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Hans Frederick Blichfeldt
Hans Frederick Blichfeldt (1873–1945) was a Danish-American mathematician at Stanford University, known for his contributions to group theory, the representation theory of finite groups, the geometry of numbers, sphere packing, and quadratic forms. He is the namesake of Blichfeldt's theorem. Life Blichfeldt was one of five children of a Danish farming couple, Erhard Christoffer Laurentius Blichfeldt and Nielsine Maria Schlaper; many of his father's ancestors were ministers. He was born on January 9, 1873 in Iller, a village in the Sønderborg Municipality of Denmark. In 1881, the family moved to Copenhagen. In 1888, he passed with high honors the entrance examinations for the University of Copenhagen, but his family was unable to afford sending him to the university. Instead, later the same year, they moved again to the US. He worked for several years as a lumberman, a railway worker, a traveling surveyor, and then as a government draftsman in Bellingham, Washington. In 189 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kogbetliantz Cinquini Szasz Blichfeldt Tzitzeica Tyler Papaioannou Kiepert Zurich1932
Ervand George Kogbetliantz ( hy, Երվանդ Գևորգի Կողբետլյանց; February 22, 1888 in Rostov-on-the-Don – 1974 in Paris, France) was an Armenian-American mathematician and the first president of the Yerevan State University. He left Russia in 1918. He received a Doctorate in mathematics from the University of Paris in 1923. His mathematical work was mainly on infinite series, on the theory of orthogonal polynomials, on an algorithm for singular value decomposition which bears his name, on algorithms for the evaluation of elementary functions in computers, and on the enumeration of prime elements of the Gaussian integers. He also invented a three-dimensional version of chess, and was working at his death with Bobby Fischer on a game of chess for three people. When he first went to America (1941), he taught Mathematics at Lehigh University. In the early 1950s, he was a consultant for IBM in New York City and taught at Columbia University. Prior to moving bac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the best universities in the world and it is among the most selective in the United States. The university is composed of an undergraduate college and five graduate research divisions, which contain all of the university's graduate programs and interdisciplinary committees. Chicago has eight professional schools: the Law School, the Booth School of Business, the Pritzker School of Medicine, the Crown Family School of Social Work, Policy, and Practice, the Harris School of Public Policy, the Divinity School, the Graham School of Continuing Liberal and Professional Studies, and the Pritzker School of Molecular Engineering. The university has additional campuses and centers in London, Paris, Beijing, Delhi, and Hong Kong, as well as in downtown ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules. Representations of groups are important because they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well understood. They are also important in physics because, for example, they describe how the symmetry group of a physical system affects the solutions of equations describing that system. The term ''representation of a group'' is also used in a more general sense to mean any "description" of a group as a group of transformations of some mathematical o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Map
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a Map (mathematics), mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of module (mathematics), modules over a ring (mathematics), ring; see Module homomorphism. If a linear map is a bijection then it is called a . In the case where V = W, a linear map is called a (linear) ''endomorphism''. Sometimes the term refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are Real number, real vector spaces (not necessarily with V = W), or it can be used to emphasize that V is a function space, which is a common convention in functional analysis. Some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Group
In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship to the polynomials that give rise to them via Galois groups is called Galois theory, so named in honor of Évariste Galois who first discovered them. For a more elementary discussion of Galois groups in terms of permutation groups, see the article on Galois theory. Definition Suppose that E is an extension of the field F (written as E/F and read "''E'' over ''F'' "). An automorphism of E/F is defined to be an automorphism of E that fixes F pointwise. In other words, an automorphism of E/F is an isomorphism \alpha:E\to E such that \alpha(x) = x for each x\in F. The set of all automorphisms of E/F forms a group with the operation of function composition. This group is sometimes denoted by \operatorname(E/F). If E/F is a Galois extension, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Group
Finite is the opposite of infinite. It may refer to: * Finite number (other) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked for person and/or tense or aspect * "Finite", a song by Sara Groves from the album '' Invisible Empires'' See also * * Nonfinite (other) Nonfinite is the opposite of finite * a nonfinite verb is a verb that is not capable of serving as the main verb in an independent clause * a non-finite clause In linguistics, a non-finite clause is a dependent or embedded clause that represen ... {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard Eugene Dickson
Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, ''History of the Theory of Numbers''. Life Dickson considered himself a Texan by virtue of having grown up in Cleburne, where his father was a banker, merchant, and real estate investor. He attended the University of Texas at Austin, where George Bruce Halsted encouraged his study of mathematics. Dickson earned a B.S. in 1893 and an M.S. in 1894, under Halsted's supervision. Dickson first specialised in Halsted's own specialty, geometry.A. A. Albert (1955Leonard Eugene Dickson 1874–1954from National Academy of Sciences Both the University of Chicago and Harvard University welcomed Dickson as a Ph.D. student, and Dickson initially accepted Harvard's offer, but chose to attend Chicago in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Abram Miller
George Abram Miller (31 July 1863 – 10 February 1951) was an early group theorist. At age 17 Miller began school-teaching to raise funds for higher education. In 1882 he entered Franklin and Marshall Academy, and progressed to Muhlenberg College in 1884. He received his B.A. in 1887 and M.A. in 1890. While a graduate student, Miller was Principal of schools in Greeley, Kansas and then professor of mathematics as Eureka College in Eureka, Illinois. He corresponded with Cumberland University in Lebanon, Tennessee for his Ph.D. in 1892. He then joined Frank Nelson Cole at University of Michigan and began to study groups. In 1895 he went to Europe where he heard Sophus Lie lecture at Leipzig and Camille Jordan at Paris. In 1897 he went to Cornell University as an assistant professor, and in 1901 to Stanford University as associate professor. In 1906 he went to University of Illinois where he taught until retirement in 1931. Henry Roy Brahana (1957) Miller helped in the enumerat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Group
In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to itself). The group of ''all'' permutations of a set ''M'' is the symmetric group of ''M'', often written as Sym(''M''). The term ''permutation group'' thus means a subgroup of the symmetric group. If then Sym(''M'') is usually denoted by S''n'', and may be called the ''symmetric group on n letters''. By Cayley's theorem, every group is isomorphic to some permutation group. The way in which the elements of a permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry. Basic properties and terminology Being a subgroup of a symmetric group, all that is necessary for a set of permutatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan–Schur Theorem
In mathematics, the Jordan–Schur theorem also known as Jordan's theorem on finite linear groups is a theorem in its original form due to Camille Jordan. In that form, it states that there is a function ''ƒ''(''n'') such that given a finite subgroup ''G'' of the group of invertible ''n''-by-''n'' complex matrices, there is a subgroup ''H'' of ''G'' with the following properties: * ''H'' is abelian. * ''H'' is a normal subgroup of ''G''. * The index of ''H'' in ''G'' satisfies (''G'' : ''H'') ≤ ''ƒ''(''n''). Schur proved a more general result that applies when ''G'' is not assumed to be finite, but just periodic. Schur showed that ''ƒ''(''n'') may be taken to be :((8''n'')1/2 + 1)2''n''2 − ((8''n'')1/2 − 1)2''n''2. A tighter bound (for ''n'' ≥ 3) is due to Speiser, who showed that as long as ''G'' is finite, one can take :''ƒ''(''n'') = ''n''! 12''n''(''π''(''n''+1)+1) where ''π''(''n'') is the prime-countin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heronian Triangle
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths , , and and area are all integers. Heronian triangles are named after Heron of Alexandria, based on their relation to Heron's formula. Heron's formula implies that the Heronian triangles are exactly the positive integer solutions of the Diophantine equation :16\,A^2=(a+b+c)(a+b-c)(b+c-a)(c+a-b); that is, the side lengths and area of any Heronian triangle satisfy the equation, and any positive integer solution of the equation describes a Heronian triangle. If the three side lengths are setwise coprime, the Heronian triangle is called ''primitive''. Triangles whose side lengths and areas are all rational numbers (positive rational solutions of the above equation) are sometimes also called ''Heronian triangles'' or rational triangles; in this article, these more general triangles will be called ''rational Heronian triangles''. Every (integral) Heronian triangle is a rational Heronian triangle. Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palo Alto, California
Palo Alto (; Spanish language, Spanish for "tall stick") is a charter city in the northwestern corner of Santa Clara County, California, United States, in the San Francisco Bay Area, named after a Sequoia sempervirens, coastal redwood tree known as El Palo Alto. The city was established in 1894 by the American industrialist Leland Stanford when he founded Stanford University in memory of his son, Leland Stanford Jr. Palo Alto includes portions of Stanford University and borders East Palo Alto, California, East Palo Alto, Mountain View, California, Mountain View, Los Altos, California, Los Altos, Los Altos Hills, California, Los Altos Hills, Stanford, California, Stanford, Portola Valley, California, Portola Valley, and Menlo Park, California, Menlo Park. At the 2010 United States Census, 2020 census, the population was 68,572. Palo Alto is one of the most expensive cities in the United States in which to live, and its residents are among the most educated in the country. Howeve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
