2014 Tagged: Math
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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The quadratic formula and low-precision arithmetic
The familiar quadratic formula can give the wrong answer in a program due to numerical precision issues. This post shows what can go wrong and how to fix it. Especially important in low-precision arithmetic.
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Math library functions that seem unnecessary
Functions include in the standard C math library that seem unnecessary at first glance and why they are necessary.
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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…
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The quadratic sandwich
If you have ever tried to minimize a function with gradient descent, you probably noticed that some functions are a joy to optimize and others are a nightmare. The difference often boils down to two properties: strong convexity and L-smoothness. These two concepts define a “sandwich” of quadratic bounds around your…
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A Long Peek into Reinforcement Learning
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The game theory of seduction and marriage with Jane Austen
The enduring success of her early 19th century novels are in large part due to their persistent relevance
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Not all elementary functions can be expressed with exp-minus-log
a personal blog
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A Brutal Look at Balanced Parentheses, Computing Machines, and Pushdown Automata
As discussed in Pattern Matching and Recursion , a well-known programming puzzle is to write a function that determines whether a string of parentheses is “balanced,” i.e. each opening parenthesis has a corresponding closing parenthesis, and the parentheses are properly nested.
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Revisiting the algorithm that changed horse race betting (2023)
Explore Bill Benter’s iconic horse betting strategy, enhanced with modern code and contrasted against three decades of evolving data.
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Trying Kolmogorov-Arnold Networks in Practice
There's been a fair bit of buzz about Kolmogorov-Arnold networks online lately. Some research papers were posted around claiming that they offer better accuracy or faster training compared to traditional neural networks/MLPs for the same parameter count.
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The Entropy of a Markov Chain
A more explicit example
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The Point of the Banach-Tarski Theorem
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
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What Are the Odds?
An unusual lottery result made the news recently: on October 1, 2022, the PCSO Grand Lotto in the Philippines, which draws six numbers from $latex {1}&fg=000000$ to $latex {55}&fg=000000$ a…
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How to average floating point numbers (2015)
When it comes to accuracy, how you add a series of arbitrary values together, and average them still matters.
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The Second Law of Thermodynamics (2011)
Web site content explains the modern view of entropy change and the dispersal of energy in a process (at a specific temperature). It has been selected for instructors in general and physical chemistry by Dr. Frank L. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles.
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Optimizing a bignum library for fun
Can I make math operations run 100x faster on really, really big numbers?
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Revisiting the Fast Inverse Square Root – Is It Still Useful?
In 2005, id Software released the source code for their 1999 game Quake III Arena under the GPL-2 license. In the file code/game/q_math.c , there is a function for calculating the reciprocal square root of a number which at first glance seems to use a very peculiar algorithm:
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Use Gröbner bases to solve polynomial equations
A self-contained introduction to Gröbner bases and solving polynomial systems
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Nash equilibria in Ballmer's binary-search interview game
Yesterday John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question,” and in the Hacker News discussion, among the predictable “interview culture is flawed!!” complaints, there was some discussion of whether binary search was even the right way to solve Ballmer’s puzzle. Here’s a…
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Playing with model trains and calling it graph theory
You’ve probably played with model trains, for instance with something like the Brio set shown below.1 And if you’ve built a layout with a model train set, yo...
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From Zero to QED: An informal introduction to formality with Lean 4
An informal introduction to formality in Lean 4
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Helmhurts: Placing a WiFi router with the Helmholtz equation
A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn't. Well, spurred on by a…
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Learning with Not Enough Data: Semi-Supervised Learning
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Darts, Dice, and Coins: A beautiful article on a beautiful algorithm
Earlier this year, I asked a question on Stack Overflow about a data structure for loaded dice . Specifically, I was interested in answering this question: