# Mathematics

Want to learn statistics? These are the best books, and they're free to download. Statistics came well before computers. It would be very different if it were the other way around. The stats most people learn in high school or college come from the time when computations were done with pen and paper. “Statistics were constrained by the computational technology available at the time,” says Stanford statistics professor Robert Tibshirani. “People use certain methods because that is how it all started and that’s what they are used to. It’s hard to change it.” People who have taken intro statistics courses might recognize terms like “normal distribution,” “t-distribution,” and “least squares regression.” As a former data scientist, there is no question I get asked more than, “What is the best way to learn statistics?”

Number crunchers The books are based on the concept of “statistical learning,” a mashup of stats and machine learning. This is important in areas like medicine, where a researcher doesn’t just want to know whether a medicine worked, but also why it worked. Why am I so bad at math? You're not, you're just looking at it wrong. — Quartz. What does mathematics look like to you? Do you see a wondrous landscape filled with connected ideas, or a sprawling mess of symbols?

The distinction matters a great deal, because your mathematical worldview is inextricably tied to your success in the subject. We are all familiar with the multiplication grid, a centerpiece of classrooms and home studies the world over: You cannot fault this image for accuracy. There is a bluntness to the grid; a seemingly disconnected array of factual truths. Perhaps they see this — a scaled drawing of the multiplication grid: With this simple tweak, the grid is beginning to speak to us. With deliberate use of color, we can extract a different type of structure — here we see the multiplication grid as a nested collection of smaller grids: The size and shape of each layer reveals new truths. Having the right mental representations is the key to developing your mathematical potential. Mental representations anchor us to our worldview of mathematics. Seeing Theory. JUMP Math, a teaching method that's proving there's no such thing as a bad math student — Quartz.

Math is a notoriously hard subject for many kids and adults. There is a gender gap, a race gap, and just generally bad performance in many countries. John Mighton, a Canadian playwright, author, and math tutor who struggled with math himself, has designed a teaching program that has some of the worst-performing math students performing well and actually enjoying math. There’s mounting evidence that the method works for all kids of all abilities. His program, JUMP (Junior Undiscovered Math Prodigies) Math, is being used by 15,000 kids in eight US states (it is aligned with the Common Core), more than 150,000 in Canada, and about 12,000 in Spain.

The US Department of Education found it promising enough to give a \$2.75 million grant in 2012 to Tracy Solomon and Rosemary Tannock, cognitive scientists at the Hospital for Sick Children and the University of Toronto, to conduct a randomized control trial with 1,100 kids and 40 classrooms. How it works Mighton says the small steps are critical. Essence of linear algebra preview. Essence of linear algebra. Puzzle Playground - Martin Gardner. OpenIntro. Hyperuniformity Found In Birds, Math And Physics. Welcome. 3Blue1Brown. Octave Online: Free Interface compatible with MATLAB. Aristotle was right about mathematics after all — Ae... What is mathematics about? We know what biology is about; it’s about living things. Or more exactly, the living aspects of living things – the motion of a cat thrown out of a window is a matter for physics, but its physiology is a topic for biology. Oceanography is about oceans; sociology is about human behaviour in the mass long-term; and so on.

When all the sciences and their subject matters are laid out, is there any aspect of reality left over for mathematics to be about? People care about the philosophy of mathematics in a way they do not care about, say, the philosophy of accountancy. One famous philosopher who finds mathematical necessity an inconvenience is Peter Singer. To the question: ‘Is mathematics about something?’ The ‘No’ answer, whose champions are known as nominalists, says that mathematics is just a language. Nominalism might have a certain down-to-earth appeal, but further reflection suggests that it can’t be right. There were many such properties. Ask your question. 21 GIFs That Explain Mathematical Concepts. “Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.” Danica McKellar As we usher in the start of a new school year, it’s time to hit the ground running in your classes!

