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Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest to Artúr Rényi and Borbála Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic Bernhard Alexander; his uncle was Franz Alexander, a Hungarian-American psychoanalyst and physician. He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the University of Budapest in 1940 and finished his studies in 1944. At this point, he was drafted to forced labour service, from which he managed to escape during transportation of his company. He was in hiding with false documents for six months. Biographers tell an incredible story about Rényi: after half of a year in hiding, he managed to get hold of a soldier's uniform and march ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Alexander
Franz Gabriel Alexander (; born Alexander Ferenc Gábor, ; 22 January 1891 – 8 March 1964) was a Hungarian-American psychoanalyst and physician, who is considered one of the founders of psychosomatic medicine and psychoanalytic criminology. Life Alexander was born into a Jewish family in Budapest, Austria-Hungary, in 1891, his father was Bernhard Alexander, a philosopher and literary critic, his nephew was Alfréd Rényi, a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory. Alexander studied in Berlin; there he was part of an influential group of German analysts mentored by Karl Abraham, including Karen Horney and Helene Deutsch, and gathered around the Berlin Psychoanalytic Institute. 'In the early 1920s, Oliver Freud was in analysis with Franz Alexander' there (Sigmund Freud's son) while 'Charles Odier, one of the first among French psychoanalysts, was analysed in Berlin by Franz Alexander' as wel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, Neuroscience, neurobiology, physics, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a Fair coin, fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a dice, die (which has six equally likely outcomes). Some other important measu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goldbach Conjecture
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold for all integers less than but remains unproven despite considerable effort. History Origins On 7 June 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII), in which he proposed the following conjecture: Goldbach was following the now-abandoned convention of considering 1 to be a prime number, so that a sum of units would be a sum of primes. He then proposed a second conjecture in the margin of his letter, which implies the first: Euler replied in a letter dated 30 June 1742 and reminded Goldbach of an earlier conversation they had had (""), in which Goldbach had remarked that the first of those two conjectures would follow from the statement This is in fact equivalent to his seco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen's Theorem
In number theory, Chen's theorem states that every sufficiently large parity (mathematics), even number can be written as the sum of either two prime number, primes, or a prime and a semiprime (the product of two primes). It is a weakened form of Goldbach's conjecture, which states that every even number is the sum of two primes. History The theorem was first stated by China, Chinese mathematician Chen Jingrun in 1966, with further details of the mathematical proof, proof in 1973. His original proof was much simplified by P. M. Ross in 1975. Chen's theorem is a significant step towards Goldbach's conjecture, and a celebrated application of sieve theory, sieve methods. Chen's theorem represents the strengthening of a previous result due to Alfréd Rényi, who in 1947 had shown there exists a finite ''K'' such that any even number can be written as the sum of a prime number and the product of at most ''K'' primes. Variations Chen's 1973 paper stated two results with nearly i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorization, factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Sieve
The large sieve is a method (or family of methods and related ideas) in analytic number theory. It is a type of sieve where up to half of all residue classes of numbers are removed, as opposed to small sieves such as the Selberg sieve wherein only a few residue classes are removed. The method has been further heightened by the larger sieve which removes arbitrarily many residue classes. Name Its name comes from its original application: given a set S \subset \ such that the elements of ''S'' are forbidden to lie in a set ''Ap'' ⊂ Z/''p'' Z modulo every prime ''p'', how large can ''S'' be? Here ''A''''p'' is thought of as being large, i.e., at least as large as a constant times ''p''; if this is not the case, we speak of a ''small sieve''. History The early history of the large sieve traces back to work of Yu. B. Linnik, in 1941, working on the problem of the least quadratic non-residue. Subsequently Alfréd Rényi worked on it, using probability methods. It was only two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungarian Academy Of Sciences
The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primary functions include the advancement of scientific knowledge, the dissemination of research findings, the support of research and development, and the representation of science in Hungary both domestically and around the world. History The origins of the Hungarian Academy of Sciences date back to 1825, when Count István Széchenyi offered one year's income from his estate to establish a ''Learned Society''. He made this offer during a session of the Diet in Pressburg (Pozsony, now Bratislava), then the seat of the Hungarian Parliament. Inspired by his gesture, other delegates soon followed suit. The Society’s mission was defined as the development of the Hungarian language and the promotion of sciences and the arts in the Hungarian l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Rényi Institute Of Mathematics
The Alfréd Rényi Institute of Mathematics () is the research institute in mathematics of the Hungarian Academy of Sciences. It was created in 1950 by Alfréd Rényi, who directed it until his death. Since its creation, the institute has been the center of mathematical research in Hungary. It received the title ''Centre of Excellence of the European Union'' (2001). The current director is András Stipsicz. The institute publishes the research journal Studia Scientiarum Mathematicarum Hungarica. Research divisions and research groups * Algebra (head: Mátyás Domokos) * Algebraic geometry and differential topology (head: András Némethi) * Algebraic Logic (head: Hajnal Andréka) * Analysis (head: András Kroó) * Combinatorics and discrete mathematics (head: Ervin Győri) * Geometry (head: Gábor Fejes Tóth) * Number theory (head: János Pintz) * Probability & statistics (head: Péter Major) * Set theory and general topology (head: Lajos Soukup) * Cryptology (head: Gábo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Debrecen
The University of Debrecen ( ) is a university located in Debrecen, Hungary. It is the oldest continuously operating institution of higher education in Hungary ever since its establishment in 1538. The university has a well established programme in the English language for international students, particularly in the Medical and Engineering field, which first established education in English in 1886. There are nearly 6000 international students studying at the university. Until 2014 technical Academy Awards (Oscars) have been awarded to five former students. The university also operates an associated Basic Medicine campus in Geochang County, South Korea. History The early formation Higher education began in Debrecen with the Calvinist College of Debrecen, which was founded in 1538. Over centuries of its existence it was one of the key institutions of higher education in Hungary. In the beginning of the 20th century the college was transformed into a university, and has a st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuri Linnik
Yuri Vladimirovich Linnik (; January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics. Biography Linnik was born in Bila Tserkva, in present-day Ukraine. He went to Saint Petersburg University where his supervisor was Vladimir Tartakovsky, and later worked at that university and the Steklov Institute. He was a member of the Academy of Sciences of the Soviet Union, as was his father, Vladimir Pavlovich Linnik. He was awarded both Stalin and Lenin Prizes. He died in Leningrad. Work in number theory * Linnik's theorem in analytic number theory * The dispersion method (which allowed him to solve the Titchmarsh problem). * The large sieve (which turned out to be extremely influential). * An elementary proof of the Hilbert-Waring theorem; see also Schnirelmann density. * The Linnik ergodic method, see , which allowed him to study the distribution properties of the representations of integers by integr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
St Petersburg
Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland on the Baltic Sea. The city had a population of 5,601,911 residents as of 2021, with more than 6.4 million people living in the Saint Petersburg metropolitan area, metropolitan area. Saint Petersburg is the List of European cities by population within city limits, fourth-most populous city in Europe, the List of cities and towns around the Baltic Sea, most populous city on the Baltic Sea, and the world's List of northernmost items#Cities and settlements, northernmost city of more than 1 million residents. As the former capital of the Russian Empire, and a Ports of the Baltic Sea, historically strategic port, it is governed as a Federal cities of Russia, federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
