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Grete Hermann
Grete Hermann (2 March 1901 – 15 April 1984) was a Germans, German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education. She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored critique of a "Hidden variable theory, no hidden-variables theorem" by John von Neumann. It has been suggested that, had her critique not remained nearly unknown for decades, the historical development of quantum mechanics might have been very different. Mathematics Hermann studied mathematics at Göttingen under Emmy Noether and Edmund Landau, where she achieved her PhD in 1926. Her doctoral thesis, "Die Frage der endlich vielen Schritte in der Theorie der Polynomideale" (in English "The Question of Finitely Many Steps in Polynomial Ideal Theory"), published in ''Mathematische Annalen'', is the foundational paper for computer algebra. It first established the existe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bremen
Bremen (Low German also: ''Breem'' or ''Bräm''), officially the City Municipality of Bremen (german: Stadtgemeinde Bremen, ), is the capital of the German state Free Hanseatic City of Bremen (''Freie Hansestadt Bremen''), a two-city-state consisting of the cities of Bremen and Bremerhaven. With about 570,000 inhabitants, the Hanseatic city is the 11th largest city of Germany and the second largest city in Northern Germany after Hamburg. Bremen is the largest city on the River Weser, the longest river flowing entirely in Germany, lying some upstream from its mouth into the North Sea, and is surrounded by the state of Lower Saxony. A commercial and industrial city, Bremen is, together with Oldenburg and Bremerhaven, part of the Bremen/Oldenburg Metropolitan Region, with 2.5 million people. Bremen is contiguous with the Lower Saxon towns of Delmenhorst, Stuhr, Achim, Weyhe, Schwanewede and Lilienthal. There is an exclave of Bremen in Bremerhaven, the "Citybremian Overseas Port ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest coverage of any mathematician of his time and was said to have been "the last representative of the great mathematicians who were equally at home in both pure and applied mathematics". He integrated pure and applied sciences. Von Neumann made major contributions to many fields, including mathematics (foundations of mathematics, measure theory, functional analysis, ergodic theory, group theory, lattice theory, representation theory, operator algebras, matrix theory, geometry, and numerical analysis), physics (quantum mechanics, hydrodynamics, ballistics, nuclear physics and quantum statistical mechanics), economics ( game theory and general equilibrium theory), computing ( Von Neumann architecture, linear programming, numerical meteo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Von Weizsäcker
Carl Friedrich Freiherr von Weizsäcker (; 28 June 1912 – 28 April 2007) was a German physicist and philosopher. He was the longest-living member of the team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership. There is ongoing debate as to whether or not he and the other members of the team actively and willingly pursued the development of a nuclear bomb for Germany during this time. A member of the prominent Weizsäcker family, he was son of the diplomat Ernst von Weizsäcker, elder brother of the former German President Richard von Weizsäcker, father of the physicist and environmental researcher Ernst Ulrich von Weizsäcker and father-in-law of the former General Secretary of the World Council of Churches Konrad Raiser. Weizsäcker made important theoretical discoveries regarding energy production in stars from nuclear fusion processes. He also did influential theoretical work on planetary formation in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neo-Kantianism
In late modern continental philosophy, neo-Kantianism (german: Neukantianismus) was a revival of the 18th-century philosophy of Immanuel Kant. The Neo-Kantians sought to develop and clarify Kant's theories, particularly his concept of the "thing-in-itself" and his moral philosophy. It was influenced by Arthur Schopenhauer's critique of the Kantian philosophy in his work ''The World as Will and Representation'' (1818), as well as by other post-Kantian philosophers such as Jakob Friedrich Fries and Johann Friedrich Herbart. Origins The "back to Kant" movement began in the 1860s, as a reaction to the German materialist controversy in the 1850s. In addition to the work of Hermann von Helmholtz and Eduard Zeller, early fruits of the movement were Kuno Fischer's works on Kant and Friedrich Albert Lange's ''History of Materialism'' (''Geschichte des Materialismus'', 1873–75), the latter of which argued that transcendental idealism superseded the historic struggle between materia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leipzig
Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as well as the second most populous city in the area of the former East Germany after (East) Berlin. Together with Halle (Saale), the city forms the polycentric Leipzig-Halle Conurbation. Between the two cities (in Schkeuditz) lies Leipzig/Halle Airport. Leipzig is located about southwest of Berlin, in the southernmost part of the North German Plain (known as Leipzig Bay), at the confluence of the White Elster River (progression: ) and two of its tributaries: the Pleiße and the Parthe. The name of the city and those of many of its boroughs are of Slavic origin. Leipzig has been a trade city since at least the time of the Holy Roman Empire. The city sits at the intersection of the Via Regia and the Via Imperii, two important medieval trad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minna Specht
Minna Specht (22 December 1879 in Schloss Reinbek – 3 February 1961 in Bremen) was a German educator, socialist and member of the German Resistance. She was one of the founders of the Internationaler Sozialistischer Kampfbund. Early years Minna Specht was born the seventh child of Mathilde and Wilhelm Specht (d. 1882). The family lived in Reinbek castle, originally the hunting lodge in Friedrichsruh, which they acquired in 1874 and turned into a hotel. The approximately 70-room castle was only open in summer, during which the children lived with a nanny and a governess in one of two small houses next door."Minna Specht: Biografisches" Philosophical-Political Academy, official website. Retrieved July 19, 2010 Ilse Fischer [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primary Decomposition
In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many ''primary ideals'' (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven by for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by . The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings. The theorem plays an important role in algebraic geometry, by asserting that every algebraic set may be uniquely decomposed into a finite union of irreducible components. It has a straightforward extension to modules stating that every submodule of a finitely generated module over a Noetherian ring is a finite intersection of primary submodules ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Ring
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Often, the term "polynomial ring" refers implicitly to the special case of a polynomial ring in one indeterminate over a field. The importance of such polynomial rings relies on the high number of properties that they have in common with the ring of the integers. Polynomial rings occur and are often fundamental in many parts of mathematics such as number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings, rings of formal power series, Ore polynomials, graded rings, have been introduced for generalizing some properties of polynomial rings. A closely related notion is that of the ring ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (ring Theory)
In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group. Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may not correspond directly to the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra meant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithms
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes ''exact'' computation with expressions containing variables that have no given value and are manipulated as symbols. Software applications that perform symbolic calculations are called ''computer algebra systems'', with the term ''system'' alluding to the complexity of the main applications that include, at least, a method to represent mathematical data in a computer, a user programming language (usually different from the languag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
