Pages tagged mathematics:
Honeybees are found to interact with Quantum fields
How could bees of little brain come up with anything as complex as a dance language? The answer could lie not in biology but in six-dimensional math and the bizarre world of quantum mechanics.
Honeybees are found to interact with Quantum fields. wild. must read later.
SpeedCrunch - fast and usable calculator
http://www.speedcrunch.org/en_US/index.html
SpeedCrunch is a fast, high precision and powerful desktop calculator. Available for LinuxLinux, WindowsMicrosoft Windows, and Apple Mac OS XApple Mac OS X.
1234567890 Day
http://www.1234567890day.com/
It's time to party like it's 1234567890 – 'cause it is!
My Birthday but in Unix Time
UNIXタイムが1234567890になるんだとか
UNIXタイムが1234567890になる瞬間を祝うためのサイト
Unix Timeが1234567890になるんだと。
Welcome to KENKEN™!
http://www.kenken.com/
fun
Math objectives
Recipe for Disaster: The Formula That Killed Wall Street
http://www.wired.com/techbiz/it/magazine/17-03/wp_quant
"In the mid-'80s, Wall Street turned to the quants—brainy financial engineers—to invent new ways to boost profits. Their methods for minting money worked brilliantly... until one of them devastated the global economy."
A First Course in Linear Algebra (A Free Textbook)
http://linear.ups.edu/opentexts.html
Math Simulations
http://www.techtrekers.com/sim.htm
Scroll down to see the SS and the LA
Gallery - The next generation of mirrors - Image 1 - New Scientist
http://www.newscientist.com/gallery/dn16585-amazing-mirrors
I don't know how he did it, but it's pretty cool.
Six monster mirrors.
How Game Theory Solved a Religious Mystery - Mind Your Decisions by Presh Talwalkar
http://mindyourdecisions.com/blog/2008/06/10/how-game-theory-solved-a-religious-mystery/
Symbol
http://www.doe.virginia.gov/Div/Winchester/jhhs/math/facts/symbol.html
Science News / A Prayer For Archimedes
http://www.sciencenews.org/view/generic/id/8974/title/A_Prayer_for_Archimedes
An intensive research effort over the last nine years has led to the decoding of much of the almost-obliterated Greek text. The results were more revolutionary than anyone had expected. The researchers have discovered that Archimedes was working out principles that, centuries later, would form the heart of calculus and that he had a more sophisticated understanding of the concept of infinity than anyone had realized.
"....The researchers have discovered that Archimedes was working out principles that, centuries later, would form the heart of calculus and that he had a more sophisticated understanding of the concept of infinity than anyone had realized."
Gaussian Processes for Machine Learning: Contents
http://www.gaussianprocess.org/gpml/chapters/
Carl Edward Rasmussen and Christopher K. I. Williams MIT Press, 2006. ISBN-10 0-262-18253-X, ISBN-13 978-0-262-18253-9. This book is © Copyright 2006 by Massachusetts Institute of Technology. The MIT Press have kindly agreed to allow us to make the book available on the web. The web version of the book corresponds to the 2nd printing. You can buy the book for a list price of 36.00 US$or 23.95 UK£. The whole book as a single pdf file. Gaussian Processes for Machine Learning Recipe for Disaster: The Formula That Killed Wall Street http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=1 By Felix Salmon at Wired Magazine, February 23, 2009. Edge: GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH http://www.edge.org/3rd_culture/goldstein05/goldstein05_index.html Gödel mistrusted our ability to communicate. Natural language, he thought, was imprecise, and we usually don't understand each other. Gödel wanted to prove a mathematical theorem that would have all the precision of mathematics—the only language with any claims to precision—but with the sweep of philosophy. He wanted a mathematical theorem that would speak to the issues of meta-mathematics. And two extraordinary things happened. One is that he actually did produce such a theorem. The other is that it was interpreted by the jazzier parts of the intellectual culture as saying, philosophically exactly the opposite of what he had been intending to say with it. goel and the nature of mathematical truth Free Mathematics Books http://www.e-booksdirectory.com/mathematics.php Free Mathematics Books - list of freely available math textbooks, monographs, lecture notes, and other documents. Look at Intro to R Book Combin Singular Value Decomposition http://www.uwlax.edu/faculty/will/svd/index.html ." Feature Column from the AMS http://www.ams.org/featurecolumn/archive/bezier.html A nice refresher for Bézier curves Main Page - Eigen http://eigen.tuxfamily.org/index.php?title=Main_Page Overview Eigen is a C++ template library for linear algebra: vectors, matrices, and related algorithms. It is: * Versatile. (See modules and tutorial). Eigen handles, without code duplication, and in a completely integrated way: o both fixed-size and dynamic-size matrices and vectors. o both dense and sparse (the latter is still experimental) matrices and vectors. o both plain matrices/vectors and abstract expressions. o both column-major (the default) and row-major matrix storage. o both basic matrix/vector manipulation and many more advanced, specialized modules providing algorithms for linear algebra, geometry, quaternions, or advanced array manipulation. * Fast. (See benchmark). o Expression templates allow to intelligently remove temporaries and enable lazy evaluation, when that is appropriate -- Eigen takes care of this automatically and handles aliasing too in most cases. o Explicit vectorization is Main Page - Eigen Eigen 2 is a C++ template library for linear algebra: vectors, matrices, and related algorithms. Welcome to the Tricki | Tricki http://www.tricki.org/ dfggggggggggggggggggdysyeeydysdysdydsydsydydsdddddddddddd Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving techniques. Wolfram Blog : Droste Effect with Mathematica http://blog.wolfram.com/2009/04/24/droste-effect-with-mathematica/ Droste Visualizing Bayes’ theorem | Ramblings http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/ Intuitive visual explanation of Bayes' theorem using Venn diagrams I recently came up with what I think is an intuitive way to explain Bayes’ Theorem. I searched in google for a while and could not find any article that explains it in this particular way. Of course there’s the wikipedia page, that long article by Yudkowsky, and a bunch of other explanations and tutorials. But none of them have any pictures. So without further ado, and with all the chutzpah I can gather, here goes my explanation. Fibonacci Sequence Illustrated by Nature [PICS] http://www.environmentalgraffiti.com/featured/fibonacci-sequence-illustrated-nature/10867 Leonardo of Pisa was born around 1170 AD in (of course) Pisa, Italy. While not quite as famous as some other Italian or Ninja Turtle Leonardos, we do have a lot to thank him for. His most notable contribution to your life