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Rudolf Lipschitz
Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German mathematician who made contributions to mathematical analysis (where he gave his name to the Lipschitz continuity condition) and differential geometry, as well as number theory, algebras with involution and classical mechanics. Biography Rudolf Lipschitz was born on 14 May 1832 in Königsberg. He was the son of a landowner and was raised at his father's estate at Bönkein which was near Königsberg. He entered the University of Königsberg when he was 15, but later moved to the University of Berlin where he studied with Gustav Dirichlet. Despite having his studies delayed by illness, in 1853 Lipschitz graduated with a PhD in Berlin. After receiving his PhD, Lipschitz started teaching at local Gymnasiums. In 1857 he married Ida Pascha, the daughter of one of the landowners with an estate near to his father's. In 1857 he earned his habilitation at the University of Bonn and remained there as a privatdoze ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Königsberg
Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named in honour of King Ottokar II of Bohemia. A Baltic port city, it successively became the capital of the Królewiec Voivodeship, the State of the Teutonic Order, the Duchy of Prussia and the provinces of East Prussia and Prussia. Königsberg remained the coronation city of the Prussian monarchy, though the capital was moved to Berlin in 1701. Between the thirteenth and the twentieth centuries, the inhabitants spoke predominantly German, but the multicultural city also had a profound influence upon the Lithuanian and Polish cultures. The city was a publishing center of Lutheran literature, including the first Polish translation of the New Testament, printed in the city in 1551, the first book in Lithuanian and the first Lutheran catechism, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra Over A Field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear". The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras and non-associative algebras. Given an integer ''n'', the ring of real square matrices of order ''n'' is an example of an associative algebra over the field of real numbers under matrix addition and matrix multiplication since matrix multiplication is associative. Three-dimensional Euclidean space with multiplication given by the vector cross product is an example of a nonassociative algebra over the field of real numbers since the vector cross product is nonassociative, satisfying the Jacobi identity i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Group
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford. The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (''pseudo-'')''Riemannian Clifford algebras'', as distinct from ''symplectic Clifford algebras''.see for ex. Introduction and basic properties A Clifford algebra is a unital associative algebra that contains and is generated by a vector space over a field , where is equipped with a quadratic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Chevalley
Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group. Life His father, Abel Chevalley, was a French diplomat who, jointly with his wife Marguerite Chevalley née Sabatier, wrote ''The Concise Oxford French Dictionary''. Chevalley graduated from the École Normale Supérieure in 1929, where he studied under Émile Picard. He then spent time at the University of Hamburg, studying under Emil Artin and at the University of Marburg, studying under Helmut Hasse. In Germany, Chevalley discovered Japanese mathematics in the person of Shokichi Iyanaga. Chevalley was awarded a doctorate in 1933 from the University of Paris for a thesis on class field theory. When World War II broke out, Chevalley was at Princeton University. After reporting to the French Embassy, h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Transformation
In linear algebra, an orthogonal transformation is a linear transformation ''T'' : ''V'' → ''V'' on a real inner product space ''V'', that preserves the inner product. That is, for each pair of elements of ''V'', we have : \langle u,v \rangle = \langle Tu,Tv \rangle \, . Since the lengths of vectors and the angles between them are defined through the inner product, orthogonal transformations preserve lengths of vectors and angles between them. In particular, orthogonal transformations map orthonormal bases to orthonormal bases. Orthogonal transformations are injective: if Tv = 0 then 0 = \langle Tv,Tv \rangle = \langle v,v \rangle, hence v = 0, so the kernel of T is trivial. Orthogonal transformations in two- or three- dimensional Euclidean space are stiff rotations, reflections, or combinations of a rotation and a reflection (also known as improper rotations). Reflections are transformations that reverse the direction front to back, orthogonal to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William K
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 should b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Algebra
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford. The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (''pseudo-'')''Riemannian Clifford algebras'', as distinct from ''symplectic Clifford algebras''.see for ex. Introduction and basic properties A Clifford algebra is a unital associative algebra that contains and is generated by a vector space over a field , where is equipped with a qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Breslau
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Privatdozent
''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifications that denote an ability (''facultas docendi'') and permission to teach (''venia legendi'') a designated subject at the highest level. To be granted the title Priv.-Doz. by a university, a recipient has to fulfill the criteria set by the university which usually require excellence in research, teaching, and further education. In its current usage, the title indicates that the holder has completed their habilitation and is therefore granted permission to teach and examine students independently without having a professorship. Conferment and roles A university faculty can confer the title to an academic who has a higher doctoral degree - usually in the form of a habilitation. The title, ''Privatdozent'', as such does not imply a sala ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a dissertation. The degree, abbreviated "Dr. habil." (Doctor habilitatus) or "PD" (for "Privatdozent"), is a qualification for professorship in those countries. The conferral is usually accompanied by a lecture to a colloquium as well as a public inaugural lecture. History and etymology The term ''habilitation'' is derived from the Medieval Latin , meaning "to make suitable, to fit", from Classical Latin "fit, proper, skillful". The degree developed in Germany in the seventeenth century (). Initially, habilitation was synonymous with "doctoral qualification". The term became synonymous with "post-doctoral qualification" in Germany in the 19th century "when holding a doctorate seemed no longer sufficient to guarantee a proficient transfer o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gymnasium (Germany)
''Gymnasium'' (; German plural: ''Gymnasien''), in the German education system, is the most advanced and highest of the three types of German secondary schools, the others being ''Hauptschule'' (lowest) and ''Realschule'' (middle). ''Gymnasium'' strongly emphasizes academic learning, comparable to the British sixth form system or with prep schools in the United States. A student attending ''Gymnasium'' is called a ''Gymnasiast'' (German plural: ''Gymnasiasten''). In 2009/10 there were 3,094 gymnasia in Germany, with students (about 28 percent of all precollegiate students during that period), resulting in an average student number of 800 students per school.Federal Statistical office of Germany, Fachserie 11, Reihe 1: Allgemeinbildende Schulen – Schuljahr 2009/2010, Wiesbaden 2010 Gymnasia are generally public, state-funded schools, but a number of parochial and private gymnasia also exist. In 2009/10, 11.1 percent of gymnasium students attended a private gymnasium. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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