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Squaring two digit numbers in your head
All my life I've done mental arithmetic the 'wrong way': I've calculated from left-to-right, instead of right-to-left. So when I do somethi...
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The latest blog posts to take off on Hacker News. 2,851 posts.
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Ask HN: How do you solve hard problems if you can't make incremental progress?
Ron Jeffries attempts to create a sudoku solver - here , here , here , here and here . (You really ought to read these articles. They are u...
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You Don't Need Math Skills To Be A Good Developer - What About A Great One
Why everyday CRUD work needs little math, but search, machine learning, cryptography and other interesting fields need plenty.
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First Clay Millennium Prize goes to Grigoriy Perelman
Poincare official problem description
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Regular Expression Matching in the Wild
The first two articles in this series, “ Regular Expression Matching Can Be Simple And Fast ” and “ Regular Expression Matching: the Virtual Machine Approach ,” introduced the foundation of DFA-based and NFA-based regular expression matching. Both were based on toy implementations optimized for teaching the basic…
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Insanely deep fractal zoom
I was really into fractals in college (I know…) when I was making rave flyers (I know!) for a friend’s parties in Iowa (I know! I know! Shut up already!). Anywa
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Chicago undergraduate mathematics bibliography
Somehow I became the canonical undergraduate source for bibliographical references, so I thought I would leave a list behind before I graduated. I list the books I have found useful in my wanderings through mathematics (in a few cases, those I found especially un useful), and give short descriptions and comparisons…
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The "Soft Maximum" function
The soft maximum approximates the maximum function, and approaches it in the limit, but is easier to work with.
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Using Fibonacci Numbers to Convert from Miles to Kilometers and Vice Versa
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
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A review of probability theory
In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory, as well as setting up basic probabilistic notation that we…
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How to determine if your A/B test is statistically significant
A/B testing tools often lie about whether something is "statistically significant." Here's an extremely simple, mathematically sound formula to compute it for yourself.
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World's shortest explanation of Gödel's theorem
From the highly eclectic blog of Mark Dominus
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Regular Expression Matching: the Virtual Machine Approach
Name the most widely used bytecode interpreter or virtual machine. Sun's JVM? Adobe's Flash? .NET and Mono? Perl? Python? PHP? These are all certainly popular, but there's one more widely used than all those combined. That bytecode interpreter is Henry Spencer's regular expression library and its many descendants.
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Beautiful plots of roots of polynomials
Click on the picture for bigger view. Roots of quadratic polynomials are in grey; roots of cubics are in cyan; roots of quartics are in red and roots of quintics are in black. The horizontal axis of symmetry is the real axis; the vertical axis of symmetry is the imaginary axis. The big hole in the middle is centered…
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Step-by-Step Math
Have you ever given up working on a math problem because you couldn’t figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.
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The 17x17 challenge. "Worth $289.00. This is not a joke."
The 17x17 challenge: worth $289.00. I am not kidding. Definition: The n x m grid is c-colorable if there is a way to c-color the vertic...
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Summary of all the MIT Introduction to Algorithms lectures
As you all may know, I watched and posted my lecture notes of the whole MIT Introduction to Algorithms course. In this post I want to summarize all the topics that were covered in the lectures and point out some of the most interesting things in them. Actually, before I wrote this article, I had started writing an...
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SciPy - the embarrassing way to code
I’ve programmed in many languages before, indeed I’ve spent at least a year working in Basic, C, C++, C#, java, assembler, modula-2, powerhouse and prolog. One thing I’ve never done before is Matlab, well except a few basic exercises for some course I did way back. A couple of years ago I started using python and more…
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How Credit Card Numbers Are Generated
Visa,Master Card,Discover, and American Express credit card validation and generation techniques using the luhn algorithm.
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Why I left math
Reading how shocked Doron Zeilberger is at the state of modern mathematics reminded me of why I left the subject. Math departments regularl...
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What every developer should know about time
How to handle time is one of those tricky issues where it is all too easy to get it wrong. So let's dive in.
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The Shocking State of Contemporary "Mathematics"
I just came back from attending the 1052nd AMS (sectional) meeting at Penn State, last weekend, and realized that the Kingdom of Mathematics is dead. Instead we have a disjoint union of narrow specialties , and people who know everything about nothing, and nothing about anything (except their very narrow acre). Not…
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The Busy Beaver Problem
Busy Beaver puts another one on the Turing Machine's tape (image from the book The New Turing Omnibus). The busy beaver problem is a fun theoretical computer science problem. Intuitively, the problem is to find the smallest program that outputs as many data as possible and eventually halts. More formally it goes…
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Functional Geometry
Peter Henderson wrote an article about a method to describe pictures with functional programs. I've implemented it in Lisp. An updated version of the article uses curves and different shapes and has some references to other applications for this method, like "An Algebra of Music".