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Affiliated operator Amenable group Arithmetic logic unit Artificial viscosity Axiom of regularity Axiom of limitation of size Backward induction Birkhoff—von Neumann theorem Blast wave fluid dynamics Taylor—von Neumann—Sedov blast wave Bounded set topological vector space Carry-save adder Cellular automata Class set theory Computer virus Commutation theorem Continuous geometry Coupling constants Decoherence theory quantum mechanics.
Von Neumann was generally regarded as the foremost mathematician of his time [2] and said to be "the last representative of the great mathematicians". Von Neumann made major contributions to many fields, including mathematics foundations of mathematicsfunctional analysisergodic theorygroup company that writes dissertation in hungary 2020representation theoryoperator algebrasgeometrytopologyand numerical analysisphysics quantum mechanicshydrodynamicsand quantum statistical mechanicseconomics game theorycomputing Von Neumann architecturelinear programmingself-replicating machinesstochastic computingand statistics.
He was a pioneer of the application of operator theory to quantum mechanics in the development of functional analysis, and a key figure in the development of game theory and the concepts of cellular automatathe universal constructor and the digital computer, company that writes dissertation in hungary 2020.
Von Neumann published over papers in his life: about 60 in pure mathematics, 60 in applied mathematics, 20 in physics, and the remainder on special mathematical subjects or non-mathematical ones.
His analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a shortlist of facts about his life he submitted to the National Academy of Scienceshe wrote, "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen inand subsequently in Berlin in — Also, my work on various forms of operator theory, Berlin and Princeton —; on the ergodic theorem, Princeton, — During World War IIvon Neumann worked on the Manhattan Project with theoretical physicist Edward Tellermathematician Stanislaw Ulam and others, problem-solving key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.
He developed the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon and coined the term "kiloton" of TNT as a measure of the explosive force generated. After the war, he served on the General Advisory Committee of the United States Atomic Energy Commissioncompany that writes dissertation in hungary 2020, and consulted for organizations including the United States Air Forcethe Army's Ballistic Research Laboratorythe Armed Forces Special Weapons Projectand the Lawrence Livermore National Laboratory.
As a Hungarian émigré, concerned that the Soviets would achieve nuclear superiority, he designed and promoted the policy of mutually assured destruction to limit the arms race. Von Neumann was born Neumann János Lajos to a wealthy, acculturated and non-observant Jewish family. In Hungarian the family name comes first, and his given names are equivalent to John Louis in English.
Von Neumann was born in BudapestKingdom of Hungarywhich was then part of the Austro-Hungarian Empire. He had moved to Budapest from Pécs at the end of the s. John's mother was Kann Margit English: Margaret Kann ; [10] her parents were Jakab Kann and Katalin Meisels of the Meisels family.
On February 20,Emperor Franz Joseph elevated John's father to the Hungarian nobility for his service to the Austro-Hungarian Empire.
The Neumann family thus acquired the hereditary appellation Margittaimeaning "of Margitta" today MarghitaRomania. The family had no connection with the town; the appellation was chosen in reference to Margaret, as was their chosen coat of arms depicting three marguerites.
Neumann János became margittai Neumann János John Neumann de Margittawhich he later changed to the German Johann company that writes dissertation in hungary 2020 Neumann. Von Neumann was a child prodigy. When he was six years old, he could divide two eight-digit numbers in his head [14] [15] and could converse in Ancient Greek.
When the six-year-old von Neumann caught his mother staring aimlessly, he asked her, "What are you calculating? When they were young, governesses taught von Neumann, his brothers and his cousins. Max believed that knowledge of languages in addition to Hungarian was essential, so the children were tutored in EnglishFrenchGerman and Italian.
He read his way through Wilhelm Oncken 's volume Allgemeine Geschichte in Einzeldarstellungen. One of the rooms in the apartment was converted into a library and reading room, with bookshelves from ceiling to floor. Von Neumann entered the Lutheran Fasori Evangélikus Gimnázium in Under the Hungarian system, children received all their education at the one gymnasium.
