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Albrecht Pfister (mathematician)
Albrecht Pfister (born July 30, 1934) is a German mathematician specializing in algebra and in particular quadratic forms. Pfister received his doctoral degree in 1961 at the Ludwig Maximilian University of Munich. The title of his doctoral thesis was ''Über das Koeffizientenproblem der beschränkten Funktionen von zwei Veränderlichen'' ("On the coefficient problem of the bounded functions of two variables"). His thesis advisors were Martin Kneser and Karl Stein. In 1966 he received his habilitation at the Georg August University of Göttingen. From 1970 until his retirement he was professor at the Johannes Gutenberg University of Mainz. In the theory of quadratic forms over fields, the Pfister forms that he introduced in 1965 bear his name. In 1970, he was an invited speaker on the topic ''Sums of squares in real function fields'' at the International Congress of Mathematicians in Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to a fixed field , such as the real or complex numbers, and one speaks of a quadratic form over . If K=\mathbb R, and the quadratic form takes zero only when all variables are simultaneously zero, then it is a definite quadratic form, otherwise it is an isotropic quadratic form. Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry ( Riemannian metric, second fundamental form), differential topology ( intersection forms of four-manifolds), and Lie theory (the Killing form). Quadratic forms are not to be confused with a quadratic equation, which has only one variable and includes terms of degree two or less. A quadra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variable (mathematics), variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in mathematical education, education, to the study of algebraic structures such as group (mathematics), groups, ring (mathematics), rings, and field (mathematics), fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albrecht Pfister
Albrecht Pfister (c. 1420 – c. 1466) was one of the first European printers to use movable type, following its invention by Johannes Gutenberg. Working in Bamberg, Germany, he is believed to have been responsible for two innovations in the use of the new technology: printing books in the German language, and adding woodcuts to printed books. The typefaces of Pfister, although similar to Gutenberg's, have their own peculiarities. Very little is known of his life. He is known to have been a cleric in Bamberg in 1448, and to have been connected with Georg I von Schaumberg at that time. By 1460 he was acting as secretary to von Schaumberg, who in 1459 had become prince-bishop of Bamberg. Nine editions are generally ascribed to him. All are believed to date to the 1460s, and possibly all to the early 1460s. These are (not in chronological order): * two editions of the popular religious work ''Der Ackermann aus Böhmen'' in German * two editions of Ulrich Boner's ''Der Edelstei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Maximilian University Of Munich
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: link=no, Ludwig-Maximilians-Universität München) is a public research university in Munich, Bavaria, Germany. Originally established as the University of Ingolstadt in 1472 by Duke Ludwig IX of Bavaria-Landshut, it is Germany's sixth-oldest university in continuous operation. In 1800, the university was moved from Ingolstadt to Landshut by King Maximilian I Joseph of Bavaria when the city was threatened by the French, before being transferred to its present-day location in Munich in 1826 by King Ludwig I of Bavaria. In 1802, the university was officially named Ludwig-Maximilians-Universität by King Maximilian I of Bavaria in honor of himself and Ludwig IX. LMU is currently the second-largest university in Germany in terms of student population; in the 2018/19 winter semester, the university had a total of 51,606 matriculated students. Of these, 9,424 were freshmen, while international ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Kneser
Martin Kneser (21 January 1928 – 16 February 2004) was a German mathematician. His father Hellmuth Kneser and grandfather Adolf Kneser were also mathematicians. He obtained his PhD in 1950 from Humboldt University of Berlin with the dissertation: ''Über den Rand von Parallelkörpern''. His advisor was Erhard Schmidt. His name has been given to Kneser graphs which he studied in 1955. He also gave a simplified proof of the Fundamental theorem of algebra. Kneser was an Invited Speaker of the ICM in 1962 at Stockholm. His main publications were on quadratic forms and algebraic groups. See also *Approximation in algebraic groups * Betke–Kneser theorem *Kneser–Tits conjecture * Kneser's theorem (combinatorics) *Kneser graphs In graph theory, the Kneser graph (alternatively ) is the graph whose vertices correspond to the -element subsets of a set of elements, and where two vertices are adjacent if and only if the two corresponding sets are disjoint. Kneser graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Stein (mathematician)
Karl Stein (1 January 1913 in Hamm, Westphalia – 19 October 2000) was a German mathematician. He is well known for complex analysis and cryptography. Stein manifolds and Stein factorization are named after him. Career Karl Stein received his doctorate with his dissertation on the topic ''Zur Theorie der Funktionen mehrerer komplexer Veränderlichen; Die Regularitätshüllen niederdimensionaler Mannigfaltigkeiten'' at the University of Münster under the supervision of Heinrich Behnke in 1937. Karl Stein was conscripted into the Wehrmacht sometime before 1942, and trained as a cryptographer to work at OKW/Chi, the Cipher Department of the High Command of the Wehrmacht. He was assigned to manage the OKW/Chi IV, Subsection a, which was a unit responsible for security of own processes, cipher devices testing, and invention of new cipher devices. He managed a staff of 11 In 1955 he became professor at the Ludwig Maximilian University of Munich and emeritated in 1981. ... [...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 transfe ... [...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 of Great Britain, George II, King of Great Britain and Elector of Electorate of Hanover, Hanover, and starting classes in 1737, the Georgia Augusta was conceived to promote the ideals of the Age of Enlightenment, 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 List of Georg-August University of Göttingen people, 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Mainz
The Johannes Gutenberg University Mainz (german: Johannes Gutenberg-Universität Mainz) is a public research university in Mainz, Rhineland Palatinate, Germany, named after the printer Johannes Gutenberg since 1946. With approximately 32,000 students (2018) in about 100 schools and clinics, it is among the largest universities in Germany. Starting on 1 January 2005 the university was reorganized into 11 faculties of study. The university is a member of the German U15, a coalition of fifteen major research-intensive and leading medical universities in Germany. The Johannes Gutenberg University is considered one of the most prestigious universities in Germany. The university is part of the IT-Cluster Rhine-Main-Neckar. The Johannes Gutenberg University Mainz, the Goethe University Frankfurt and the Technische Universität Darmstadt together form the Rhine-Main-Universities (RMU). History The first University of Mainz goes back to the Archbishop of Mainz, Prince-elector ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pfister Form
In mathematics, a Pfister form is a particular kind of quadratic form, introduced by Albrecht Pfister in 1965. In what follows, quadratic forms are considered over a field ''F'' of characteristic not 2. For a natural number ''n'', an ''n''-fold Pfister form over ''F'' is a quadratic form of dimension 2''n'' that can be written as a tensor product of quadratic forms :\langle\!\langle a_1, a_2, \ldots , a_n \rangle\!\rangle \cong \langle 1, -a_1 \rangle \otimes \langle 1, -a_2 \rangle \otimes \cdots \otimes \langle 1, -a_n \rangle, for some nonzero elements ''a''1, ..., ''a''''n'' of ''F''. (Some authors omit the signs in this definition; the notation here simplifies the relation to Milnor K-theory, discussed below.) An ''n''-fold Pfister form can also be constructed inductively from an (''n''−1)-fold Pfister form ''q'' and a nonzero element ''a'' of ''F'', as q \oplus (-a)q. So the 1-fold and 2-fold Pfister forms look like: :\langle\!\langle a\rangle\!\rangle\cong \langle 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999, pp. 3-5 The University of Chicago, which had opened in 1892, organized an International Mathematical Con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly 1 millionDemographia: World Urban Areas , Demographia.com, April 2016 on an area of . Located on the , the southeastern coast of France on the Mediterranean Sea, at the foot of the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