is probably found on the top row of your keyboard. While traveling through North Africa, Leo discovered that the local number system of 0-9 was far superior than the obscure combination of X’s, V’s and I’s the Romans had invented a millennium earlier to confuse later generations of elementary school students. Leonardo brought this number system to Europe and eventually we invented Sudoku with it. New Pattern Found in Prime Numbers http://www.physorg.com/news160994102.html (PhysOrg.com) -- Prime numbers have intrigued curious thinkers for centuries. On one hand, prime numbers seem to be randomly distributed among the natural numbers with no other law than that of chance. But on the other hand, the global distribution of primes reveals a remarkably smooth regularity. This combination of randomness and regularity has motivated researchers to search for patterns in the distribution of primes that may eventually shed light on their ultimate nature. May 2009. Luque, Lacasa on Generalised Benford's Law. “New insights and concepts coming from nonlinear science, such as multiplicative processes, help us to look at prime numbers from a different perspective. According to this focus, it becomes significant that even today it is still possible to discover unnoticed hints of statistical regularity in such sequences, without being an expert in number theory. However, the most significant issue in this work is not to unveil this pattern in primes and Riemann zeros, but to understand the reason and implications of such unexpected structure, not just for number theoretical issues but, interestingly, for other disciplines as well. For instance, these results deepen our understanding of correlations in systems composed of many elements.” (PhysOrg.com) -- Prime numbers have intrigued curious thinkers for centuries. On one hand, prime numbers seem to be randomly distributed among the natural numbers with no other law than that of chance. But on the other hand, the global distribution of primes reveals a remarkably smooth regularity. This ... “Imagine that you have$1,000 in your bank account, with an interest rate of 1% per month,” Lacasa said. “The first month, your money will become $1,000*1.01 =$1,010. The next month, $1,010*1.01, and so on. After n months, you will have$1,000*(1.01)^n. Notice that you will need many months to go from $1,000 to$2,000, while to go from $8,000 to$9,000 will be much easier. When you analyze your accounting data, you will realize that the first digit 1 is more represented than 8 or 9, precisely as Benford's law dictates. This is a very basic example of a multiplicative process where 0.01 is the multiplicative constant. “Physicists have shown that many processes in nature can be modeled as stochastic multiplicative processes, where the previously constant value of 0.01 is now a random variable and the data equivalent to the money of our latter example is another random variable with an underlying distribution 1/x. Stochastic processes with such distributions are shown to follow BL....”
SMS: "Tim Gowers - Computational Complexity and Quantum Compuation"
http://sms.cam.ac.uk/collection/545358
Computational complexity lectures
Fields Medalist Tim Gowers' lectures on computational complexity.
Guest Column: Math and the City - Olivia Judson Blog - NYTimes.com
http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/
As one of Olivia Judson’s biggest fans, I feel honored and a bit giddy to be filling in for her. But maybe I should confess up front that, unlike Olivia and the previous guest writers, I’m not a biologist, evolutionary or otherwise. In fact, I’m (gasp!) a mathematician. One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden. This week’s column is about one such pattern. It’s a beautiful law of collective organization that links urban studies to zoology. It reveals Manhattan and a mouse to be variations on a single structural theme. The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as th
One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden. This week’s column is about one such pattern. It’s a beautiful law of collective organization that links urban studies to zoology. It reveals Manhattan and a mouse to be variations on a single structural theme. [...] These numerical coincidences seem to be telling us something profound. It appears that Aristotle’s metaphor of a city as a living thing is more than merely poetic. There may be deep laws of collective organization at work here, the same laws for aggregates of people and cells.
Why elephants and cities have the same basic infrastructure
"For instance, if one city is 10 times as populous as another one, does it need 10 times as many gas stations?"
Math Exercises
http://www.emathematics.net/index.php
Margaret Wertheim on the beautiful math of coral | Video on TED.com
http://www.ted.com/index.php/talks/margaret_wertheim_crochets_the_coral_reef.html
mathematics environment video
Parallelism and Hyperbolic geometry in models that are crotcehed
kindergarten for adults...play tanks (rather than think tanks)
Yenka.com
http://www.yenka.com/
computer simulation software
Great website for showing GTT concepts
How maths killed Lehman Brothers
http://plus.maths.org/issue51/features/boedihardjo/index.html
You can in fact calculate it, easily. The 100 customers each have a 3% chance of defaulting, so you expect three customers to default next year. That is, you will need to pay $3 million next year. Assuming the interest rate is about 3% each year, next year's$3 million would be worth 3/(3/100+1)=3/1.03=2.91 million now. Therefore HSBC will have to pay you at least $2.91 million for the insurance. Obviously Lehman Brothers wasn't a charity and so, to make money, they would double the price to$5.82 million and expect to make $2.91 million out of each of these deals on average. This kind of insurance is called a credit derivative swap (CDS). Two Centuries On, a Cryptologist Cracks a Presidential Code - WSJ.com http://online.wsj.com/article/SB124648494429082661.html For more than 200 years, buried deep within Thomas Jefferson's correspondence and papers, there lay a mysterious cipher -- a coded message that appears to have remained unsolved. Until now. The cryptic message was sent to President Jefferson in December 1801 by his friend and frequent correspondent, Robert Patterson, a mathematics professor at the University of Pennsylvania. President Jefferson and Mr. Patterson were both officials at the American Philosophical Society -- a group that promoted scholarly research in the sciences and humanities -- and were enthusiasts of ciphers and other codes, regularly exchanging letters about them. Sweet The DFT “à Pied”: Mastering The Fourier Transform in One Day - The DSP Dimension http://www.dspdimension.com/admin/dft-a-pied/ Detexify LaTeX handwritten symbol recognition http://detexify.kirelabs.org/classify.html Anyone who works with LaTeX knows how time-consuming it