Math can be pretty tough, but since it is the language in which scientists interpret the Universe, there’s really no getting around learning it. Check out these gifs that will help you visualize some tricky aspects of math, so you can dominate your exams this year. Ellipse: Via: giphy Solving Pascal triangles: Via: Hersfold via Wikimedia Commons Use FOIL to easily multiply binomials: Via: mathcaptain Here’s how you solve logarithms: Via: imgur Use this trick so you don’t get mixed up when doing matrix transpositions: Via: Wikimedia Commons What the Pythagorean Theorem is really trying to show you: Via: giphy Exterior angles of polygons will ALWAYS add up to 360 degrees: Via: math.stackexchange Via: imgur Via: Wikimedia Commons Via: reddit.

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Wolfram Web Resources. Math Worksheets | Dynamically Created Math Worksheets. Math2.org. Visual Math Learning: A Free Online Tutorial for Teaching Math. Visual Calculus. 21 GIFs That Explain Mathematical Concepts. How do japanese multiply?? Mathemagic. Gödel's Incompleteness Theorem | Miskatonic University Press.

What is Mathematics: Gödel's Theorem and Around. Incompleteness. By K. Podnieks. What is mathematics, logic, mathematics, foundations, incompleteness theorem, mathematical, Gödel, Godel, book, Goedel, tutorial, textbook, methodology, philosophy, nature, theory, formal, axiom, theorem, incompleteness, online, web, free, download, teaching, learning, study, student, Podnieks, Karlis Personal page - click here. Visiting Gödel Places in Vienna, December 2012 K.Podnieks. Frege’s Puzzle from a Model-Based Point of View. The Reasoner, Vol. 6, N 1, January 2012, pp. 5-6. K.Podnieks, J.Tabak. Mathematical Challenge (powers of 2, exponentiation, etc.)Gödel's Theorem in 15 Minutes (English, Latvian, Russian) Quote of the Day Personal page - click here.

8 math talks to blow your mind. Mathematics gets down to work in these talks, breathing life and logic into everyday problems. Prepare for math puzzlers both solved and unsolvable, and even some still waiting for solutions. Ron Eglash: The fractals at the heart of African designs When Ron Eglash first saw an aerial photo of an African village, he couldn’t rest until he knew — were the fractals in the layout of the village a coincidence, or were the forces of mathematics and culture colliding in unexpected ways?

Here, he tells of his travels around the continent in search of an answer. How big is infinity? Arthur Benjamin does “Mathemagic” A whole team of calculators is no match for Arthur Benjamin, as he does astounding mental math in the blink of an eye. Scott Rickard: The beautiful math behind the ugliest music What makes a piece of music beautiful? Benoit Mandelbrot: Fractals and the art of roughness The world is based on roughness, explains legendary mathematician Benoit Mandelbrot. Numberphile. Closer To Truth asks Roger Penrose: What Things Really Exist? 17 Equations That Changed The World. Euclid's Elements, Introduction. Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences.

The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages. I'm creating this version of Euclid's Elements for a couple of reasons. The main one is to rekindle an interest in the Elements, and the web is a great way to do that. Another reason is to show how Java applets can be used to illustrate geometry. The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional. This edition of Euclid's Elements uses a Java applet called the Geometry Applet to illustrate the diagrams. ANCIENT GREEK GEOMETRY. The Geometry Junkyard. The Berlin Numeracy Test > Try It. Zipf, Power-law, Pareto - a ranking tutorial. Lada A. Adamic Information Dynamics Lab Information Dynamics Lab, HP Labs Palo Alto, CA 94304 A line appears on a log-log plot.

One hears shouts of "Zipf! ","power-law! " All three terms are used to describe phenomena where large events are rare, but small ones quite common. Zipf's law usually refers to the 'size' y of an occurrence of an event relative to it's rank r. Pareto was interested in the distribution of income. What is usually called a power law distribution tells us not how many people had an income greater than x, but the number of people whose income is exactly x. Although the literature surrounding both the Zipf and Pareto distributions is vast, there are very few direct connections made between Zipf and Pareto, and when they exist, it is by way of a vague reference [1] or an overly complicated mathematical analysis[2,3].

