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Peter Roquette
Peter Roquette (born 8 October 1927) is a German mathematician working in algebraic geometry, algebra, and number theory. He was born in Königsberg. Roquette studied in Erlangen, Berlin, and Hamburg. In 1951 he defended a dissertation at the University of Hamburg under Helmut Hasse, providing a new proof of the Riemann hypothesis for algebraic function fields over a finite field (the first proof was given by André Weil in 1940). In 1951/1952 he was an assistant at the Mathematical Research Institute at Oberwolfach and from 1952 to 1954 at the University of Munich. From 1954 to 1956 he worked at the Institute for Advanced Study in Princeton. In 1954 he was Privatdozent at Munich, and from 1956 to 1959 he worked in the same position at Hamburg. In 1959 he became an associate professor at the University of Saarbrucken and in the same year at the University of Tübingen. From 1967 he was professor at the Ruprecht-Karls-University of Heidelberg, where he retired in 1996. Roquette wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Roquette
Peter Roquette (born 8 October 1927) is a German mathematician working in algebraic geometry, algebra, and number theory. He was born in Königsberg. Roquette studied in Erlangen, Berlin, and Hamburg. In 1951 he defended a dissertation at the University of Hamburg under Helmut Hasse, providing a new proof of the Riemann hypothesis for algebraic function fields over a finite field (the first proof was given by André Weil in 1940). In 1951/1952 he was an assistant at the Mathematical Research Institute at Oberwolfach and from 1952 to 1954 at the University of Munich. From 1954 to 1956 he worked at the Institute for Advanced Study in Princeton. In 1954 he was Privatdozent at Munich, and from 1956 to 1959 he worked in the same position at Hamburg. In 1959 he became an associate professor at the University of Saarbrucken and in the same year at the University of Tübingen. From 1967 he was professor at the Ruprecht-Karls-University of Heidelberg, where he retired in 1996. Roquette wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Saarbrucken
Saarland University (german: Universität des Saarlandes, ) is a public research university located in Saarbrücken, the capital of the German state of Saarland. It was founded in 1948 in Homburg in co-operation with France and is organized in six faculties that cover all major fields of science. In 2007, the university was recognized as an excellence center for computer science in Germany. Thanks to bilingual German and French staff, the university has an international profile, which has been underlined by its proclamation as "''European University''" in 1950 and by establishment of Europa-Institut as its "''crown and symbol''" in 1951. Nine academics have been honored with the highest German research prize, the Gottfried Wilhelm Leibniz Prize, while working at Saarland University. History Saarland University, the first to be established after World War II, was founded in November 1948 with the support of the French Government and under the auspices of the University of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Academy Of Sciences Leopoldina
The German National Academy of Sciences Leopoldina (german: Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften), short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on January 1, 1652, based on academic models in Italy, it was originally named the ''Academia Naturae Curiosorum'' until 1687 when Emperor Leopold I raised it to an academy and named it after himself. It was since known under the German name ''Deutsche Akademie der Naturforscher Leopoldina'' until 2007, when it was declared to be Germany's National Academy of Sciences. History ' The Leopoldina was founded in the imperial city of Schweinfurt on 1 January 1652 under the Latin name sometimes translated into English as "Academy of the Curious as to Nature." It was founded by four local physicians- Johann Laurentius Bausch, the first president of the society, Johann Michael Fehr, Georg Balthasar Metzger, and Georg Balthasar Wohlfarth; and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heidelberg Academy Of Sciences
The Heidelberg Academy of Sciences and Humanities (German: ''Heidelberger Akademie der Wissenschaften''), established in 1909 in Heidelberg, Germany, is an assembly of scholars and scientists in the German state of Baden-Wuerttemberg. The Academy is a member of the Union of German Academies of Sciences and Humanities The Union of German Academies of Sciences and Humanities (German: Union der deutschen Akademien der Wissenschaften) is an umbrella organisation for eight German academies of sciences and humanities. The member academies are: *Berlin-Brandenburg Ac .... References External linksHeidelberg Academy of Sciences and Humanities website 1909 establishments in Germany Scientific organizations established in 1909 Union of German Academies of Sciences and Humanities Education in Heidelberg {{Germany-org-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emmy Noether
Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noether'' (1907/08, NR. 2988); reproduced in: ''Emmy Noether, Gesammelte Abhandlungen – Collected Papers,'' ed. N. Jacobson 1983; online facsimile aphysikerinnen.de/noetherlebenslauf.html). Sometimes ''Emmy'' is mistakenly reported as a short form for ''Amalie'', or misreported as "Emily". e.g. (, ; ; 23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She discovered Noether's First and Second Theorem, which are fundamental in mathematical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars. The earliest mathematical texts available are from Mesopotamia and Egypt – '' Plimpton 322'' ( Babylonian c. 2000 – 1900 BC), the ''Rhind Mathematical Papyrus'' ( Egyptian c. 1800 BC) and the '' Moscow Mathematical Papyrus'' (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most anci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-standard Analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson. He wrote: ... the idea of infinitely small or ''infinitesimal'' quantities seems to appeal naturally to our intuition. At any rate, the use of infinitesimals was widespread during the formative stages of the Differential and Integral Calculus. As for the objection ... that the distance between two distinct real numbers cannot be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or infinitely ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mahler's Theorem
In mathematics, Mahler's theorem, introduced by , expresses continuous ''p''-adic functions in terms of polynomials. Over any field of characteristic 0, one has the following result: Let (\Delta f)(x)=f(x+1)-f(x) be the forward difference operator. Then for polynomial functions ''f'' we have the Newton series :f(x)=\sum_^\infty (\Delta^k f)(0), where :=\frac is the ''k''th binomial coefficient polynomial. Over the field of real numbers, the assumption that the function ''f'' is a polynomial can be weakened, but it cannot be weakened all the way down to mere continuity. Mahler's theorem states that if ''f'' is a continuous p-adic-valued function on the ''p''-adic integers then the same identity holds. The relationship between the operator Δ and this polynomial sequence is much like that between differentiation and the sequence whose ''k''th term is ''x''''k''. It is remarkable that as weak an assumption as continuity is enough; by contrast, Newton series on the field of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics. Biography He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wałbrzych, in Poland. In 1933, he emigrated to British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynamics an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonstandard Arithmetic
Standardization or standardisation is the process of implementing and developing technical standards based on the consensus of different parties that include firms, users, interest groups, standards organizations and governments. Standardization can help maximize compatibility, interoperability, safety, repeatability, or quality. It can also facilitate a normalization of formerly custom processes. In social sciences, including economics, the idea of ''standardization'' is close to the solution for a coordination problem, a situation in which all parties can realize mutual gains, but only by making mutually consistent decisions. History Early examples Standard weights and measures were developed by the Indus Valley civilization.Iwata, Shigeo (2008), "Weights and Measures in the Indus Valley", ''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd edition)'' edited by Helaine Selin, pp. 2254–2255, Springer, . The centralized wei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-adic Field
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two -adic numbers are considered to be close when their difference is divisible by a high power of : the higher the power, the closer they are. This property enables -adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles. These numbers were first described by Kurt Hensel in 1897, though, with hindsight, some of Ernst Kummer's earlier work can be interpreted as implicitly using -adic numbers.Translator's introductionpage 35 "Indeed, with hindsight it becomes apparent that a discret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