can be to find a symbol in symbols-a4.pdf that you just can't memorize. Detexify is an attempt to simplify this search. LaTeX handwritten symbol recognition super neato Gives Latex syntax for characters by hand-drawing them. A Calculus Analogy: Integrals as Multiplication | BetterExplained http://betterexplained.com/articles/a-calculus-analogy-integrals-as-multiplication/ hen we want to use regular multiplication, but can’t, we bring out the big guns and integrate. Area is just a visualization technique, don’t get too caught up in it. Now go learn calculus!” Mathesaurus http://mathesaurus.sourceforge.net/ The idea of the "Mathesaurus" is to provide a quick reference for switching to open-source mathematical computation environments for computer algebra, numeric processing and data visualisation. "The idea of the "Mathesaurus" is to provide a quick reference for switching to open-source mathematical computation environments for computer algebra, numeric processing and data visualisation." Solve Computational Geometry Problems | PC Plus http://www.pcplus.co.uk/node/3089/ From the simple to the intricate, geometry is an inescapable part of graphics programming. Arthur Benjamin's formula for changing math education | Video on TED.com http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.html TED Talks Someone always asks the math teacher, "Am I going to use calculus in real life?" And for most of us, says Arthur Benjamin, the answer is no. He offers a bold proposal on how to make math education relevant in the digital age. Philosophy, Physics, Mathematics - “Dangerous Knowledge” http://video.google.com/videoplay?docid=-5122859998068380459 Turned up on oursignal.com ... Plain English Explanation of Big O Notation http://www.cforcoding.com/2009/07/plain-english-explanation-of-big-o.html I've met too many developers who don't grok big O Feature Column from the AMS http://www.ams.org/featurecolumn/archive/svd.html An intuitive explanation of the geometric meaning behind SVD. Good explanation of the SVD Geometric interpretation of SVD. MATH TOOL CHEST - ONLINE http://macmillanmh.com/math/mathtoolchest/mtc_online/ A free site of math games for many concepts with many choices. Interesting and not boring resources! good range of online resources to use as teaching resources in the numeracy area includes a spiner, tablesstuff, place value, pattern blocks etc. Great tools - Place value, patterns, number lines, counters etc. Eleven mathematics games and activities written in English and Spanish. The games and activities are designed for learning about the basics of mathematics including graphs, fractions, and money. Unconscionable Math « Taunter Media http://tauntermedia.com/2009/07/28/unconscionable-math/ The House hearings on rescission – the retroactive cancellation of individual health insurance policies – were over a month ago, but after its initial run through Daily Kos it seems to have waited a bit before popping up on Baseline and Slate. James Kwak at Baseline described the practice as rare, affecting only 0.5% of the population. The faint light bulb above my head began to flicker: could that be true…that’s not rare – that is amazingly common. Rescission is not rare, if you happen to be sick. rescission – the retroactive cancellation The House hearings on rescission – the retroactive cancellation of individual health insurance policies – were over a month ago, but after its initial run through Daily Kos it seems to have waited a bit before popping up on Baseline and Slate. James Kwak at Baseline described the practice as rare, affecting only 0.5% of the population. The faint light bulb above my head began to flicker: could that be true…that’s not rare – that is amazingly common. "The House hearings on rescission – the retroactive cancellation of individual health insurance policies – were over a month ago... James Kwak at Baseline described the practice as rare, affecting only 0.5% of the population. The faint light bulb above my head began to flicker: could that be true…that’s not rare – that is amazingly common." But I will make this simple point in the hope some speechwriter pressed for a deadline picks it up: if a bank manager went to half of his highest net worth clients and said “sorry, you misspelled your address when you opened your account, I’m confiscating your balance,” he would be lucky to get himself assigned to minimum security If, as I suspect, rescission is targeted toward the truly bankrupting cases – the top 1%, the folks with over$35,000 of annual claims who could never be profitable for the carrier – then the probability of having your policy torn up given a massively expensive condition is pushing 50%. One in two. You have three times better odds playing Russian Roulette.
Mindcipher: Challenge Yourself...
http://www.mindcipher.net/
Mathematical Model for Surviving a Zombie Attack | Wired Science | Wired.com
http://www.wired.com/wiredscience/2009/08/zombies/
Hee hee hee
It is possible to successfully fend off a zombie attack, according to Canadian mathematicians. The key is to hit hard and hit often.
Zombies.pdf (application/pdf Object)
http://www.mathstat.uottawa.ca/~rsmith/Zombies.pdf
Potential models for zombie outbreaks.
PDF
Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all.
Free Mathsframe Interactive Whiteboard Teacher Resources
http://www.mathsframe.co.uk/free_resources.asp
Free resources for teaching maths using primary framework objectives
Games for IWB or Pcs
Great math resource for grade 3-6.
Interaktív táblán jól alkalmazható matematika változtatható tartalmú és nehézségű gyakorló animációk.
Beyond space and time: Fractals, hyperspace and more - New Scientist
http://www.newscientist.com/special/beyond-space-and-time
multiple dimensions 10D
The 3D world of solid objects and limitless space is something we accept with scarcely a second thought. Time, the fourth dimension, gets a little trickier. But it's when we start to explore worlds that embody more – or indeed fewer – dimensions that things get really tough.
like the ten dimensions video...but words!
Thinking about dimensions other than the three we're used to can rattle one's mind. That's why it's usually left to stoned conversationalists and theoretical physicists. To help the rest of us navigate flatland, fractal landscapes, and hyperspace, New Scientist put together a concise and fun tour titled "Beyond Space and Time."
We don't have any trouble coping with three dimensions – or four at a pinch. The 3D world of solid objects and limitless space is something we accept with scarcely a second thought. Time, the fourth dimension, gets a little trickier. But it's when we start to explore worlds that embody more – or indeed fewer – dimensions that things get really tough.
The Coin Flip: A Fundamentally Unfair Proposition? - Coding the Wheel
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition
The Coin Flip: A Fundamentally Unfair Proposition?
