Portal:Mathematics
The Mathematics Portal
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. 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 two members of the French parliament were killed when a delayed-action German bomb exploded in the town hall at Bapaume on 25 March 1917?
- ... that Catechumen, a Christian first-person shooter, was funded only in the aftermath of the Columbine High School massacre?
- ... that Latvian-Soviet artist Karlis Johansons exhibited a skeletal tensegrity form of the Schönhardt polyhedron seven years before Erich Schönhardt's 1928 paper on its mathematics?
- ... that people in Madagascar perform algebra on tree seeds in order to tell the future?
- ... that although the problem of squaring the circle with compass and straightedge goes back to Greek mathematics, it was not proven impossible until 1882?
- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that owner Matthew Benham influenced both Brentford FC in the UK and FC Midtjylland in Denmark to use mathematical modelling to recruit undervalued football players?
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
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- ... that according to Kawasaki's theorem, an origami crease pattern with one vertex may be folded flat if and only if the sum of every other angle between consecutive creases is 180º?
- ... that, in the Rule 90 cellular automaton, any finite pattern eventually fills the whole array of cells with copies of itself?
- ... that, while the criss-cross algorithm visits all eight corners of the Klee–Minty cube when started at a worst corner, it visits only three more corners on average when started at a random corner?
- ...that in senary, all prime numbers other than 2 and 3 end in 1 or a 5?
- ...that, for all prime numbers p, the pth Perrin number is divisible by p?
- ...that it is impossible to trisect a general angle using only a ruler and a compass?
- ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?
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Game theory is a branch of mathematics that is often used in the context of economics. It studies strategic interactions between agents. In strategic games, agents choose strategies which will maximize their return, given the strategies the other agents choose. The essential feature is that it provides a formal modelling approach to social situations in which decision makers interact with other agents. Game theory extends the simpler optimisation approach developed in neoclassical economics.
The field of game theory came into being with the 1944 classic Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. A major center for the development of game theory was RAND Corporation where it helped to define nuclear strategies.
Game theory has played, and continues to play a large role in the social sciences, and is now also used in many diverse academic fields. Beginning in the 1970s, game theory has been applied to animal behaviour, including evolutionary theory. Many games, especially the prisoner's dilemma, are used to illustrate ideas in political science and ethics. Game theory has recently drawn attention from computer scientists because of its use in artificial intelligence and cybernetics. (Full article...)
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