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Edmund Georg Hermann 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 partic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Ostrowski
Alexander Markowich Ostrowski ( uk, Олександр Маркович Островський; russian: Алекса́ндр Ма́ркович Остро́вский; 25 September 1893, in Kiev, Russian Empire – 20 November 1986, in Montagnola, Lugano, Switzerland) was a mathematician. 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 Landau and 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Ehrlich
Paul Ehrlich (; 14 March 1854 – 20 August 1915) was a Nobel Prize-winning German physician and scientist who worked in the fields of hematology, immunology, and antimicrobial chemotherapy. Among his foremost achievements were finding a cure for syphilis in 1909 and inventing the precursor technique to Gram staining bacteria. The methods he developed for staining tissue made it possible to distinguish between different types of blood cells, which led to the ability to diagnose numerous blood diseases. His laboratory discovered arsphenamine (Salvarsan), the first effective medicinal treatment for syphilis, thereby initiating and also naming the concept of chemotherapy. Ehrlich popularized the concept of a magic bullet. He also made a decisive contribution to the development of an antiserum to combat diphtheria and conceived a method for standardizing therapeutic serums. In 1908, he received the Nobel Prize in Physiology or Medicine for his contributions to immunology. He wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvector Centrality
In graph theory, eigenvector centrality (also called eigencentrality or prestige score) is a measure of the influence of a node in a network. Relative scores are assigned to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes. A high eigenvector score means that a node is connected to many nodes who themselves have high scores. Google's PageRank and the Katz centrality are variants of the eigenvector centrality. Using the adjacency matrix to find eigenvector centrality For a given graph G:=(V,E) with , V, vertices let A = (a_) be the adjacency matrix, i.e. a_ = 1 if vertex v is linked to vertex t, and a_ = 0 otherwise. The relative centrality score, x_v, of vertex v can be defined as: : x_v = \frac 1 \lambda \sum_ x_t = \frac 1 \lambda \sum_ a_ x_t where M(v) is the set of neighbors of v and \lambda is a constant. With a small rearrangement this c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a dissertation. The degree, abbreviated "Dr. habil." (Doctor habilitatus) or "PD" (for "Privatdozent"), is a qualification for professorship in those countries. The conferral is usually accompanied by a lecture to a colloquium as well as a public inaugural lecture. History and etymology The term ''habilitation'' is derived from the Medieval Latin , meaning "to make suitable, to fit", from Classical Latin "fit, proper, skillful". The degree developed in Germany in the seventeenth century (). Initially, habilitation was synonymous with "doctoral qualification". The term became synonymous with "post-doctoral qualification" in Germany in the 19th century "when holding a doctorate seemed no longer sufficient to guarantee a proficient transfer o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leopold Landau
Leopold Landau (July 16, 1848 – December 28, 1920) was a German gynecologist born in Warsaw. Life and career Landau studied medicine at the Universities of Breslau, Würzburg and Berlin, obtaining his doctorate at the latter institution in 1870. After serving as an assistant surgeon during the Franco-Prussian War, he was a lecturer in gynecology at the University of Breslau (1872–76). Afterwards, he returned to Berlin as a lecturer of gynecology, where in 1893 he became a full professor. In 1892 with his brother, Theodor Landau (1861–1932), he opened a ''Frauenklinik'' (''Women's clinic'') in Berlin that became well known throughout Germany. From here, he conducted medical research, publishing noted works on myoma and radical vaginal operations. With his brother, he was co-author of ''Die Vaginale Radicaloperation: Technik und Geschichte'' (1896), being later translated into English and published a''The history and technique of the vaginal radical operation''(1897). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The people of the Kingdom of Israel and the ethnic and religious group known as the Jewish people that descended from them have been subjected to a number of forced migrations in their history" and Hebrews of historical History of ancient Israel and Judah, Israel and Judah. Jewish ethnicity, nationhood, and religion are strongly interrelated, "Historically, the religious and ethnic dimensions of Jewish identity have been closely interwoven. In fact, so closely bound are they, that the traditional Jewish lexicon hardly distinguishes between the two concepts. Jewish religious practice, by definition, was observed exclusively by the Jewish people, and notions of Jewish peoplehood, nation, and community were suffused with faith in the Jewish God, ... [...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 Function (mathematics), functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear engineering, nuclear, aerospace engineering, aerospace, mechanical engineering, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is Analyticity of holomorphic functions, analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of 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 are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...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 predominates, 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 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 one in 2300 is prime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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