Urinal protocol vulnerability « xkcd
http://blag.xkcd.com/2009/09/02/urinal-protocol-vulnerability/
math humor
When a guy goes into the bathroom, which urinal does he pick? Most guys are familiar with the International Choice of Urinal Protocol. It’s discussed at length elsewhere, but the basic premise is that the first guy picks an end urinal, and every subsequent guy chooses the urinal which puts him furthest from anyone else peeing. At least one buffer urinal is required between any two guys or Awkwardness ensues.
What's luck got to do with it? The math of gambling - physics-math - 11 August 2009 - New Scientist
http://www.newscientist.com/article/mg20327202.600-whats-luck-got-to-do-with-it-the-maths-of-gambling.html?full=true
Even if you can't beat the system, there are some cunning ways to tilt the odds in your favour
Math Interactives
http://www.learnalberta.ca/content/mejhm/index.html?l=0
Math Apprentice
http://www.mathapprentice.com/
An online, interactive math game. Allows students to understand how math applies to all careers.
awesome flash site that shows kids how math is used in the real world, with real world jobs. Describes how they use math and provides a fun interactive activity that gives students a chance to practice using the math
Math Apprentice answers the question that nearly every student will ask during his or her math career: When are we ever going to use this stuff in the real world? Sure, there are some obvious real world connections. Money, time, and measurement are all very relevant concepts. Other areas of math, such as number theory and functions, are more cryptic and can seem disconnected from real life. Math Apprentice reveals the connections by showing students how math is used in a variety of interesting professions.
What it is: Math Apprentice is an awesome flash site that shows kids how math is used in the real world, with real world jobs. Students can explore math through games that feature bicycle designers, biologists, artists, mechanics, inventors, doctors, engineers, astronomers, game designers, programmers, chefs, veterinarians, sportscasters, and meteorologists. Students can explore the math of these jobs as a math apprentice by selecting a character and cruising around a virtual world where they can visit places of business where math happens. The character describes how they use math and provides a fun interactive activity that gives students a chance to practice using the math.
Great interactive games
Upper elementary and middle school level, shows kids how math is used in the real world, with real world jobs
Anscombe's quartet - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Anscombe%27s_quartet
e linear relations
The Carol syndrome
http://plus.maths.org/issue51/features/rey/index.html
Plus Maths Magazine: Feature Article
The Carol syndrome
A mathematical explanation of how pretty girls scare boys away.
Mooie vrouwen worden zelden aangesproken. Wiskundige onderbouwing waarom
dy/dan » Blog Archive » What I Would Do With This: Groceries
http://blog.mrmeyer.com/?p=4646
"The express lane isn't faster. The manager backed me up on this one. You attract more people holding fewer total items, but as the data shows above, when you add one person to the line, you're adding 48 extra seconds to the line length (that's "tender time" added to "other time") without even considering the items in her cart. Meanwhile, an extra item only costs you an extra 2.8 seconds. Therefore, you'd rather add 17 more items to the line than one extra person! I can't believe I'm dropping exclamation points in an essay on grocery shopping but that's how this stuff makes me feel."
All other things being equal, which lane is the fastest?
good description of classes of people on twitter.
Hate to take the linkbait but I disagree with @techcrunch on the golden ratio for Twitter. I want all types in my feed http://bit.ly/1ZLZui [from http://twitter.com/JMaultasch/statuses/3557139305]
Comenta varias "máximas" de las relaciones entre cantidad de gente que sigue un usuario y cantidad de gente que lo sigue.
A Twitter aranyszabálya, ami alapján elég hatékonyan el lehet dönteni, hogy egy minket újonnan követő embert visszakövetünk-e. Lényege, hogy ha a follower-following arány negatív (több following-ja van a usernek, mint ahány follower), akkor ez nagy valószínűséggel azt mutatja, hogy nem érdemes őt követni, mert nem érdekes a tartalma vagy mert valamilyen spammer. Ha az arány pozitív , akkor valszeg érdemes követni. Minél nagyobb az arány + vagy - irányba, annál igazabb lesz ez a szabály egy bizonyos pontig. Egyes IRL sztároknak többmillió followerük van, akik nem tudják ennek a mennyiségnek a felét sem visszakövetni, de nem biztos hogy ilyen nagy mértékben van jó tartalmuk. A túl nagy + aránnyal rendelkezőkre sokszor mondják, hogy nem is igazi Twitter userek, mert csak nagyon kevés embert követnek. A szabályt sok felhasználó használja és úgy tűnik valóban működik, de ellentmond a Twitter egyik alapelvének, miszerint ha elkezdesz követni valakit akkor elvárod, hogy az vissza is kövessen.
Perl Cannot Be Parsed: A Formal Proof
http://www.perlmonks.org/?node_id=663393
For those not familiar with the history of this discussion, the term "parse" here is being used in its strict sense to mean static parsing -- taking a piece of code and determining its structure without executing it. In that strict sense the Perl program does not parse Perl. As Jeffrey pointed out it means that you can't reliably parse perl code without executing it. This means that things like static code analysis, code transformation and syntax hilighting will never be reliable. This is a drawback indeed, but on the other hand it means that modules can extend Perl's syntax, and that other nifty stuff can be accomplished. So I understand this node as a proof of a property that is seldom fully understood.
[ UPDATE 14 Aug 2009: A series of three articles in The Perl Review, now available online, expands on this node. In that series, the proof is carefully laid out in three different versions, and is much more thoroughly explained. ]
Online Resources in nLab
http://ncatlab.org/nlab/show/Online+Resources
Lambda Calculus (at Safalra's Website)
http://safalra.com/science/lambda-calculus/
al introduction to lambda calculus
Programmers should know math.. just not all of it - Invisible to the eye
http://giorgiosironi.blogspot.com/2009/10/programmers-should-know-math-just-not.html
I have made a breakdown of the main arguments taught in high school and university which are utilized in computer science. I divided this list in a basic section and specific applications one.
linear
Math Overflow
http://mathoverflow.net/
.:: eGlossary Terms ::.
The McGraw Hill Mathematics eGlossary provides written and verbal definitions and explanations of mathematics terms. The glossary is divided by grade level. Select your grade level then the first letter of the term for which you need an explanation. The explanation is offered in text form as well as verbal (click the speaker icon to listen). The eGlossary is also available in other languages including Spanish, Russian, and Chinese.
