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William T. Trotter
William Thomas Trotter Jr. is an American mathematician, who is on the faculty of the Department of Mathematics at the Georgia Institute of Technology. His main expertise is partially ordered sets, but he has also done significant work in other areas of combinatorics, such as the Szemerédi–Trotter theorem The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given points and lines in the Euclidean plane, the number of incidences (''i.e.'', the number of point-line pairs, such that the point ... and Chvátal-Rödl-Szemerédi-Trotter theorem. Trotter is the author of the book ''Combinatorics and partially ordered sets: dimension theory'' (Johns Hopkins University Press, 1992). With Mitchel Keller, he is also the author of a self-published textbook, ''Applied Combinatorics'' (2017). References External linksWilliam T. (Tom) Trotter Living people 20th-century American mathematicians 21st-century American mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georgia Institute Of Technology
The Georgia Institute of Technology, commonly referred to as Georgia Tech or, in the state of Georgia, as Tech or The Institute, is a public research university and institute of technology in Atlanta, Georgia. Established in 1885, it is part of the University System of Georgia and has satellite campuses in Savannah, Georgia; Metz, France; Shenzhen, China; and Singapore. The school was founded as the Georgia School of Technology as part of Reconstruction plans to build an industrial economy in the post-Civil War Southern United States. Initially, it offered only a degree in mechanical engineering. By 1901, its curriculum had expanded to include electrical, civil, and chemical engineering. In 1948, the school changed its name to reflect its evolution from a trade school to a larger and more capable technical institute and research university. Today, Georgia Tech is organized into six colleges and contains about 31 departments/units, with emphasis on science and technology. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Ordered Set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a Set (mathematics), set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word ''partial'' in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable. Informal definition A partial order defines a notion of Comparability, comparison. Two elements ''x'' and ''y'' may stand in any of four mutually exclusive relationships to each other: either ''x'' ''y'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Szemerédi–Trotter Theorem
The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given points and lines in the Euclidean plane, the number of incidences (''i.e.'', the number of point-line pairs, such that the point lies on the line) is O \left ( n^ m^ + n + m \right ). This bound cannot be improved, except in terms of the implicit constants. As for the implicit constants, it was shown by János Pach, Radoš Radoičić, Gábor Tardos, and Géza Tóth that the upper bound 2.5n^ m^ + n + m holds. Since then better constants are known due to better crossing lemma constants; the current best is 2.44. On the other hand, Pach and Tóth showed that the statement does not hold true if one replaces the coefficient 2.5 with 0.42. An equivalent formulation of the theorem is the following. Given points and an integer , the number of lines which pass through at least of the points is O \left( \frac + \frac \right ). The original proof of Endre Szemeréd ... [...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] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( 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 historical period. The 1st century also saw the 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 instability, which was finally brought to an end by Vespasian, ninth Roman empero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georgia Tech Faculty
Georgia most commonly refers to: * Georgia (country), a country in the Caucasus region of Eurasia * Georgia (U.S. state), a state in the Southeast United States Georgia may also refer to: Places Historical states and entities * Related to the country in the Caucasus ** Kingdom of Georgia, a medieval kingdom ** Georgia within the Russian Empire ** Democratic Republic of Georgia, established following the Russian Revolution ** Georgian Soviet Socialist Republic, a constituent of the Soviet Union * Related to the US state ** Province of Georgia, one of the thirteen American colonies established by Great Britain in what became the United States ** Georgia in the American Civil War, the State of Georgia within the Confederate States of America. Other places * 359 Georgia, an asteroid * New Georgia, Solomon Islands * South Georgia and the South Sandwich Islands Canada * Georgia Street, in Vancouver, British Columbia, Canada * Strait of Georgia, British Columbia, Canada United K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