The Hungarian school system produced a generation noted for intellectual achievement, which included Theodore von Kármán bornGeorge de Hevesy bornMichael Polanyi bornLeó Szilárd bornDennis Gabor bornEugene Wigner bornEdward Teller bornand Paul Erdős born Although Max insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give him advanced instruction in those areas in which he had displayed an aptitude, company that writes dissertation in hungary 2020.
At the age of 15, company that writes dissertation in hungary 2020, he began to study advanced calculus under the renowned analyst Gábor Szegő.
According to his friend Theodore von Kármánvon Neumann's father wanted John to follow him into industry and thereby invest his time in a more financially useful endeavor than mathematics. In fact, his father asked von Kármán to persuade his company that writes dissertation in hungary 2020 not to take mathematics as his major.
This was not something that von Neumann had much knowledge of, so it was arranged for him to take a two-year, non-degree course in chemistry at the University of Berlinafter which he sat for the entrance exam to the prestigious ETH Zurich[29] which he passed in September candidate in mathematics.
For his thesis, he chose to produce an axiomatization of Cantor's set theory. in mathematics simultaneously with his chemical engineering degree, of which Wigner wrote, "Evidently a Ph. thesis and examination did not constitute an appreciable effort. Von Neumann's habilitation was completed on December 13,and he started his lectures as a Privatdozent at the University of Berlin in On New Year's Day invon Neumann married Marietta Kövesi, who had studied economics at Budapest University.
As of Marina is a distinguished professor emerita of business administration and public policy at the University of Michigan. In Octobervon Neumann married Klara Danwhom he had met during his last trips back to Budapest before the outbreak of World War II.
Before marrying Marietta, von Neumann was baptized a Catholic in None of the family had converted to Christianity while Max was alive, but all did afterward.
Inhe was offered a lifetime professorship at the Institute for Advanced Study in New Jersey when that institution's plan to appoint Hermann Weyl fell through. His brothers changed theirs to "Neumann" and "Vonneumann". He passed the exams easily but was rejected because of his age. Klara and John von Neumann were socially active within the local academic community.
He once wore company that writes dissertation in hungary 2020 three-piece pinstripe while riding down the Grand Canyon astride a mule. Von Neumann held a lifelong passion for ancient history and was renowned for his historical knowledge. A professor of Byzantine history at Princeton once said that von Neumann had greater expertise in Byzantine company that writes dissertation in hungary 2020 than he did.
Von Neumann liked to eat and drink; his wife, Klara, said that he could count everything except calories. He enjoyed Yiddish and "off-color" humor especially limericks. He never used it, preferring the couple's living room with its television playing loudly. When Cuthbert Hurd hired him as a consultant to IBMHurd often quietly paid the fines for his traffic tickets. Von Neumann's closest friend in the United States was mathematician Stanislaw Ulam.
A later friend of Ulam's, Gian-Carlo Rotawrote, company that writes dissertation in hungary 2020, "They would spend hours on end gossiping and giggling, swapping Jewish jokes, company that writes dissertation in hungary 2020, and drifting in and out of mathematical talk. The axiomatization of mathematics, on the model of Euclid 's Elementshad reached new levels of rigour and breadth at the end of the 19th century, particularly in arithmetic, thanks to the axiom schema of Richard Dedekind and Charles Sanders Peirceand in geometry, thanks to Hilbert's axioms.
Zermelo—Fraenkel set theory provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics, but did not explicitly exclude the possibility of the existence of a set that belongs to itself.
In his doctoral thesis ofvon Neumann demonstrated two techniques to exclude such sets—the axiom of foundation and the notion of class. The axiom of foundation proposed that every set can be constructed from the bottom up in an ordered succession of steps by way of the principles of Zermelo and Fraenkel. If one set belongs to another, then the first must necessarily come before the second in the succession.
This excludes the possibility of a set belonging to itself. To demonstrate that the addition of this new axiom to the others did not produce contradictions, von Neumann introduced a method of demonstration called the method of inner modelswhich became an essential instrument in set theory. The second approach to the problem of sets belonging to themselves took as its base the notion of classand defines a set as a class that belongs to other classes, while a proper class is defined as a class that does not belong to other classes.
On the Zermelo—Fraenkel approach, the axioms impede the construction of a set of all sets that do not belong to themselves. In contrast, on von Neumann's approach, the class of all sets that do not belong to themselves can be constructed, but it is a proper classnot a set.