Multilingual glossary with hundreds of math terms defined in Arabic, Bengali, Chinese, Haitian Creole, English, Hmong, Korean, Russian, Spanish, Tagalog, Urdu, and Vietnamese. Just select a letter of the alphabet to get a list of mathematical terms beginning with that letter, choose a language, and click on a term. The response will be a chart listing the term in English, the term in whatever language you chose, and the definition in your chosen language. Many definitions are accompanied by illustrations.
This site was kind of neat because it listed all the key mathematical terms starting with 6th grade. It makes the terms easily accessible.
http://heather.cs.ucdavis.edu/~matloff/r.html
http://heather.cs.ucdavis.edu/~matloff/r.html
As the title implies, it is written for those with experience in programming, ranging from those who've just taken a course to professionals in the field
A Quick, Painless Tutorial and Reference on the R Statistical Package
100 Incredible Open Lectures for Math Geeks | Online College Tips - Online Colleges
http://www.onlinecollege.org/2009/10/19/100-incredible-open-lectures-for-math-geeks/
Lalala, math, some of these I should watch sometime.
While many math geeks out there may have been teased for their love of numbers, it’s math that makes the world go round, defining everything from the economy to how the universe itself operates. You can indulge your love of mathematics in these great lectures and lecture series. Some are meant to review the basics and others will keep you on the cutting edge of what renowned researchers are doing in the field, but all will help you expand your knowledge and spend a few hours enjoying a topic you love.
Applied Mathematical Programming
http://web.mit.edu/15.053/www/
This book is the main text for 15.053 Introduction to Optimization taught at MIT. To make the book available online, most chapters have been re-typeset. Chapters 6, 7 and 10 were not, but are still available (as direct scans of the original chapters).
Book on Optimization used for teaching in MIT
Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977) This book is the main text for 15.053 Introduction to Optimization taught at MIT.
Functional Geometry
http://www.frank-buss.de/lisp/functional.html
Nice bit of drawing code.

Illuminations: Dynamic Paper
http://illuminations.nctm.org/ActivityDetail.aspx?ID=205
Can create specific type of paper like graph, spinners, etc
Wolfram|Alpha Blog : Step-by-Step Math
http://blog.wolframalpha.com/2009/12/01/step-by-step-math
A New Theory of Awesomeness and Miracles, by James Bridle, concerning Charles Babbage, Heath Robinson, MENACE and MAGE
http://shorttermmemoryloss.com/menace/
Being NOTES and SLIDES on a talk given at PLAYFUL 09, concerning CHARLES BABBAGE, HEATH ROBINSON, MENACE and MAGE
'...slightly larger than the Crab Nebula. And that is pretty awesome.'
Bill the Lizard: Six Visual Proofs
http://www.billthelizard.com/2009/07/six-visual-proofs_25.html
Eureqa | Cornell Computational Synthesis Laboratory
http://ccsl.mae.cornell.edu/eureqa
Eureqa is a software tool for detecting equations and hidden mathematical relationships in your data. Its primary goal is to identify the simplest mathematical formulas which could describe the underlying mechanisms that produced the data. Eureqa is free to download and use. Below you will find the program download, video tutorial, user forum, and other and reference materials.
"Eureqa is a software tool for detecting equations and hidden mathematical relationships in your data."
Eureqa is a software tool for detecting equations and hidden mathematical relationships in your data. Its primary goal is to identify the simplest mathematical formulas which could describe the underlying mechanisms that produced the data. Eureqa is free to download and use.
It's just what I've always wanted! Thank you!
Uses GA to discover the most likely equation behind your pile of data. Very pretty.
Mathematically Correct Breakfast -- Mobius Sliced Linked Bagel
http://www.georgehart.com/bagel/bagel.html
How to Slice a Bagel into Two Linked Halves
Robert Lang folds way-new origami | Video on TED.com
http://www.ted.com/talks/robert_lang_folds_way_new_origami.html
Úžasné způsoby jak skládat origami.
Puzzles - XKCD Wiki
http://wiki.xkcd.com/irc/Puzzles
100 people are being held prisoner in a jail. They are told that in one hour, they will all be taken to separate windowless, soundproof cells. One at a time, and in a random order, they will be taken from their cells, interrogated, and then sent back to their cells. All interrogations will take place in the same room, which contains one light bulb and the switch that operates it. The light is initially off, but the inmates are free to toggle the switch as often as they want, whenever they are in the interrogation room, and the prison guards will not toggle the switch at all. No prisoner can see the light from his cell. Only one prisoner is interrogated at a time, each prisoner can be interrogated multiple times, and they have no way of communicating besides the light switch. The length and amount of time between interrogations is random, so no help there.
Puzzles! Yummy.
Interesting maths puzzles to keep me occupied this summer.
Learning Haskell through Category Theory, and Adventuring in Category Land: Like Flatterland, Only About Categories « Benjamin L. Russell’s Adventures in Programming Language Theory Wonderland
, I hadn’t found an appropriate publication on category theory that addressed the subject at the proper pace,
Arrow, Structures and Functors
MathConnections - home
http://mathconnections.wikispaces.com/
Do you have students who wonder... * When will I ever use this in my life? * Will I really use math outside of school? * Do I really use it my everyday life? * Who really uses math in their jobs? * What kind of math is needed for different kinds of jobs? * Does math really make a difference?
MathJax
http://www.mathjax.org/
LaTeX and MathML math notation in HTML pages
MathJax is an open source, Ajax-based math display solution designed with a goal of consolidating advances in many web technologies in a single definitive math-on-the-web platform supporting all major browsers.
‘MathJax is an open source, Ajax-based math display solution designed with a goal of consolidating advances in many web technologies in a single definitive math-on-the-web platform supporting all major browsers.’
High-quality display of LaTeX and MathML math notation in HTML pages
Learning via Primary Historical Sources
http://www.cs.nmsu.edu/historical-projects/
This is a Phase II expansion grant from the National Science Foundation (2008-2011). The goal of the project is to develop, classroom test, evaluate and disseminate projects based on primary historical sources in Discrete Mathematics, Combinatorics, Logic and Computer Science courses.
