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Thoralf Skolem
Thoralf Albert Skolem (; 23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic and set theory. Life Although Skolem's father was a primary school teacher, most of his extended family were farmers. Skolem attended secondary school in Kristiania (later renamed Oslo), passing the university entrance examinations in 1905. He then entered Det Kongelige Frederiks Universitet to study mathematics, also taking courses in physics, chemistry, zoology and botany. In 1909, he began working as an assistant to the physicist Kristian Birkeland, known for bombarding magnetized spheres with electrons and obtaining aurora-like effects; thus Skolem's first publications were physics papers written jointly with Birkeland. In 1913, Skolem passed the state examinations with distinction, and completed a dissertation titled ''Investigations on the Algebra of Logic''. He also traveled with Birkeland to the Sudan to observe the zodiacal light. He spent the winter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sandsvær
Sandsvær is a area in Kongsberg, Viken county, Norway. The area is identical to the former municipality in Buskerud county named Sandsvær. Sandsvær is situated in the valley of Lågendalen on the Numedalslågen river, and is bordered by Kongsberg town in the north, and the county border to Vestfold og Telemark county in the south. Historically, Sandsvær as a part of ''Sandsvær og Numedal fogderi'' had belonged to Akershus ''amt'' from 7 February 1685 In 1760 ''Sandsvær fogderi'' was moved administratively to Buskerud. The municipality was created as Kongsberg landdistrikt in 1837. The municipality existed until 1 January 1908, when it was split to form the new municipalities Ytre Sandsvær and Øvre Sandsvær. Prior to the split Sandsvær had a population of 5,709. Both municipalities were later incorporated into Kongsberg. The name The Old Norse form of the name was ''Sandshverfi''. The first element is the genitive case of ''sandr'' m 'sand Sand is a granular materia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kristian Birkeland
Kristian Olaf Bernhard Birkeland (13 December 1867 – 15 June 1917) was a Norwegian scientist. He is best remembered for his theories of atmospheric electric currents that elucidated the nature of the aurora borealis. In order to fund his research on the aurorae, he invented the electromagnetic cannon and the Birkeland–Eyde process of fixing nitrogen from the air. Birkeland was nominated for the Nobel Prize seven times. Life and death Birkeland was born in Christiania (Oslo today) to Reinart Birkeland and Ingeborg (née Ege) and wrote his first scientific paper at the age of 18. Birkeland married Ida Charlotte Hammer in May 1905. They had no children and, due to Birkeland's preoccupation with his work, they divorced in 1911. Suffering from severe paranoia due to his use of barbital as a sleeping aid, he died under mysterious circumstances in his room in the Hotel Seiyoken in Tokyo while visiting colleagues at the University of Tokyo. A post-mortem revealed that Birkeland had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Theory
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These ''lattice-like'' structures all admit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Equations
In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one. An exponential Diophantine equation is one in which unknowns can appear in exponents. Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves, algebraic surfaces, or, more generally, algebraic sets, their study is a part of algebraic geometry that is called ''Diophantine geometry''. The word ''Diophantine'' refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra. The mathematical study of Diophantine problems that Di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bergen
Bergen (), historically Bjørgvin, is a city and municipality in Vestland county on the west coast of Norway. , its population is roughly 285,900. Bergen is the second-largest city in Norway. The municipality covers and is on the peninsula of Bergenshalvøyen. The city centre and northern neighbourhoods are on Byfjorden, 'the city fjord', and the city is surrounded by mountains; Bergen is known as the "city of seven mountains". Many of the extra-municipal suburbs are on islands. Bergen is the administrative centre of Vestland county. The city consists of eight boroughs: Arna, Bergenhus, Fana, Fyllingsdalen, Laksevåg, Ytrebygda, Årstad, and Åsane. Trading in Bergen may have started as early as the 1020s. According to tradition, the city was founded in 1070 by King Olav Kyrre and was named Bjørgvin, 'the green meadow among the mountains'. It served as Norway's capital in the 13th century, and from the end of the 13th century became a bureau city of the Hanseatic Leag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bergen, Norway
Bergen (), historically Bjørgvin, is a city and municipalities of Norway, municipality in Vestland county on the Western Norway, west coast of Norway. , its population is roughly 285,900. Bergen is the list of towns and cities in Norway, second-largest city in Norway. The municipality covers and is on the peninsula of Bergenshalvøyen. The city centre and northern neighbourhoods are on Byfjorden (Hordaland), Byfjorden, 'the city fjord', and the city is surrounded by mountains; Bergen is known as the "city of Seven Mountains, Bergen, seven mountains". Many of the extra-municipal suburbs are on islands. Bergen is the administrative centre of Vestland county. The city consists of eight boroughs: Arna, Norway, Arna, Bergenhus, Fana, Fyllingsdalen, Laksevåg, Ytrebygda, Årstad, Bergen, Årstad, and Åsane. Trading in Bergen may have started as early as the 1020s. According to tradition, the city was founded in 1070 by King Olaf III of Norway, Olav Kyrre and was named Bjørgvin, ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Oslo
The University of Oslo ( no, Universitetet i Oslo; la, Universitas Osloensis) is a public research university located in Oslo, Norway. It is the highest ranked and oldest university in Norway. It is consistently ranked among the top universities in the world and as one of the leading universities of Northern Europe; the Academic Ranking of World Universities ranked it the 58th best university in the world and the third best in the Nordic countries. In 2016, the Times Higher Education World University Rankings listed the university at 63rd, making it the highest ranked Norwegian university. Originally named the Royal Frederick University, the university was established in 1811 as the de facto Norwegian continuation of Denmark-Norway's common university, the University of Copenhagen, with which it shares many traditions. It was named for King Frederick VI of Denmark and Norway, and received its current name in 1939. The university was commonly nicknamed "The Royal Frederick ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norwegian Academy Of Science And Letters
The Norwegian Academy of Science and Letters ( no, Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway. History The Royal Frederick University in Christiania was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841. The city of Trondhjem had no university, but had a learned society, the Royal Norwegian Society of Sciences and Letters, established in 1760. The purpose of a learned society in Christiania was to support scientific studies and aid publication of academic papers. The idea of the Humboldt-inspired university, where independent research stood strong, had taken over for the instrumental view of a university as a means to produce civil servants. The city already had societies for specific professions, for instance the Norwegian Medical Society which was founded in 1833. However, these societies were open for both acad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra meant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metamathematics
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics. History Metamathematical metatheorems about mathematics itself were originally differentiated from ordinary mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded in 1734 by George II, King of Great Britain and Elector of Hanover, and starting classes in 1737, the Georgia Augusta was conceived to promote the ideals of the Enlightenment. It is the oldest university in the state of Lower Saxony and the largest in student enrollment, which stands at around 31,600. Home to many noted figures, it represents one of Germany's historic and traditional institutions. According to an official exhibition held by the University of Göttingen in 2002, 44 Nobel Prize winners had been affiliated with the University of Göttingen as alumni, faculty members or researchers by that year alone. The University of Göttingen was previously supported by the German Universities Excellence Initiative, holds memberships ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
