Portal:Mathematics
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Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Used for calculation, it is considered the most important subject. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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 ...that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type the complete works of William Shakespeare?
 ... that there are 115,200 solutions to the ménage problem of permuting six femalemale couples at a twelveperson table so that men and women alternate and are seated away from their partners?
 ... that mathematician Paul Erdős called the Hadwiger conjecture, a stillopen generalization of the fourcolor problem, "one of the deepest unsolved problems in graph theory"?
 ...that the six permutations of the vector (1,2,3) form a regular hexagon in 3d space, the 24 permutations of (1,2,3,4) form a truncated octahedron in four dimensions, and both are examples of permutohedra?
 ...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14piece tiling puzzle similar to tangram?
 ...that some functions can be written as an infinite sum of trigonometric polynomials and that this sum is called the Fourier series of that function?
 ...that the identity elements for arithmetic operations make use of the only two whole numbers that are neither composites nor prime numbers, 0 and 1?
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 ... that the Summa de arithmetica (title page shown), thought to be the first printed work on algebra, contains the first published description of doubleentry accounting?
 ... that rings of modular forms are stacky thanks to GAGA?
 ... that in the musical Fermat's Last Tango, mathematicians Euclid and Newton are played by women?
 ... that when Rosa M. Morris scored 130 percent in her mathematics exams, a special case had to be made at graduation to avoid handicapping other students?
 ... that Clyde Foster, a mathematician with NASA, persuaded former Nazi rocket scientist Wernher von Braun to support a computer science program at historically black Alabama A&M University?
 ... that before becoming a professional mathematician, Chikako Mese was a recordbreaking high school softball player?
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Flowcharts are often used to represent algorithms Image credit: User:Booyabazooka 
An algorithm is a procedure (a finite set of welldefined instructions) for accomplishing some task which, given an initial state, will terminate in a defined endstate. The computational complexity and efficient implementation of the algorithm are important in computing, and this depends on suitable data structures.
Informally, the concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). Algorithms can be composed to create more complex algorithms.
The concept of an algorithm originated as a means of recording procedures for solving mathematical problems such as finding the common divisor of two numbers or multiplying two numbers. The concept was formalized in 1936 through Alan Turing's Turing machines and Alonzo Church's lambda calculus, which in turn formed the foundation of computer science.
Most algorithms can be directly implemented by computer programs; any other algorithms can at least in theory be simulated by computer programs. In many programming languages, algorithms are implemented as functions or procedures. (Full article...)
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