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Randall Dougherty
Randall Dougherty (born 1961) is an American mathematician. Dougherty has made contributions in widely varying areas of mathematics, including set theory, logic, real analysis, discrete mathematics, computational geometry, information theory, and coding theory. Dougherty is a three-time winner of the U.S.A. Mathematical Olympiad (1976, 1977, 1978) and a three-time medalist in the International Mathematical Olympiad. He is also a three-time Putnam Fellow (1978, 1979, 1980). Dougherty earned his Ph.D. in 1985 at University of California, Berkeley under the direction of Jack Silver. With Matthew Foreman he showed that the Banach-Tarski decomposition is possible with pieces with the Baire property, solving a problem of Marczewski that remained unsolved for more than 60 years. With Chris Freiling and Ken Zeger, he showed that linear codes are insufficient to gain the full advantages of network coding In computer networking, linear network coding is a program in which inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banach–Tarski Paradox
The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them without changing their shape. However, the pieces themselves are not "solids" in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces. An alternative form of the theorem states that given any two "reasonable" solid objects (such as a small ball and a huge ball), the cut pieces of either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox". The theorem is called a paradox because it contradicts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ohio State University Faculty
Faculty may refer to: * Faculty (academic staff), the academic staff of a university (North American usage) * Faculty (division), a division within a university (usage outside of the United States) * Faculty (instrument), an instrument or warrant in canon law, especially a judicial or quasi-judicial warrant from an ecclesiastical court or tribunal * Faculty (company), a British artificial intelligence company * Aspects of intelligence ("cognitive faculties") * Senses of sight, hearing, touch, etc. ("perceptive faculties") * ''The Faculty ''The Faculty'' is a 1998 American science fiction horror film directed by Robert Rodriguez and written by Kevin Williamson. It stars Jordana Brewster, Clea DuVall, Laura Harris, Josh Hartnett, Shawn Hatosy, Famke Janssen, Piper Laurie, ...'', a 1998 horror/sci-fi movie by Robert Rodriguez * ''The Faculty'' (TV series), a 1996 American sitcom * The rights of a priest to celebrate or perform various liturgical functions {{disa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic Church monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word ''universitas'' (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hild ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 (Roman numerals, I) through AD 100 (Roman numerals, C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or History by period, historical period. The 1st century also saw the Christianity in the 1st century, appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1961 Births
Events January * January 3 ** United States President Dwight D. Eisenhower announces that the United States has severed diplomatic and consular relations with Cuba (Cuba–United States relations are restored in 2015). ** Aero Flight 311 (Koivulahti air disaster): Douglas DC-3C OH-LCC of Finnish airline Aero crashes near Kvevlax (Koivulahti), on approach to Vaasa Airport in Finland, killing all 25 on board, due to pilot error: an investigation finds that the captain and first officer were both exhausted for lack of sleep, and had consumed excessive amounts of alcohol at the time of the crash. It remains the deadliest air disaster to occur in the country. * January 5 ** Italian sculptor Alfredo Fioravanti marches into the U.S. Consulate in Rome, and confesses that he was part of the team that forged the Etruscan terracotta warriors in the Metropolitan Museum of Art. ** After the 1960 military coup, General Cemal Gürsel forms the new government of Turkey (25th gov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Coding
In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may be used to improve a network's throughput, efficiency, and scalability, as well as reducing attacks and eavesdropping. The nodes of a network take ''several'' packets and combine for transmission. This process may be used to attain the maximum possible information flow in a network. It has been proven that, theoretically, linear coding is enough to achieve the upper bound in multicast problems with one source. However linear coding is not sufficient in general; even for more general versions of linearity such as convolutional coding and filter-bank coding. Finding optimal coding solutions for general network problems with arbitrary demands remains an open problem. Encoding and decoding In a linear network coding problem, a group of nodes P are involved in moving the data from S sou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chris Freiling
Christopher Francis Freiling is a mathematician responsible for Freiling's axiom of symmetry in set theory. He has also made significant contributions to coding theory, in the process establishing connections between that field and matroid theory. Freiling obtained his Ph.D. in 1981 from the University of California, Los Angeles under the supervision of Donald A. Martin Donald Anthony Martin (born December 24, 1940), also known as Tony Martin, is an American set theorist and philosopher of mathematics at UCLA, where he is an emeritus professor of mathematics and philosophy. Education and career Martin rece .... He is a member of the faculty of the Department of Mathematics at California State University, San Bernardino. CSUSB Mathematics Department, retrieved 2015-04-11. Select ...
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Edward Marczewski
Edward Marczewski (15 November 1907 – 17 October 1976) was a Polish mathematician. He was born Szpilrajn but changed his name while hiding from Nazi persecution. Marczewski was a member of the Warsaw School of Mathematics. His life and work after the Second World War were connected with Wrocław, where he was among the creators of the Polish scientific centre. Marczewski's main fields of interest were measure theory, descriptive set theory, general topology, probability theory and universal algebra. He also published papers on real and complex analysis, applied mathematics and mathematical logic. Marczewski proved that the topological dimension, for arbitrary metrisable separable space ''X'', coincides with the Hausdorff dimension under one of the metrics in ''X'' which induce the given topology of ''X'' (while otherwise the Hausdorff dimension is always greater or equal to the topological dimension). This is a fundamental theorem of fractal theory. (Certain contributions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baire Property
A subset A of a topological space X has the property of Baire (Baire property, named after René-Louis Baire), or is called an almost open set, if it differs from an open set by a meager set; that is, if there is an open set U\subseteq X such that A \bigtriangleup U is meager (where \bigtriangleup denotes the symmetric difference).. Definitions A subset A \subseteq X of a topological space X is called almost open and is said to have the property of Baire or the Baire property if there is an open set U\subseteq X such that A \bigtriangleup U is a meager subset, where \bigtriangleup denotes the symmetric difference. Further, A has the Baire property in the restricted sense if for every subset E of X the intersection A\cap E has the Baire property relative to E. Properties The family of sets with the property of Baire forms a σ-algebra. That is, the complement of an almost open set is almost open, and any countable union or intersection of almost open sets is again alm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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