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William Burnside
:''This English mathematician is sometimes confused with the Irish mathematician William S. Burnside (1839–1920).'' __NOTOC__ William Burnside (2 July 1852 – 21 August 1927) was an English mathematician. He is known mostly as an early researcher in the theory of finite groups. Burnside was born in London in 1852. He went to school at Christ's Hospital until 1871 and attended St. John's and Pembroke Colleges at the University of Cambridge, where he was the Second Wrangler (bracketed with George Chrystal) in 1875. He lectured at Cambridge for the following ten years, before being appointed professor of mathematics at the Royal Naval College in Greenwich. While this was a little outside the main centres of British mathematical research, Burnside remained a very active researcher, publishing more than 150 papers in his career. Burnside's early research was in applied mathematics. This work was of sufficient distinction to merit his election as a fellow of the Royal Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William S
William is a male given name of Germanic origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of England in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will, Wills, Willy, Willie, Bill, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie or the play ''Douglas''). Female forms are Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the given name ''Wilhelm'' (cf. Proto-Germanic ᚹᛁᛚᛃᚨᚺᛖᛚᛗᚨᛉ, ''*Wiljahelmaz'' > German ''Wilhelm'' and Old Norse ᚢᛁᛚᛋᛅᚼᛅᛚᛘᛅᛋ, ''Vilhjálmr''). By regular sound changes, the native, inherited English form of the name shoul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christ's Hospital
Christ's Hospital is a public school (English independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The school was founded in 1552 and received its first royal charter in 1553. Since its establishment, Christ's Hospital has been a charity school, with a core aim to offer children from humble backgrounds the chance of a better education. Charitable foundation Christ's Hospital is unusual among British independent schools in that the majority of the students receive bursaries. This stems from its founding charter as a charitable school. School fees are paid on a means-tested basis, with substantial subsidies paid by the school or their benefactors, so that pupils from all walks of life are able to have private education that would otherwise be beyond the means of their parents. The trustees of the foundation are the Council of Almoners, chaired by the Treasurer of Christ's Hospital, who govern the foundation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Character Theory
In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on the characters, and without any explicit matrix realization of representations themselves. This is possible because a complex representation of a finite group is determined (up to isomorphism) by its character. The situation with representations over a field of positive characteristic, so-called "modular representations", is more delicate, but Richard Brauer developed a powerful theory of characters in this case as well. Many deep theorems on the structure of finite groups use characters of modular representations. Applications Characters of irreducible representations encode many important propert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solvable Group
In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. Motivation Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equation. Specifically, a polynomial equation is solvable in radicals if and only if the corresponding Galois group is solvable (note this theorem holds only in characteristic 0). This means associated to a polynomial f \in F /math> there is a tower of field extensionsF = F_0 \subseteq F_1 \subseteq F_2 \subseteq \cdots \subseteq F_m=Ksuch that # F_i = F_ alpha_i/math> where \alpha_i^ \in F_, so \alpha_i is a solution to the equation x^ - a where a \in F_ # F_m contains a splitting field for f(x) Example For example, the smallest Galois field extension of \mathbb containing the elemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burnside's Theorem
In mathematics, Burnside's theorem in group theory states that if ''G'' is a finite group of order p^a q^b where ''p'' and ''q'' are prime numbers, and ''a'' and ''b'' are non-negative integers, then ''G'' is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct primes. History The theorem was proved by using the representation theory of finite groups. Several special cases of the theorem had previously been proved by Burnside, Jordan, and Frobenius. John Thompson pointed out that a proof avoiding the use of representation theory could be extracted from his work on the N-group theorem, and this was done explicitly by for groups of odd order, and by for groups of even order. simplified the proofs. Proof The following proof — using more background than Burnside's — is by contradiction. Let ''paqb'' be the smallest product of two prime powers, such that there is a non-solvable group ''G'' whose order is equal to this number. :* ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferdinand Georg Frobenius
Ferdinand Georg Frobenius (26 October 1849 – 3 August 1917) was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms. He was also the first to introduce the notion of rational approximations of functions (nowadays known as Padé approximants), and gave the first full proof for the Cayley–Hamilton theorem. He also lent his name to certain differential-geometric objects in modern mathematical physics, known as Frobenius manifolds. Biography Ferdinand Georg Frobenius was born on 26 October 1849 in Charlottenburg, a suburb of Berlin from parents Christian Ferdinand Frobenius, a Protestant parson, and Christine Elizabeth Friedrich. He entered the Joachimsthal Gymnasium in 1860 when he was nearly eleven. ... [...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] |
Great Britain
Great Britain is an island in the North Atlantic Ocean off the northwest coast of continental Europe. With an area of , it is the largest of the British Isles, the largest European island and the ninth-largest island in the world. It is dominated by a maritime climate with narrow temperature differences between seasons. The 60% smaller island of Ireland is to the west—these islands, along with over 1,000 smaller surrounding islands and named substantial rocks, form the British Isles archipelago. Connected to mainland Europe until 9,000 years ago by a landbridge now known as Doggerland, Great Britain has been inhabited by modern humans for around 30,000 years. In 2011, it had a population of about , making it the world's third-most-populous island after Java in Indonesia and Honshu in Japan. The term "Great Britain" is often used to refer to England, Scotland and Wales, including their component adjoining islands. Great Britain and Northern Ireland now constitute the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, education and public engagement and fostering international and global co-operation. Founded on 28 November 1660, it was granted a royal charter by King Charles II as The Royal Society and is the oldest continuously existing scientific academy in the world. The society is governed by its Council, which is chaired by the Society's President, according to a set of statutes and standing orders. The members of Council and the President are elected from and by its Fellows, the basic members of the society, who are themselves elected by existing Fellows. , there are about 1,700 fellows, allowed to use the postnominal title FRS (Fellow of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greenwich
Greenwich ( , ,) is a town in south-east London, England, within the ceremonial county of Greater London. It is situated east-southeast of Charing Cross. Greenwich is notable for its maritime history and for giving its name to the Greenwich Meridian (0° longitude) and Greenwich Mean Time. The town became the site of a royal palace, the Palace of Placentia from the 15th century, and was the birthplace of many Tudors, including Henry VIII and Elizabeth I. The palace fell into disrepair during the English Civil War and was demolished to be replaced by the Royal Naval Hospital for Sailors, designed by Sir Christopher Wren and his assistant Nicholas Hawksmoor. These buildings became the Royal Naval College in 1873, and they remained a military education establishment until 1998 when they passed into the hands of the Greenwich Foundation. The historic rooms within these buildings remain open to the public; other buildings are used by University of Greenwich and Trinity Laban C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Naval College, Greenwich
The Royal Naval College, Greenwich, was a Royal Navy training establishment between 1873 and 1998, providing courses for naval officers. It was the home of the Royal Navy's staff college, which provided advanced training for officers. The equivalent in the British Army was the Staff College, Camberley, and the equivalent in the Royal Air Force was the RAF Staff College, Bracknell. History The Royal Naval College, Greenwich, was founded by an Order in Council dated 16 January 1873. The establishment of its officers consisted of a President, who was always a Flag Officer; a Captain, Royal Navy; a Director of Studies; and Professors of Mathematics, Physical Science, Chemistry, Applied Mechanics, and Fortification. It was to take in officers who were already Sub-Lieutenants and to operate as "the university of the Navy". The Director of Studies, a civilian, was in charge of an Academic Board, while the Captain of the College was a naval officer who acted as chief of staff. The Roy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