This is a Phase II expansion grant from the National Science Foundation (2008-2011). The goal of the project is to develop, classroom test, evaluate and disseminate projects based on primary historical sources in Discrete Mathematics, Combinatorics, Logic and Computer Science courses. This is a collaborative project between Mathematics (Math) and Computer Science (CS) faculty at New Mexico State University (NMSU) and Colorado State University at Pueblo (CSU-P).
Learning Discrete Mathematics and Computer Science via Primary Historical Sources
The goal of the project is to develop, classroom test, evaluate and disseminate projects based on primary historical sources in Discrete Mathematics, Combinatorics, Logic and Computer Science courses.
"An infinite number of mathematicians walk into a bar. The first one orders a ..." - hot soup? anyone?
http://derdritte.soup.io/post/6961628/An-infinite-number-of-mathematicians-walk-into
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says "You're all idiots", and pours two beers.
Excellent math joke.
BBC NEWS | Science/Environment | Audio slideshow: The art of mathematics
http://news.bbc.co.uk/2/hi/science/nature/7617191.stm
nifty slide show of mathematical works (fractals, etc.), with explanation by mathematician
Fractal amazingness
for students
Schoonheid in beeld en wiskunde!
The Khan Academy is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere. We have 1000+ videos on YouTube covering everything from basic arithmetic and algebra to differential equations, physics, chemistry, biology and finance which have been recorded by Salman Khan.
"Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand. It turns out that chaos theory answers a question that mankind has asked for millennia - how did we get here? In this documentary, Professor Jim Al-Khalili sets out to uncover one of the great mysteries of science - how does a universe that starts off as dust end up with intelligent life? How does order emerge from disorder? It's a mindbending, counterintuitive and for many people a deeply troubling idea. But Professor Al-Khalili reveals the science behind much of beauty and structure in the natural world and discovers that far from it being magic or an act of God, it is in fact an intrinsic part of the laws of physics. Amazingly, it turns out that the mathematics of chaos can explain how and why the universe creates exquisite order and pattern. The natural worl
The Universe of Discourse : World's shortest explanation of Gödel's theorem
http://blog.plover.com/math/Gdl-Smullyan.html
7/10
Two Centuries On, a Cryptologist Cracks a Presidential Code - WSJ.com
http://online.wsj.com/article/SB124648494429082661.html?mod=yhoofront
Interesting, though the codebreaker did use a computer to solve it.
WSJ.com is available in the following editions and languages:
A cipher by Mr. Patterson. Simple to use without a computer, hard to crack.
For more than 200 years, buried deep within Thomas Jefferson's correspondence and papers, there lay a mysterious cipher -- a coded message that appears to have remained unsolved. Until now.
FF(16進数の掛け算)を覚えよう - やねうらお－よっちゃんイカを食べながら年収1億円稼げる(かも知れない)仕事術
http://d.hatena.ne.jp/yaneurao/20090106#p1
うわお。オレも計算機使ってる
いやあ、面白い
- やねうらお−よっちゃんイカを食べながら年収1億円稼げる(かも知れない)仕事術
From Fish to Infinity - Opinionator Blog - NYTimes.com
http://opinionator.blogs.nytimes.com/2010/01/31/from-fish-to-infinity/
A debut column on math features an introduction to numbers, from upsides (they're efficient) to down (they're ethereal).
I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.
STEVEN STROGATZ - Opinionator Blog - NYTimes.com
http://opinionator.blogs.nytimes.com/category/steven-strogatz/
Math Run - how fast is your brain? A simple Brain Training Game for everyone
http://mathrun.net/
Math Run - how fast is your brain? A simple Brain Training Game for everyone
Applying Mathematics To Web Design - Smashing Magazine
http://www.smashingmagazine.com/2010/02/09/applying-mathematics-to-web-design/
“Mathematics is beautiful.” This may sound absurd to people who wince at numbers and equations. But some of the most beautiful things in nature and our universe...
by @SmashingMag
"Layouts featured in this post were created specifically for the purpose of this article. During the design process we made sure that all of the designs shown in this article are essentially mathematical in nature; that is, they exhibit order, symmetry and limitation. We also have followed the Web design algorithm in this process — the designs have distinct themes, styles and elements. To keep things simple and clear, we tried to stick to minimalist designs and also preferred single-page layouts. Obviously, examples in this article are supposed to serve as a simple foundation for your designs and not as the finished designs."
mathematics support for students - mathcentre
http://www.mathcentre.ac.uk/students.php
web support estudiants de matematiques
This is a UK-based site with leaflets and booklets to download, revision exercises with answers, maths video tutorials, and other resources, for students needing maths help in Bioscience, Business, Economics, Engineering, Heath Sciences, Physical Sciences, and Mathematics and Statistics.
We are a group of people who run university maths support centres, who teach maths, and who design new media products for learning. We come from the Universities of Loughborough, Leeds and Coventry, from the Educational Broadcasting Services Trust, and from UK Learning and Teaching Support Networks. We have setup mathcentre to deliver mathematics support materials, free of charge, to students, teachers, lecturers and everyone looking for post-16 maths help. mathcentre gives you the opportunity to study important areas of pre-university mathematics, which you may have studied before or may be new to you - the maths you know you'll need for your course.
Stupid Coding Tricks: The T-SQL Mandelbrot - The Daily WTF
JOB
Did This Man Just Rewrite Science? - New York Times
http://query.nytimes.com/gst/fullpage.html?res=9D02EEDA113DF932A25755C0A9649C8B63&sec=&spon=&pagewanted=1
This insight is the jumping-off point of Dr. Wolfram's glossy 1,263-page book, ''A New Kind of Science,'' published a month ago by Dr. Wolfram himself to the accompaniment of articles comparing Dr. Wolfram to Isaac Newton.
A New Kind of Science
simples rules and algorithms define nature, not complex ones
Mathematics Books | Math-Blog
http://math-blog.com/mathematics-books/
the best math books for the subject at hand
Mathematics is wonderful!