Overall, von Neumann's major achievement in set theory was an "axiomatization of set theory and connected with that elegant theory of the ordinal and cardinal numbers as well as the first strict formulation of principles of definitions by the transfinite induction ". Banach and Tarski proved that, company that writes dissertation in hungary 2020, using isometric transformations, the result of taking apart and reassembling a two-dimensional figure would necessarily have the same area as the original.
This would make creating two unit squares out of one impossible. But in a paper, [64] von Neumann proved that paradoxical decompositions could use a group of transformations that include as a subgroup a free group with two generators. The group of area-preserving transformations contains such subgroups, and this opens the possibility of performing paradoxical decompositions using these subgroups. The class of groups von Neumann isolated in his work on Banach—Tarski decompositions was very important in many areas of mathematics, including von Neumann's own later work in measure theory see below.
With the aforementioned contributions of von Neumann to sets, the axiomatic system of the theory of sets avoided the contradictions of earlier systems and became usable as a foundation for mathematics, despite the lack of a proof of its company that writes dissertation in hungary 2020. The next question was whether it provided definitive answers to all mathematical questions that could be posed in it, or whether it might be improved by adding stronger axioms that could be used to prove a broader class of theorems.
Building on the work of Ackermannvon Neumann began attempting to prove using the finistic methods of Hilbert's school the consistency of first-order arithmetic. He succeeded in proving the consistency of a fragment of arithmetic of natural numbers through the use of restrictions on induction.
A strongly negative answer to whether it was definitive arrived in September at the historic Second Conference on the Epistemology of the Exact Sciences of Königsbergin which Kurt Gödel announced his first theorem of incompleteness : the usual axiomatic systems are incomplete, in the sense that they cannot prove every truth expressible in their language.
Moreover, every consistent extension of these systems necessarily remains incomplete. Less than a month later, von Neumann, who had participated in the Conference, communicated to Gödel an interesting consequence of his theorem: that the usual axiomatic systems are unable to demonstrate their own consistency.
In a series of papers published invon Neumann made foundational contributions to ergodic theorya branch of mathematics that involves the states of dynamical systems with an invariant measure. In measure theorythe "problem of measure" for an n -dimensional Euclidean space R n may be stated as: "does there exist a positive, normalized, invariant, and additive set function on the class of all subsets of R n?
Von Neumann's work argued that the "problem is essentially group-theoretic in character": [75] the existence of a measure could be determined by looking at the properties of the transformation group of the given space. The positive solution for spaces of dimension at most two, and the negative solution for higher dimensions, comes from the fact that the Euclidean group is a solvable group for dimension at most two, and is not solvable for higher dimensions.
In a number of von Neumann's papers, the methods of argument he employed are considered even more significant than the results. In anticipation of his later study of dimension theory in algebras of operators, von Neumann used results on equivalence by finite decomposition, and reformulated the problem of measure in terms of functions.
Von Neumann also gave a new proof on the uniqueness of Haar measures by using the mean values of functions, although this method only worked for compact groups.
Using his previous work on measure theory von Neumann made several contributions to the theory of topological groupsbeginning with a paper on almost periodic functions on groups, where von Neumann extended Bohr's theory of almost periodic functions to arbitrary groups. In a paper, he used the newly discovered Haar measure in the solution of Hilbert's fifth problem for the case of compact groups, company that writes dissertation in hungary 2020.
It was defined as a complex vector space with a hermitian scalar productcompany that writes dissertation in hungary 2020, with the corresponding norm being both separable and complete. He continued with the development of the spectral theory of operators in Hilbert space in 3 seminal papers between and In addition he wrote a paper detailing how the usage of infinite matricescommon at the time in spectral theory, was inadequate as a representation for hermitian operators.
His work on operator theory lead to his most profound invention in pure mathematics, the study of von Neumann algebras and in general of operator algebras. In other work in functional analysis von Neumann was also the first mathematician to apply new topological ideas from Hausdorff to Hilbert spaces. He also gave the first general definition of locally convex spaces.
Von Neumann founded the study of rings of operators, through the von Neumann algebras. Murrayon the company that writes dissertation in hungary 2020 case, the general study of factors classification of von Neumann algebras.
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