2311
How to Teach Math?
The only way to learn mathematics is to do mathematics—Paul Halmos Angie Hodge is an Associate Professor of mathematics at Northern Arizona University. Her interests as stated on her website …
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
2312
Why 'gallons per mile' is better than 'miles per gallon'
Why we should really be quoting fuel consumption figures as 'gallons per mile' and not 'miles per gallon'.
2313
Milton Friedman’s Interest Rate Fallacy
Milton Friedman’s interest rate fallacy is one of the most mystifying and counterintuitive facts in modern finance.
2314
NP-complete isn't always hard
A common assumption I see on the ‘net is that NP-complete problems are impossible to solve. I recently read that dependency management in Python is hard because package resolution is NP-complete. This is true in principle, but the reality is more complicated. When we say “NP-complete is hard” we’re talking about…
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Make a "Magic Eye" image using Excel
I’ve been on a weird kick lately making images using Excel. [Here’s one post. I hope to post more soon.] If you add a background color to each cell in a spreadsheet and resize the cell …
2317
Entropy in the Universe
If you click on this picture, you’ll see a zoomable image of the Milky Way with 84 million stars: But stars contribute only a tiny fraction of the total entropy in the observable Universe. If…
2318
Solving “Two Sum” in C with a tiny hash table
I came across a question: How does one efficiently solve Two Sum in C? There’s a naive quadratic time solution, but also an amortized linear time solution using a hash table. Without a built-in or standard library hash table, the latter sounds onerous. However, a mask-step-index table , a hash table construction…
2319
Traveling Salesman: the most misunderstood problem
Whenever people start talking about NP-Complete problems, or even NP problems, one of the first examples they reach for is the classic Traveling Salesperson Problem. TSP makes sense because it int...
2320
PID Controller: A Simple Control Loop Mechanism
A mid-depth cap with classic style for any occasion, this Nike Club Cap comes in smooth cotton twill that's been softly washed for casual, daily comfort. Soft and unstructured, the precurved bill makes for easy styling, and the adjustable back-strap lets you find the right fit. Nike Hat Size 6 1/2 6 5/8 6 3/4 6 7/8 7…
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Turing Machines
An interactive introduction to Turing machines, the theoretical foundation of modern computing.
2323
How to Be Wrong (2016)
“To be wrong, or not to be wrong?” That is the wrong question. You are going to spend a lot of your time being wrong, especially if you become a scientist or mathematician. The question…
2324
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
2325
Solving a linear optimization problem on incentive allocation
At Lyft, scientists solve all kinds of optimization problems. While solvers can come in handy, there are times when complicated or…
2326
Linear Algebra of Types (2019)
It gives my brain a pleasant thrum to learn new mathematics which mimics the algebra I learned in middle school. Basically this means that the new system has operations with properties that match those of regular numbers as much as possible. Two pretty important operations are addition and multiplication with the…
2327
Kolmogorov Complicity and the Parable of Lightning (2017)
A good scientist, in other words, does not merely ignore conventional wisdom, but makes a special effort to break it. Scientists go looking for trouble. — Paul Graham, What You Can’t Sa…
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Correlation is usually not causation. But why not?
Correlations are oft interpreted as evidence for causation; this is oft falsified; do causal graphs explain why this is so common, because the number of possible indirect paths greatly exceeds the direct paths necessary for useful manipulation?
2330
Ten Ways to Check if an Integer Is a Power Of Two in C
To write a program to check if an integer is a power of two, you could follow two basic strategies: check the number based on its decimal value, or check it based on its binary representation. The former approach is more human-friendly but generally less efficient; the latter approach is more machine-friendly but…
2331
A fast alternative to the modulo reduction (2016)
Suppose you want to pick an integer at random in a set of N elements. Your computer has functions to generate random 32-bit integers, how do you transform such numbers into indexes no larger than N? Suppose you have a hash table with a capacity N. Again, you need to transform your hash values (typically 32-bit ……
2332
One Plus One Equals Two (2006)
From the highly eclectic blog of Mark Dominus
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Open Questions
Some anomalies/questions which are not necessarily important, but do puzzle me or where I find existing explanations to be unsatisfying.
2335
16-bit math look-up tables – the unexpected power of scaled-integer math
Floating-point math puts a big overhead on a computer that doesn't have a floating-point coprocessor; but we really do need floating-point for all but the simplest operations— or do we?? Can we really do things like trig, log, and square-root functions without floating point?
2336
When the bubble bursts
We are clearly not in a steady-state situation. Is this a bubble or a revolution? The answer surely includes a bit of revolution—the fields of vision and speech recognition have been turned over by great empirical successes created by deep neural architectures and more generally machine learning has found plentiful…
2337
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…
2338
Chemists develop new way to split water
The news portal offers current information about studies, research and life at Münster University.
2339
Closed form arc length parametrization is impossible for quadratic Bézier curves
Bézier curves are widely used for defining vector graphics. They are basically polynomial parametric curves, but given in the Bernstein basis, which enables us to define the curve using control points. The first and last control point define the start and endpoint of the curves, the intermediate control points kind of…
2340
Compiling to λ-calculus
Though it contains forms only for function applications, variable references and anonymous functions, it is equivalent to a Turing machine.