Mathalicious
http://www.mathalicious.com/
At Mathalicious, our mission is to help transform the way math is taught by providing you with the best, most meaningful and most relevant math content available.  Our lessons are aligned to traditional state standards.  Unlike most math resources, though, our content emphasizes both conceptual understanding and real-world application.
Answers the questions - "What does this mean?" and "when will I use this?"
12 Reasons To Be Learning Graph Theory
http://andresosinski.com.ar/blog_view_entry/?id=1
RT @Kellblog: 12 Reasons To Be Learning (or at least paying attention to) Graph Theory http://bit.ly/a1F9hY #linkeddata #rdf #eav #gt
Odds Are, It's Wrong - Science News
http://www.sciencenews.org/view/feature/id/57091/title/Odds_Are,_Its_Wrong
Good story on how much science is messed up by misuse of statistics
Tom Siegfried, Mar 27, 2010 "uring the past century, though, a mutant form of math has deflected science’s heart from the modes of calculation that had long served so faithfully. Science was seduced by statistics, the math rooted in the same principles that guarantee profits for Las Vegas casinos. Supposedly, the proper use of statistics makes relying on scientific results a safe bet. But in practice, widespread misuse of statistical methods makes science more like a crapshoot." "Statistical tests are supposed to guide scientists in judging whether an experimental result reflects some real effect or is merely a random fluke, but the standard methods mix mutually inconsistent philosophies and offer no meaningful basis for making such decisions. Even when performed correctly, statistical tests are widely misunderstood and frequently misinterpreted. As a result, countless conclusions in the scientific literature are erroneous, and tests of medical dangers or treatments are often contra"
On the abuse and misuse of statistics by science
Science fails to face the shortcomings of statistics
A useful article outlining the shortcomings of statistics when it comes to ascertaining scientific fact. Half of all medical data could be wrong. "For better or for worse, science has long been married to mathematics. Generally it has been for the better. Especially since the days of Galileo and Newton, math has nurtured science. Rigorous mathematical methods have secured science’s fidelity to fact and conferred a timeless reliability to its findings."
Science fails to face the shortcomings of statistics
Prime Numbers and the Benford’s Law | Pyevolve
http://pyevolve.sourceforge.net/wordpress/?p=527
"Prime Numbers and the Benford's Law | Pyevolve" http://hub.tm/?RHOqX [from http://twitter.com/carreonG/statuses/1747034327]
Pyevolve - A complete genetic algorithm framework written in pure python
Sean Gourley on the mathematics of war | Video on TED.com
http://www.ted.com/index.php/talks/sean_gourley_on_the_mathematics_of_war.html
Argues that you should look at the insurgency according to its structure.. more fragmented groups, or fewer but stronger groups?
Long running conflicts depend on a stability of number of factions vs. strength of factions, if you have lots of weaker factions, they're not strong enough to commit as effective attacks, if you have fewer, but stronger factions, you can start leveraging negotiation.
「ビートルズ名曲冒頭の音の謎」を数学者が解明 | WIRED VISION
http://wiredvision.jp/news/200811/2008110622.html
「解析の結果、このコードには、プロデューサーのジョージ・マーティンが演奏したと思われる5つのピアノ音が含まれていることが判明した。」
Elementary Mathematics
http://www.bcps.org/offices/lis/curric/elem/elemgeo.html
List of ideas for grades 1-6 on math.
worksheets and activities from kindy to year 6
A large range of lessons which are divided clearly into grades. The lesson are easy to read and are able to prepare a teacher for the lesson.
This website focuses on the content strand geometry. It has a list of lessons and activities ranging from grade 1 to 5 which teachers could use to support the learning of geometry.

http://d.hatena.ne.jp/Koumei_S/20090322/1237727846
xkcd - A Webcomic - Fermirotica
http://xkcd.com/563/
as awesome as dimensional analysis is, it's still a pain in the ass
xkcd - A Webcomic - #563: Fermirotica
Statistics...
Teacher Zone - Free Library of Math Video Lessons
http://teacher.tenmarks.com/
A library of math video lessons. It seems to go upt to grade 10.
Biblioteca Livre de Vídeo Aulas de Matemática
A comprehensive compilation of mathematical video online tutorials
the most comprehensive library of math video lessons on the planet
Math lesson videos
Free library of math lessons
baseplane - technology platforms » Big O Notation in Design Theory » baseplane - technology platforms
http://baseplane.com/2008/03/22/big-o-notation-in-design-theory/
Coding Horror: Why Do Computers Suck at Math?
http://www.codinghorror.com/blog/archives/001266.html
=850*77.1
"Computers are supposed to be pretty good at this math stuff. What gives? How is it possible to produce such blatantly incorrect results from seemingly trivial calculations? Should we even be trusting our computers to do math at all?"
"Computers are awesome, yes, but they aren't infinite.. yet. So any prospects of storing any infinitely repeating number on them are dim at best. The best we can do is work with approximations at varying levels of precision that are "good enough", where "good enough" depends on what you're doing, and how you're doing it. And it's complicated to get right."
How do you spark off an interest in maths when the curriculum seems dreary? | Education | The Guardian
http://www.guardian.co.uk/education/2009/jun/23/maths-marcus-du-sautoy
An interesting article highlighting the need to spark student interest in maths through the use of magic numbers, links to music and the creative arts and through an emphasis that, “A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas,” (cited du Sautoy, 2009). The article is a brilliant read for math teachers in the diverse classroom who need to understand that for some students, “the subject comes alive when they learn how mathematics is not an isolated subject, but runs seductively below the surface of many other subjects in the curriculum,” (du Sautoy, 2009). The article may be beneficial for those teachers aiming to engage the disengaged and may provide teachers with ideas for extension activities for gifted and talented students. Well worth a read for any teacher wanting to spice up their mathematics curriculum.
Guardian article written by Marcus du Sautoy 23/06/09 on livening up the maths curriculum with big, creative mathematical adventures. Links to gallery of useful archietectural photos. Recommended by CH. Links to other useful Guardian articles on maths by same author.
