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 a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that the 1914 Lubin vault fire in Philadelphia destroyed several thousand unique early silent films?
- ... that mathematics professor Ari Nagel has fathered more than a hundred children?
- ... that after Florida schools banned 54 mathematics books, Chaz Stevens petitioned that they also ban the Bible?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that Fairleigh Dickinson's upset victory over Purdue was the biggest upset in terms of point spread in NCAA tournament history, with Purdue being a 23+1⁄2-point favorite?
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- ... that one can list every positive rational number without repetition by breadth-first traversal of the Calkin–Wilf tree?
- ... that the Hadwiger conjecture implies that the external surface of any three-dimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient?
- ... that an equitable coloring of a graph, in which the numbers of vertices of each color are as nearly equal as possible, may require far more colors than a graph coloring without this constraint?
- ... that no matter how biased a coin one uses, flipping a coin to determine whether each edge is present or absent in a countably infinite graph will always produce the same graph, the Rado graph?
- ...that it is possible to stack identical dominoes off the edge of a table to create an arbitrarily large overhang?
- ...that in Floyd's algorithm for cycle detection, the tortoise and hare move at very different speeds, but always finish at the same spot?
- ...that in graph theory, a pseudoforest can contain trees and pseudotrees, but cannot contain any butterflies, diamonds, handcuffs, or bicycles?
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The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages Image credit: Matt Crypto |
Cryptography (or cryptology) is derived from Greek κρυπτός kryptós "hidden," and the verb γράφω gráfo "write". In modern times, it has become a branch of information theory, as the mathematical study of information and especially its transmission from place to place. The noted cryptographer Ron Rivest has observed that "cryptography is about communication in the presence of adversaries." It is a central contributor to several fields: information security and related issues, particularly, authentication, and access control. One of cryptography's primary purposes is hiding the meaning of messages, not usually the existence of such messages. In modern times, cryptography also contributes to computer science. Cryptography is central to the techniques used in computer and network security for such things as access control and information confidentiality. Cryptography is also used in many applications encountered in everyday life; the security of ATM cards, computer passwords, and electronic commerce all depend on cryptography. (Full article...)
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