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Infinity is bigger than you think - Numberphile

Infinity is bigger than you think - Numberphile

http://www.youtube.com/watch?v=elvOZm0d4H0

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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.

Meditation How to meditate, and what this does for you. Meditation is a basic practice for self-realization. Basically, you sit straight and concentrate on a particular point in your body (usually the belly, or the breath). When you notice that your have drifted away from this point of concentration, you gently return to it. What it does for you This practice in a gradual way helps in lots of aspects of your life.

Quadratic function A quadratic function, in mathematics, is a polynomial function of the form The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis. The expression ax2 + bx + c in the definition of a quadratic function is a polynomial of degree 2, or a 2nd degree polynomial, because the highest exponent of x is 2. Proof claimed for deep connection between primes The usually quiet world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved. Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers — a 'Diophantine' problem. The abc conjecture, proposed independently by David Masser and Joseph Oesterle in 1985, might not be as familiar to the wider world as Fermat’s Last Theorem, but in some ways it is more significant.

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? Algebra "Algebraist" redirects here. For the novel by Iain M. Banks, see The Algebraist. The quadratic formula expresses the solution of the degree two equation in terms of its coefficients , where Mathgen paper accepted! I’m pleased to announce that Mathgen has had its first randomly-generated paper accepted by a reputable journal! On August 3, 2012, a certain Professor Marcie Rathke of the University of Southern North Dakota at Hoople submitted a very interesting article to Advances in Pure Mathematics, one of the many fine journals put out by Scientific Research Publishing. (Your inbox and/or spam trap very likely contains useful information about their publications at this very moment!) This mathematical tour de force was entitled “Independent, Negative, Canonically Turing Arrows of Equations and Problems in Applied Formal PDE”, and I quote here its intriguing abstract:

Julia set A Julia set Three-dimensional slices through the (four-dimensional) Julia set of a function on the quaternions. The Julia set of a function f is commonly denoted J(f), and the Fatou set is denoted F(f).[1] These sets are named after the French mathematicians Gaston Julia[2] and Pierre Fatou[3] whose work began the study of complex dynamics during the early 20th century. 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.

Group (mathematics) Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Point groups are used to help understand symmetry phenomena in molecular chemistry; and Poincaré groups can express the physical symmetry underlying special relativity. One of the most familiar groups is the set of integers Z which consists of the numbers ..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ...,[3] together with addition. The following properties of integer addition serve as a model for the abstract group axioms given in the definition below.

Catalog Page for PIA16075 This composite image, with magnified insets, depicts the first laser test by the Chemistry and Camera, or ChemCam, instrument aboard NASA's Curiosity Mars rover. The composite incorporates a Navigation Camera image taken prior to the test, with insets taken by the camera in ChemCam. The circular insert highlights the rock before the laser test. The square inset is further magnified and processed to show the difference between images taken before and after the laser interrogation of the rock. The test took place on Aug. 19, 2012. In the composite, the fist-sized rock, called "Coronation," is highlighted. Unicity distance Consider an attack on the ciphertext string "WNAIW" encrypted using a Vigenère cipher with a five letter key. Conceivably, this string could be deciphered into any other string — RIVER and WATER are both possibilities for certain keys. This is a general rule of cryptanalysis: with no additional information it is impossible to decode this message. Of course, even in this case, only a certain number of five letter keys will result in English words. Trying all possible keys we will not only get RIVER and WATER, but SXOOS and KHDOP as well.

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.

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