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Ernst Schröder (mathematician)
Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Baden, Germany – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic, by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental ''Vorlesungen über die Algebra der Logik'' (''Lectures on the Algebra of Logic'', 1890–1905), in three volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day. Life Schröder learned mathematics at Heidelberg, Königsberg, and Zürich, under Otto Hesse, Gustav Kirchhoff, and Franz Neumann. After teaching school for a few years, he moved to the Technische Hochschule Darmstadt in 1874. Two years later, he took up a chair in math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mannheim, Germany
Mannheim (; Palatine German: or ), officially the University City of Mannheim (german: Universitätsstadt Mannheim), is the second-largest city in the German state of Baden-Württemberg after the state capital of Stuttgart, and Germany's 21st-largest city, with a 2020 population of 309,119 inhabitants. The city is the cultural and economic centre of the Rhine-Neckar Metropolitan Region, Germany's seventh-largest metropolitan region with nearly 2.4 million inhabitants and over 900,000 employees. Mannheim is located at the confluence of the Rhine and the Neckar in the Kurpfalz (Electoral Palatinate) region of northwestern Baden-Württemberg. The city lies in the Upper Rhine Plain, Germany's warmest region. Together with Hamburg, Mannheim is the only city bordering two other federal states. It forms a continuous conurbation of around 480,000 inhabitants with Ludwigshafen am Rhein in the neighbouring state of Rhineland-Palatinate, on the other side of the Rhine. Some norther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Heidelberg
} Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest university and one of the world's oldest surviving universities; it was the third university established in the Holy Roman Empire. Heidelberg is one of the most prestigious and highly ranked universities in Europe and the world. Heidelberg has been a coeducational institution since 1899. The university consists of twelve faculties and offers degree programmes at undergraduate, graduate and postdoctoral levels in some 100 disciplines. The language of instruction is usually German, while a considerable number of graduate degrees are offered in English as well as some in French. As of 2021, 57 Nobel Prize winners have been affiliated with the city o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Theory
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These ''lattice-like'' structures all admit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of '' naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the 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 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 education, to the study of algebraic structures such as groups, rings, and 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, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantification (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order logic, first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope (logic), scope is called a quantified formula. A quantified formula must contain a Free variables and bound variables, bound variable and a subformula specifying a property of the referent of that variable. The mostly commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as Dual (mathematics), duals; in classical logic, they are interdefinable using negation. They can also be used to define more complex quantifiers, as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Grassmann
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It can be use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Grassmann
Hermann Günther Grassmann (german: link=no, Graßmann, ; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. Biography Hermann Grassmann was the third of 12 children of Justus Günter Grassmann, an ordained minister who taught mathematics and physics at the Stettin Gymnasium, where Hermann was educated. Grassmann was an undistinguished student until he obtained a high mark on the examinations for admission to Prussian universities. Beginning in 1827, he studied theology at the University of Berlin, also taking classes in classical languages, philosophy, and literature. He does not appear to have taken courses in mathematics or physics. Although lacking university training in mathematics, it was the field that most interested him when he returned to Stettin in 1830 after completing h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karlsruhe Institute Of Technology
The Karlsruhe Institute of Technology (KIT; german: Karlsruher Institut für Technologie) is a public research university in Karlsruhe, Germany. The institute is a national research center of the Helmholtz Association. KIT was created in 2009 when the University of Karlsruhe (), founded in 1825 as a public research university and also known as the "Fridericiana", merged with the Karlsruhe Research Center (), which had originally been established in 1956 as a national nuclear research center (, or KfK). KIT is a member of the TU9, an incorporated society of the largest and most notable German institutes of technology.TU9 As part of the German Universities Excellence Initiative KIT was one of three universities which were awarded excellence status in 2006. In the following "German Excellence Strategy" KIT was awarded as one of eleven "Excellence Universities" in 2019. KIT is among the leading technical universities in Germany and Europe. According to different bibliometric ranking ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Ernst Neumann
Franz Ernst Neumann (11 September 1798 – 23 May 1895) was a German mineralogist, physicist and mathematician. Biography Neumann was born in Joachimsthal, Margraviate of Brandenburg, near Berlin. In 1815 he interrupted his studies at Berlin to serve as a volunteer in the Hundred Days against Napoleon, and was wounded in the Battle of Ligny. Subsequently, he entered Berlin University as a student of theology, but soon turned to scientific subjects. His earlier papers were mostly concerned with crystallography, and the reputation they gained him led to his appointment as Privatdozent at the University of Königsberg, where in 1828 he became extraordinary, and in 1829 ordinary, professor of mineralogy and physics. His 1831 study on the specific heats of compounds included what is now known as Neumann's Law: the molecular heat of a compound is equal to the sum of the atomic heats of its constituents. Devoting himself next to optics, he produced memoirs which earned him a high place ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav Kirchhoff
Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term black-body radiation in 1862. Several different sets of concepts are named "Kirchhoff's laws" after him, concerning such diverse subjects as black-body radiation and spectroscopy, electrical circuits, and thermochemistry. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen. Life and work Gustav Kirchhoff was born on 12 March 1824 in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. His family were Lutherans in the Evangelical Church of Prussia. He graduated from the Albertus University of Königsberg in 1847 where he attended the mathematico-physical seminar directed by Carl Gustav Jacob Jacobi, Franz Ernst Neumann and Friedrich Julius Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
