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. 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 the mathematical infinity symbol ∞ may be derived from the Roman numerals for 1000 or for 100 million?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that the number of cannonballs in a square pyramid with cannonballs along each edge is ?
- ... that despite a mathematical model deeming the ice cream bar flavour Goody Goody Gum Drops impossible, it was still created?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
- ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that mathematician Mathias Metternich was one of the founders of the Jacobin club of the Republic of Mainz?
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- ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?
- ...that the 1966 publication disproving Euler's sum of powers conjecture, proposed nearly 200 years earlier, consisted of only two sentences?
- ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions?
- ... that economists blame market failures on non-convexity?
- ... that, according to the pizza theorem, a circular pizza that is sliced off-center into eight equal-angled wedges can still be divided equally between two people?
- ... that the clique problem of programming a computer to find complete subgraphs in an undirected graph was first studied as a way to find groups of people who all know each other in social networks?
- ... that the Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle?
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Flowcharts are often used to represent algorithms Image credit: User:Booyabazooka |
An algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. 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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