Edge: GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH
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 truthFree Mathematics Books
Free Mathematics Books - list of freely available math textbooks, monographs, lecture notes, and other documents.
Look at Intro to R Book
CombinWelcome to the Tricki | Tricki
Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving techniques.New Pattern Found in Prime Numbers
(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....”Math Exercises
computer simulation software
Great website for showing GTT conceptsWhy are There 60 Minutes in an Hour? | Scienceray
Porqué hay 60 minutos en una hora.Trucos para aprobar un examen de oposicion, test psicotécnicos gratis, aumentar el coeficiente intelectual o con tests de figuras, memoria, matematicos, razonamiento verbal y numericas. Para oposiciones, trabajos... on-line
Operaciones matemáticasHow maths killed Lehman Brothers
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).A Calculus Analogy: Integrals as Multiplication | BetterExplained
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!”MATH TOOL CHEST - 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.Free Mathsframe Interactive Whiteboard Teacher Resources
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.Math Interactives
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 jobsOnline Resources in nLab
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.Wolfram|Alpha Blog : Step-by-Step Math
Science for parents of primary kids - UK government website.Puzzles - XKCD Wiki
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.
Interesting maths puzzles to keep me occupied this summer.MathConnections - home
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?The ArithmAttack
Arithmetic AttackKhan Academy
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.STEVEN STROGATZ - Opinionator Blog - NYTimes.com
Math Run - how fast is your brain? A simple Brain Training Game for everyonemathematics support for students - mathcentre
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.Mathematics Books | Math-Blog
the best math books for the subject at hand
Mathematics is wonderful!Prime Numbers and the Benford’s Law | Pyevolve
"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 pythonBBC NEWS | Magazine | How to understand risk in 13 clicks
parallel sets diagramJohn Graham-Cumming: Squaring two digit numbers in your head
x^2Crickweb | Flash Page
Symmetry. Sorting shapes by lines of symmetry.
Sort shapes as to reflective symmetry
Determine which shapes have 0, 1, 2 or more lines of symmetry.
How many lines of symmetry does a square have? Find out this and more in this symmetry sorting activity. Available as a bounce back demo or without bounce back for assessment.
print for quizCoding Horror: Why Do Computers Suck at Math?
"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
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 mathCoding Horror: Finishing The Game
"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 thesquare root
Calculation by handThe nicest math book I own | Math-Blog
The Princeton Companion to Mathematics