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Max August Zorn
Max August Zorn (; June 6, 1906 – March 9, 1993) was a German mathematician. He was an algebraist, group theorist, and numerical analyst. He is best known for Zorn's lemma, a method used in set theory that is applicable to a wide range of mathematical constructs such as vector spaces, and ordered sets amongst others. Zorn's lemma was first postulated by Kazimierz Kuratowski in 1922, and then independently by Zorn in 1935. Life and career Zorn was born in Krefeld, Germany. He attended the University of Hamburg. He received his PhD in April 1930 for a thesis on alternative algebras. He published his findings in '' Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg''. Zorn showed that split-octonions could be represented by a mixed-style of matrices called Zorn's vector-matrix algebra. Max Zorn was appointed to an assistant position at the University of Halle. However, he did not have the opportunity to work there for long as he was forced to leave Germ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krefeld
Krefeld ( , ; li, Krieëvel ), also spelled Crefeld until 1925 (though the spelling was still being used in British papers throughout the Second World War), is a city in North Rhine-Westphalia, Germany. It is located northwest of Düsseldorf, its center lying just a few kilometers to the west of the river Rhine; the borough of Uerdingen is situated directly on the Rhine. Because of its economic past, Krefeld is often referred to as the "Velvet and Silk City". It is accessed by the autobahns A57 ( Cologne– Nijmegen) and A44 ( Aachen–Düsseldorf– Dortmund– Kassel). Krefeld's residents now speak ', or standard German, but the native dialect is a Low Franconian variety, sometimes locally called ', ', ', or sometimes simply '. The Uerdingen line isogloss, separating general dialectical areas in Germany and neighboring Germanic-speaking countries, runs through and is named after Krefeld's Uerdingen district, originally an independent municipality. History Early histor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Ordered Set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word ''partial'' in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable. Informal definition A partial order defines a notion of comparison. Two elements ''x'' and ''y'' may stand in any of four mutually exclusive relationships to each other: either ''x'' ''y'', or ''x'' and ''y'' are ''inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subset
In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ''B''. The relationship of one set being a subset of another is called inclusion (or sometimes containment). ''A'' is a subset of ''B'' may also be expressed as ''B'' includes (or contains) ''A'' or ''A'' is included (or contained) in ''B''. A ''k''-subset is a subset with ''k'' elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the Boolean inclusion relation. Definition If ''A'' and ''B'' are sets and every element of ''A'' is also an element of ''B'', then: :*''A'' is a subset of ''B'', denoted by A \subseteq B, or equivalently, :* ''B'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Order
In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation \leq on some set X, which satisfies the following for all a, b and c in X: # a \leq a ( reflexive). # If a \leq b and b \leq c then a \leq c ( transitive). # If a \leq b and b \leq a then a = b ( antisymmetric). # a \leq b or b \leq a ( strongly connected, formerly called total). Total orders are sometimes also called simple, connex, or full orders. A set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, and loset are also used. The term ''chain'' is sometimes defined as a synonym of ''totally ordered set'', but refers generally to some sort of totally ordered subsets of a given partially ordered set. An extension of a given partial order to a total order is called a linear extension of that partial order. Strict and non-strict total orders A on a set X is a strict partial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale University
Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the world. It is a member of the Ivy League. Chartered by the Connecticut Colony, the Collegiate School was established in 1701 by clergy to educate Congregational ministers before moving to New Haven in 1716. Originally restricted to theology and sacred languages, the curriculum began to incorporate humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first PhD in the United States in 1861 and organizing as a university in 1887. Yale's faculty and student populations grew after 1890 with rapid expansion of the physical campus and scientific research. Yale is organized into fourteen constituent schools: the original undergraduate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sterling Fellow
Sterling may refer to: Common meanings * Sterling silver, a grade of silver * Sterling (currency), the currency of the United Kingdom ** Pound sterling, the primary unit of that currency Places United Kingdom * Stirling, a Scottish city whose alternative historical spelling is Sterling United States * Sterling, Alaska * Sterling, Colorado * Sterling Micropolitan Statistical Area, Colorado * Sterling, Connecticut * Sterling, Georgia * Sterling, in Bingham County, Idaho * Sterling Wildlife Management Area, Idaho * Sterling, Illinois * Sterling, a ghost town in Jackson County, Iowa * Sterling, Kansas * Sterling, Massachusetts * Sterling, Michigan * Sterling Heights, Michigan * Sterling State Park, Michigan * Sterling Center, Minnesota * Sterling, Missouri * Sterling, in Madison County, Montana * Sterling, Nebraska * Sterling, New York * Sterling, in Mecklenburg County, North Carolina * Mount Sterling (Great Smoky Mountains), North Carolina * Sterling, North Dakota * Sterl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chicago Tribune