"I've never understood why education is so compartmentalised" - "... the maths we were doing in the classroom wasn't really what maths was about. It was something much more exciting, creative, imaginative. Those books provided me with a key to the secret garden of mathematics" - "In that garden I discovered that mathematics also has great stories. Unsolved mysteries like the enigma of prime numbers. Magical mathematical machines that could help you see in four dimensions. Mathematicians who had journeyed to infinity and beyond..." - lighting the fire, relating to the abstract
How do you spark off an interest in maths when the curriculum seems dreary? It's all about mystery, big stories and journeys to infinity and beyond, says Marcus du Sautoy
I've never understood why education is so compartmentalised. My son looks at his timetable: maths first lesson, history second lesson, music before lunch. The curriculum gives no hint at how integrated all these subjects are. To look at the historical evolution of mathematical ideas provides an invaluable perspective on why the mathematics was created in the first place.
great essay on encouraging a passion for math
The Floating-Point Guide - What Every Programmer Should Know About Floating-Point Arithmetic
http://floating-point-gui.de/
Aims to provide both short and simple answers to the common recurring questions of novice programmers about floating-point numbers not 'adding up' correctly, and more in-depth information about how IEEE 754 floats work, when and how to use them correctly, and what to use instead when they are not appropriate.
Dan Meyer: Math class needs a makeover | Video on TED.com
http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
How we can reshape the math curriculum for critical thinking.
Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. At TEDxNYED, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.
Guest Column: Loves Me, Loves Me Not (Do the Math) - Olivia Judson Blog - NYTimes.com
http://judson.blogs.nytimes.com/2009/05/26/guest-column-loves-me-loves-me-not-do-the-math/
differential equations
RT - "Romeo and Juliet behave like simple harmonic oscillators" - unfortunately phase shifted!! - http://alturl.com/otbb [from http://twitter.com/vivek_kumar/statuses/2647778575]
by steven strogatz.
RT @iwestminster “Love me, love me not” reduces love to a mathematical equation http://tr.im/mNUs (I was never good at #math:) #homeschool [from http://twitter.com/CircleReader/statuses/1961151636]
Blog column by Steven Strogatz.
Love of Romeo and Juliet, ODE style... by Steven Strogatz
Coding Horror: Finishing The Game
http://www.codinghorror.com/blog/archives/001204.html
"This problem, although seemingly simple, is hard to understand. For cognitive reasons that are not fully understood, while our intuitions regarding a priori possibilities are fairly good, we are easily misled when we try to use probability to quantify our knowledge. This is a fancypants way of saying there were almost a thousand comments on that post, with not a lot of agreement to be found. "
someone who told you they had two children, and one of them is a girl. What are the
square root
Calculation by hand
CS-TR-339 Computer Go Tech Report
http://www.itee.uq.edu.au/~janetw/Computer%20Go/CS-TR-339.html
An Introduction to the Computer Go Field and Associated Internet Resources
The nicest math book I own | Math-Blog
http://math-blog.com/2008/12/22/the-nicest-math-book-i-own/
The Princeton Companion to Mathematics
A Non-Mathematical Introduction to Using Neural Networks | Heaton Research
http://www.heatonresearch.com/content/non-mathematical-introduction-using-neural-networks
Conceptua™ Math
http://www.conceptuamath.com/fractions.html
tools designed for teacher-facilitated instruction, and include sample problems to give teachers instructional suggestions. For each tool you will find a short instructional video, standards alignment (including the recent Common Core State Standards), key vocabulary, and IEP goals
Focus on teaching fractions!
Conceptua (MeTRIC): standards-based, teacher facilitated math tools... procedural, higher-order concepts, etc.
This site provides visual math lessons. Though this site specializes in fractions, there are pieces any level math teacher can grab from here.
Steven Strogatz on the Elements of Math - Series - The New York Times
http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html
"Steven Strogatz, an award-winning professor, takes readers from the basics to the baffling in a 15-part series on mathematics. Beginning with a column on why numbers are helpful, he goes on to investigate topics including negative numbers, calculus and group theory, finishing with the mysteries of infinity."
15 articles on Maths from The New York Times. Assessment tasks perhaps?
15 artigos interessantes sobre matemática
Measuring Measures - blog - Learning about Network Theory
In this post, Drew Conway (a PhD Candidate at New York University, studying networks) and I will walk you through a guide that we hope may be of use to others trying to find their way through network theor
Less Wrong: Bayes' Theorem Illustrated (My Way)
http://lesswrong.com/lw/2b0/bayes_theorem_illustrated_my_way
Great illustration.
No, really, pi is wrong: The Tau Manifesto by Michael Hartl | Tau Day, 2010
http://tauday.com/
quite convincing :)
Tau = 2*Pi. Revelation of the century.
The Tau Manifesto
When Intuition And Math Probably Look Wrong - Science News
http://sciencenews.org/view/generic/id/60598/title/When_intuition_and_math_probably_look_wrong
Hint: 13/27
Great! When intuition and math probably look wrong: http://bit.ly/9ohKuV #mathematics #science – Amir Kassaei (AmirKassaei) http://twitter.com/AmirKassaei/statuses/17519030506
Accurately computing running variance
http://www.johndcook.com/standard_deviation.html
The most direct way of computing sample variance or standard deviation can have severe numerical problems. [...] There is a way to compute variance that is more accurate and is guaranteed to always give positive results. Furthermore, the method computes a running variance. That is, the method computes the variance as the x's arrive one at a time. The data do not need to be saved for a second pass.
"This better way of computing variance goes back to a 1962 paper by B. P. Welford and is presented in Donald Knuth's Art of Computer Programming, Vol 2, page 232, 3rd edition. Although this solution has been known for decades, not enough people know about it. Most people are probably unaware that computing sample variance can be difficult until the first time they compute a standard deviation and get an exception for taking the square root of a negative number. It is not obvious that the method is correct even in exact arithmetic. It's even less obvious that the method has superior numerical properties, but it does."
A simple way to compute running sample variance (standard deviation).
Computing mean, variance and standard deviation on a stream of data.
MIT OpenCourseWare | Electrical Engineering and Computer Science | 6.042J Mathematics for Computer Science, Spring 2005 | Lecture Notes
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2005/lecture-notes/
Mathematics for Computer Science