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Edmund Landau
Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis. Biography Edmund Landau was born to a Jewish family in Berlin. His father was Leopold Landau, a gynecologist, and his mother was Johanna Jacoby. Landau studied mathematics at the University of Berlin, receiving his doctorate in 1899 and his habilitation (the post-doctoral qualification required to teach in German universities) in 1901. His doctoral thesis was 14 pages long. In 1895, his paper on scoring chess tournaments is the earliest use of eigenvector centrality. Landau taught at the University of Berlin from 1899 to 1909, after which he held a chair at the University of Göttingen. He married Marianne Ehrlich, the daughter of the Nobel Prize-winning biologist Paul Ehrlich, in 1905. At the 1912 International Congress of Mathematicians Landau listed four problems in number theory about primes that he said were pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population within city limits, highest population within its city limits of any city in the European Union. The city is also one of the states of Germany, being the List of German states by area, third smallest state in the country by area. Berlin is surrounded by the state of Brandenburg, and Brandenburg's capital Potsdam is nearby. The urban area of Berlin has a population of over 4.6 million and is therefore the most populous urban area in Germany. The Berlin/Brandenburg Metropolitan Region, Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's second-largest metropolitan region after the Rhine-Ruhr region, as well as the List of EU metropolitan areas by GDP, fifth-biggest metropolitan region by GDP in the European Union. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grete Hermann
Grete Hermann (2 March 1901 – 15 April 1984) was a 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 the no hidden variables proof by John von Neumann. Mathematics Hermann studied mathematics at Göttingen under Emmy Noether and Edmund Landau, where she achieved her PhD in 1926. Her doctoral thesis, ''The Question of Finitely Many Steps in Polynomial Ideal Theory'' (), published in '' Mathematische Annalen'', is the foundational paper for modern computer algebra. It first established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings. Hermann's algorithm for primary decomposition is still in contemporary use. Assistant to Leonard Nelson From 1925 to 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jewish
Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly interrelated, as Judaism is their ethnic religion, though it is not practiced by all ethnic Jews. Despite this, religious Jews regard Gerim, converts to Judaism as members of the Jewish nation, pursuant to the Conversion to Judaism, long-standing conversion process. The Israelites emerged from the pre-existing Canaanite peoples to establish Kingdom of Israel (Samaria), Israel and Kingdom of Judah, Judah in the Southern Levant during the Iron Age.John Day (Old Testament scholar), John Day (2005), ''In Search of Pre-Exilic Israel'', Bloomsbury Publishing, pp. 47.5 [48] 'In this sense, the emergence of ancient Israel is viewed not as the cause of the demise of Canaanite culture but as its upshot'. Originally, J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable, that is, '' holomorphic functions''. The concept can be extended to functions of several complex variables. Complex analysis is contrasted with real analysis, which dea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau Prime Ideal Theorem
In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula for counting the number of prime ideals of a number field ''K'', with norm at most ''X''. Example What to expect can be seen already for the Gaussian integers. There for any prime number ''p'' of the form 4''n'' + 1, ''p'' factors as a product of two Gaussian primes of norm ''p''. Primes of the form 4''n'' + 3 remain prime, giving a Gaussian prime of norm ''p''2. Therefore, we should estimate :2r(X)+r^\prime(\sqrt) where ''r'' counts primes in the arithmetic progression 4''n'' + 1, and ''r''′ in the arithmetic progression 4''n'' + 3. By the quantitative form of Dirichlet's theorem on primes, each of ''r''(''Y'') and ''r''′(''Y'') is asymptotically :\frac. Therefore, the 2''r''(''X'') term dominates, and is asymptotically :\frac. General number fields This general pattern holds for number fields in general, so that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number Theorem
In mathematics, the prime number theorem (PNT) describes the asymptotic analysis, asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is , where is the prime-counting function (the number of primes less than or equal to ''N'') and is the natural logarithm of . This means that for large enough , the probability that a random integer not greater than is prime is very close to . Consequently, a random integer with at most digits (for large enough ) is about half as likely to be prime as a random integer with at most digits. For example, among the positive integers of at most 1000 digits, about on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vojtěch Jarník
Vojtěch Jarník (; 22 December 1897 – 22 September 1970) was a Czech mathematician. He worked for many years as a professor and administrator at Charles University, and helped found the Czechoslovak Academy of Sciences. He is the namesake of Jarník's algorithm for minimum spanning trees. Jarník worked in number theory, mathematical analysis, and graph algorithms. He has been called "probably the first Czechoslovak mathematician whose scientific works received wide and lasting international response". As well as developing Jarník's algorithm, he found tight bounds on the number of lattice points on convex curves, studied the relationship between the Hausdorff dimension of sets of real numbers and how well they can be approximated by rational numbers, and investigated the properties of nowhere-differentiable functions. Education and career Jarník was born on 22 December 1897. He was the son of , a professor of Romance language philology at Charles University, and his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Walfisz
Arnold Walfisz (2 July 1892 – 29 May 1962) was a Jewish-Polish mathematician working in analytic number theory. Life After the ''Abitur'' in Warsaw, Poland, Arnold Walfisz studied (1909−14 and 1918−21) in Germany at Munich, Berlin, Heidelberg and Göttingen. Edmund Landau was his doctoral-thesis supervisor at the University of Göttingen. Walfisz lived in Wiesbaden from 1922 through 1927, then he returned to Warsaw, worked at an insurance company and at the mathematical institute of the university (habilitation in 1930). In 1935, together with , he founded the mathematical journal ''Acta Arithmetica''. In 1936, Walfisz became professor at the University of Tbilisi in Soviet Georgia. He wrote approximately 100 mathematical articles and three books. Work By using a theorem by Carl Ludwig Siegel providing an upper bound for the real zeros (see Siegel zero) of Dirichlet L-functions formed with real non-principal characters, Walfisz obtained the Siegel–Walfisz theorem, fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Ludwig Siegel
Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was a German mathematician specialising in analytic number theory. He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation, Siegel's method, Siegel's lemma and the Siegel mass formula for quadratic forms. He has been named one of the most important mathematicians of the 20th century.Pérez, R. A. (2011''A brief but historic article of Siegel'' NAMS 58(4), 558–566. André Weil, without hesitation, named Siegel as the greatest mathematician of the first half of the 20th century. Atle Selberg said of Siegel and his work: Biography Siegel was born in Berlin, where he enrolled at the Humboldt University in Berlin in 1915 as a student in mathematics, astronomy, and physics. Amongst his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. His best-known student ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Ostrowski
Alexander Markowich Ostrowski (; ; 25 September 1893 – 20 November 1986) was a mathematician. Biography His father Mark having been a merchant, Alexander Ostrowski attended the Kiev College of Commerce, not a high school, and thus had an insufficient qualification to be admitted to university. However, his talent did not remain undetected: Ostrowski's mentor, Dmitry Grave, wrote to Edmund Landau and Kurt Hensel for help. Subsequently, Ostrowski began to study mathematics at Marburg University under Hensel's supervision in 1912. During World War I he was interned, but thanks to the intervention of Hensel, the restrictions on his movements were eased somewhat, and he was allowed to use the university library. After the war ended, Ostrowski moved to Göttingen where he wrote his doctoral dissertation and was influenced by David Hilbert, Felix Klein, and Landau. In 1920, after having obtained his doctorate from the University of Göttingen, Ostrowski moved to Hamburg where he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
