Elegant Coding: Eleven Equations True Computer Science Geeks Should (at Least Pretend to) Know. This idea is a complete rip off an article that appeared in Wired a little while ago and it got me thinking what would my list for Computer Science look like? Plus I thought it might be a fun post and unlike the Wired list this one goes to eleven. So here they are in no particular order: Binomial Coefficient The Binomial Coefficient equation generates Pascal’s Triangle and gives you the coefficients for the Binomial Theorem these ideas are often attributed to Pascal but in fact they have been known in part for over a millennia. As I mentioned that this list is no particular order and I don’t wish to play favorites but if there is one equation here that you should really consider learning and committing to memory this is it.
Demorgan’s Laws Logical form: Set Form: Eigenvector and Eigenvalue Pumping Lemma for Regular Languages No Comp Sci list would be complete with at least one formula from either Formal Language Theory or Automata Theory. Information Entropy Bayes' Theorem Natural Join O(n) A single paper everyone should read? I am surprised to see that so many people suggest meta-mathematical articles, which try to explain how one should do good mathematics in one or the other form.
Personally, I usually find it a waste of time to read these, and there a few statements to which I agree so wholeheartedly as the one of Borel: "I feel that what mathematics needs least are pundits who issue prescriptions or guidelines for presumably less enlightened mortals. " The mere idea that you can learn how to do mathematics (or in fact anything useful) from reading a HowTo seems extremely weird to me. I would rather read any classical math article, and there are plenty of them. The subject does not really matter, you can learn good mathematical thinking from each of them, and in my opinion much easier than from any of the above guideline articles. I am not suggesting that any mathematician should read all of them, but any one of them will do. Dodécaèdre rhombique. Genetic Algorithms Tutorial - Part 1 | LeoLoL. Data Structures- Graph Theory And Coloring - Software Development Tutorials. Mandelbrot Set in HTML 5 Canvas. "Mandelbrot Set" is an experiment on HTML5 and the <canvas> tag.
It is compatible with all modern web browsers. It can be used as a benchmark of the Javascript engine of your browser in combination with the client machine that it runs on. For example a Google Chrome on a reasonable 2GHz+ dual-core machine should produce a 360x360 Mandelbrot set in about 0.1 second. Hope you'll find this application useful, Kostas Symeonidis License and Contact Information "Mandelbrot Set" is released as open source under the GNU General Public License version 3 (GPLv3). And "e" appears from nowhere.
Here is an example of e turning up unexpectedly. Select a random number between 0 and 1. Now select another and add it to the first. Keep doing this, piling on random numbers. How many random numbers, on average, do you need to make the total greater than 1? The answer is e. (See sketch of proof below) In the original post, a quick Clojure implementation is programmed, and in Re: Factor, a Factor implementation is added. I switched to my emacs session and started slime. The first function was easy to define. (defn PlusRandom [initial steps]; Initial and step start at 0. Ugly, I can hear you mutter. (defn PlusRandomAux [initial steps] ; Initial and step start at 0. ; Will return how many times ; it takes to be greater than ; 1 (if (> initial 1) steps (recur (PlusRandomAux (+ initial (rand)) (+ 1 steps)))))(defn PlusRandom [] (PlusRandomAux)) (defn AveragePlusRandom [iterates]; Takes the average of "iterates" iterations of the previous ; function.
The first step is key.