The ''Chicago Tribune'' is a daily newspaper based in Chicago, Illinois, United States, owned by Tribune Publishing. Founded in 1847, and formerly self-styled as the "World's Greatest Newspaper" (a slogan for which WGN radio and television are named), it remains the most-read daily newspaper in the Chicago metropolitan area and the Great Lakes region. It had the sixth-highest circulation for American newspapers in 2017. In the 1850s, under Joseph Medill, the ''Chicago Tribune'' became closely associated with the Illinois politician Abraham Lincoln, and the Republican Party's progressive wing. In the 20th century under Medill's grandson, Robert R. McCormick, it achieved a reputation as a crusading paper with a decidedly more American-conservative anti- New Deal outlook, and its writing reached other markets through family and corporate relationships at the '' New York Daily News'' and the '' Washington Times-Herald.'' The 1960s saw its corporate parent owner, Tribune Comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eric Zorn
Eric Zorn (born January 6, 1958) is a former American op-ed columnist and daily blogger for the ''Chicago Tribune'' who specialized in local news as well as politics. Early life and education Zorn is a graduate of the University of Michigan, where he majored in English literature and creative writing. He is the grandson of Max Zorn, author of Zorn's Lemma. Career After serving a four-month internship at the ''Miami Herald'', Zorn started working for the ''Chicago Tribune'' in summer 1980. He has been a columnist for it since 1986. About four times a year for some years, Zorn and fellow ''Tribune'' columnist Mary Schmich wrote a week of columns that consisted of a back-and-forth exchange of letters. Each December since 1999 (except for COVID-19 pandemic 2020), Schmich and Zorn have hosted the "Songs of Good Cheer" holiday caroling parties at the Old Town School of Folk Music to raise money for the Tribune Holiday Fund charities. Zorn co-wrote the 1990 book ''Murder of Innocen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazi
Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Nazi Germany. During Hitler's rise to power in 1930s Europe, it was frequently referred to as Hitlerism (german: Hitlerfaschismus). The later related term " neo-Nazism" is applied to other far-right groups with similar ideas which formed after the Second World War. Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. It incorporates a dictatorship, fervent antisemitism, anti-communism, scientific racism, and the use of eugenics into its creed. Its extreme nationalism originated in pan-Germanism and the ethno-nationalist '' Völkisch'' movement which had been a prominent aspect of German nationalism since the late 19th century, and it was strongly influenced by the paramilitary groups tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Halle
Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university in the German state of Saxony-Anhalt. MLU offers German and international (English) courses leading to academic degrees such as BA, BSc, MA, MSc, doctoral degrees, and Habilitation. The university was created in 1817 through the merger of the University of Wittenberg (founded in 1502) and the University of Halle (founded in 1694). MLU is named after Protestant reformer Martin Luther, who was a professor in Wittenberg. Today, the university campus is located in Halle, while ''Leucorea Foundation'' in Wittenberg serves as MLU's convention centre. Both Halle and Wittenberg are about one hour from Berlin via the Berlin–Halle railway, which offers Intercity-Express (ICE) trains. History University of Wittenberg (''Universität Wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Split-octonion
In mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers. Unlike the standard octonions, they contain non-zero elements which are non-invertible. Also the signatures of their quadratic forms differ: the split-octonions have a split signature (4,4) whereas the octonions have a positive-definite signature (8,0). Up to isomorphism, the octonions and the split-octonions are the only two 8-dimensional composition algebras over the real numbers. They are also the only two octonion algebras over the real numbers. Split-octonion algebras analogous to the split-octonions can be defined over any field. Definition Cayley–Dickson construction The octonions and the split-octonions can be obtained from the Cayley–Dickson construction by defining a multiplication on pairs of quaternions. We introduce a new imaginary unit ℓ and write a pair of quaternions (''a'', ''b'') in the form ''a'' + ℓ''b''. The product is defined by the rule: :( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abhandlungen Aus Dem Mathematischen Seminar Der Universität Hamburg
(English: ''Reports from the Mathematical Seminar of the University of Hamburg'') is a peer-reviewed mathematics journal published by Springer Science+Business Media. It publishes articles on pure mathematics and is scientifically coordinated by the ''Mathematisches Seminar'', an informal cooperation of mathematicians at the Universität Hamburg; its Managing Editors are Professors and Tobias Dyckerhoff. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. History The ''Abhandlungen'' were set up as a new journal by Wilhelm Blaschke in 1922 at the newly created Department of Mathematics (called ''Mathematisches Seminar'') at the newly founded Hamburgische Universität. Blaschke invited both Hermann Weyl and David Hilbert to the ''Mathematisches Seminar'' (in 1920 and 1921, respectively) to deliver talk series on their views concerning the Foundations of Mathematics. These talks formed part of the early history of the Grundlagenkrise der Mathematik and Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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