These don’t all really seem to necessarily be “equations” but they are all extremely useful things you should know. The article contains some details on the following: Binomial Coefficient Demorgan’s Laws Eigenvector and Eigenvalue Pumping Lemma for Regular Languages Information Entropy Bayes’ Theorem Fermat’s Little Theorem Natural Join The Fixed-Point (Y) Combinator O(N) Euler’s Identity [...]

“A very long time ago, I was curious how to detect the strength of the bass and treble in music, in order to synchronize some graphical effects. I had no idea how to do such a thing, so I tried to figure it out, but I didn’t get very far. Eventually I learned that I [...]

Microsoft has published a scientific research paper ([PDF] Real-Time Human Pose Recognition in Parts from Single Depth Images (Microsoft Research)) detailing how Microsoft Kinect’s body tracking algorithm works. There is also a video (Kinect Research (youtube.com)) to go along with it. Also, I came across a separate article (Kinect’s AI breakthrough explained (I-Programmer.info)) which summaries [...]

This is something definitely worth sharing, very useful for anyone who wants to learn more about different sorting algorithms.  If you want to learn more about different types of sorting this is the perfect place to start. It even has animations to show how different algorithms work and pseudo-code to help you get started with [...]

“Yesterday the Census Bureau announced the new apportionment of the 435 representatives to states based on the 2010 census. Illinois lost one representative. Texas gains four. Not only do these affect the makeup of the House of Representatives but also the Electoral College that chooses the president. Since 1940 the apportionment is not done by [...]

What is it? Big O Notation describes the limiting behavior of a function when the argument trends toward a certain value. Basically, it helps to describe the complexity and performance of an algorithm. This notation can also help to understand the execution time needed or space required by an algorithm. O(1) This describes an algorithm [...]

Rudy Andrut has auralized a bunch of sorting algorithms based on their visualizations. They sound pretty amazing! Also, if you are looking for the visualizations that were previously done check them out here: sorting algorithm visualizations (sortvis.org). Here are the videos:

Originally algorithms were designed to process a single item at a time in sequential order. However, modern computer hardware is able to process multiple pieces of data at the same time in parallel. This leads to Parallel and Distributed Computing algorithms for solving more complex problems efficiently. I came across an interesting webpage which gives [...]