Figure 1a below shows the distribution of AOL users' visits to various sites on a December day in 1997. Acknowledgements References 1. 2. 3. 4. 5. 6. 7. 8. 9. Statistics, Probability, and Survey Sampling. Statlect, the digital textbook. WHAT ARE THE ODDS?  The Ins and Outs of Probability. Game Theory 101: Game Theory Made Easy. Game Theory Explains How Cooperation Evolved. When the manuscript crossed his desk, Joshua Plotkin, a theoretical biologist at the University of Pennsylvania, was immediately intrigued.

The physicist Freeman Dyson and the computer scientist William Press, both highly accomplished in their fields, had found a new solution to a famous, decades-old game theory scenario called the prisoner’s dilemma, in which players must decide whether to cheat or cooperate with a partner. The prisoner’s dilemma has long been used to help explain how cooperation might endure in nature. After all, natural selection is ruled by the survival of the fittest, so one might expect that selfish strategies benefiting the individual would be most likely to persist.

But careful study of the prisoner’s dilemma revealed that organisms could act entirely in their own self-interest and still create a cooperative community. Press and Dyson’s new solution to the problem, however, threw that rosy perspective into question. Candace diCarlo Tit for Tat. Discrete Mathematics for Dummies. Finite Mathematics and Applied Calculus. Fractal Geometry. Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3] Beauty of mathematics. Another Look at Prime Numbers. Primes are numeric celebrities: they're used in movies, security codes, puzzles, and are even the subject of forlorn looks from university professors. But mathematicians delight in finding the first 20 billion primes, rather than giving simple examples of why primes are useful and how they relate to what we know. Somebody else can discover the "largest prime" -- today let's share intuitive insights about why primes rock: Primes are building blocks of all numbers.

And just like in chemistry, knowing the chemical structure of a material helps understand and predict its properties.Primes have special properties like being difficult to determine (yes, even being difficult can be a positive trait). These properties have applications in cryptography, cycles, and seeing how other numbers multiply together. So what are prime numbers again? A basic tenet of math is that any number can be written as the multiplication of primes. Well, not really. Analogy: Prime Numbers and Chemical Formulas Why?

1. The Prime Pages (prime number research, records and resources) The On-Line Encyclopedia of Integer Sequences® (OEIS®) Infinity is bigger than you think - Numberphile. Hilbert's Infinite Hotel - 60-Second Adventures in Thought (4/6) Imagining the Tenth Dimension - 2012 Version. Imagining the "Zeroth" Dimension. RAMANUJAN: Letters from an Indian Clerk. Leaner Fourier Transforms. By Helen Knight, MIT New algorithm can separate signals into their individual frequencies using a minimal number of samples. The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing. The algorithm allowed computers to quickly perform Fourier transforms — fundamental operations that separate signals into their individual frequencies — leading to developments in audio and video engineering and digital data compression.

But ever since its development in the 1960s, computer scientists have been searching for an algorithm to better it. Last year MIT researchers Piotr Indyk and Dina Katabi did just that, unveiling an algorithm that in some circumstances can perform Fourier transforms hundreds of times more quickly than the fast Fourier transform (FFT). Close to theoretical minimum The Fourier transform is a fundamental mathematical notion that allows signals to be broken down into their component parts.

Braess’ Paradox – or Why improving something can make it worse | Oasys Software Blog. On Earth Day in 1990 they closed New York’s 42nd Street for the parade[1] and in 1999 one of the three main traffic tunnels in South Korea’s capital city was shut down for maintenance[2]. Bizarrely, despite both routes being heavily used for traffic, the result was not the predicted chaos and jams, instead the traffic flows improved in both cases.

Inspired by their experience, Seoul’s city planners subsequently demolished a motorway leading into the heart of the city and experienced exactly the same strange result, with the added benefit of creating a 5-mile long, 1,000 acre park for the local inhabitants[3]. It is counter-intuitive that you can improve commuters’ travel times by reducing route options: after all planners normally want to improve things by adding routes. This paradox was first explored by Dietric Braess in 1968[4,5] where he explored the maths behind how adding route choices to a network can sometimes make everyone’s travel time worse. 6*3+26 = 44 minutes Lv + Rv = 1000.