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Matiyasevich
Yuri Vladimirovich Matiyasevich, (russian: Ю́рий Влади́мирович Матиясе́вич; born 2 March 1947 in Leningrad) is a Russian mathematician and computer scientist. He is best known for his negative solution of Hilbert's tenth problem (Matiyasevich's theorem), which was presented in his doctoral thesis at LOMI (the Leningrad Department of the Steklov Institute of Mathematics). Biography * In 1962–1963, Matiyasevich studied at Saint Petersburg Lyceum 239; * In 1963–1964, he studied aKolmogorov School in 1964 he was the absolute winner of the All-Union Olympiad in mathematics * In 1964–1969, Matiyasevich studied at thMathematics & Mechanics Facultyof Leningrad State University. By qualifying for the USSR team for the International Mathematical Olympiad (where he won a gold medal), Yuri Matiyasevich was accepted without exams to Leningrad State University, skipping the last year of high school studies. * In 1966, he presented a talk at Internatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matiyasevich's Theorem
In mathematics, a Diophantine equation is an equation of the form ''P''(''x''1, ..., ''x''''j'', ''y''1, ..., ''y''''k'') = 0 (usually abbreviated ''P''(', ') = 0) where ''P''(', ') is a polynomial with integer coefficients, where ''x''1, ..., ''x''''j'' indicate parameters and ''y''1, ..., ''y''''k'' indicate unknowns. A Diophantine set is a subset ''S'' of \mathbb^j, the set of all ''j''-tuples of natural numbers, so that for some Diophantine equation ''P''(', ') = 0, :\bar \in S \iff (\exists \bar \in \mathbb^)(P(\bar,\bar)=0) . That is, a parameter value is in the Diophantine set ''S'' if and only if the associated Diophantine equation is satisfiable under that parameter value. The use of natural numbers both in ''S'' and the existential quantification merely reflects the usual applications in computability and model theory. It does not matter whether natural numbers refer to the set of nonnegative integers or positive integers since the two definitions for Diophantine set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert's Tenth Problem
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm which, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values. For example, the Diophantine equation 3x^2-2xy-y^2z-7=0 has an integer solution: x=1,\ y=2,\ z=-2. By contrast, the Diophantine equation x^2+y^2+1=0 has no such solution. Hilbert's tenth problem has been solved, and it has a negative answer: such a general algorithm does not exist. This is the result of combined work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson which spans 21 years, with Matiyasevich completing the theorem in 1970. The theorem is now known as Matiyasevich's theorem or the MRDP theorem (an initialism for the surnames of the four principal contributo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petersburg Mathematical Society
The Saint Petersburg Mathematical Society (russian: Санкт-Петербургское математическое общество) is a mathematical society run by Saint Petersburg mathematicians. Historical notes The St. Petersburg Mathematical Society was founded in 1890 and was the third founded mathematical society in Russia after those of Moscow (1867) and Khar'kov (1879)... Its founder and first president was Vasily Imshenetskii, who also had founded earlier the Khar'kov Mathematical Society. The Society was dissolved and subsequently revived twice, each time changing its name: sometime in between 1905 and 1917, the society ceased to function and by 1917 it had completely dissolved, perhaps due to the social agitations that destroyed many existing Russian scientific institutions. It was re-established by the initiative of Alexander Vasilyev in 1921 as the Petrograd Physical and Mathematical Society (subsequently called the Leningrad Physical and Mathematical Soci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leningrad Mathematical Society
The Saint Petersburg Mathematical Society (russian: Санкт-Петербургское математическое общество) is a mathematical society run by Saint Petersburg mathematicians. Historical notes The St. Petersburg Mathematical Society was founded in 1890 and was the third founded mathematical society in Russia after those of Moscow (1867) and Khar'kov (1879)... Its founder and first president was Vasily Imshenetskii, who also had founded earlier the Khar'kov Mathematical Society. The Society was dissolved and subsequently revived twice, each time changing its name: sometime in between 1905 and 1917, the society ceased to function and by 1917 it had completely dissolved, perhaps due to the social agitations that destroyed many existing Russian scientific institutions. It was re-established by the initiative of Alexander Vasilyev in 1921 as the Petrograd Physical and Mathematical Society (subsequently called the Leningrad Physical and Mathematical Soci ... [...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 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 analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg Lyceum 239
Presidential Physics and Mathematics Lyceum No. 239 (russian: link=no, Президентский физико-математический лицей №239), is a public high school in Saint Petersburg, Russia that specializes in mathematics and physics. The school opened in 1918 and it became a specialized city school in 1961. The school is noted for its strong academic programs. It is the alma mater of numerous winners of International Mathematical Olympiads and it has produced many notable alumni. The lyceum has been named the best school in Russia in 2015, 2016, and 2017. History The school was founded in 1918. Originally, it was located in the Lobanov-Rostovsky Palace, also known as "house with lions" at the corner of Saint Isaac's Square and Admiralteysky Prospect. It was one of only handful of schools to remain open during Siege of Leningrad. In 1961 the school was granted status of city's school with specialization in physics and mathematics. In 1964 the school m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Student Olympiads
Soviet Student Olympiad was an annual set of contests for students in USSR. There were two separate multi-round competitions every year: for higher education (universities) and general education (starting from 7th to 10th/11th grade). Both competitions had several rounds, and winners from lower rounds would go to the next round. Not only individual members, but teams were awarded too. The main difference between two Olympiads was that the school one had separate threads for every grade, while the university one was for all students. Contest format Both Olympiads had the same format of the contests. Students would come in teams representing their location, e.g. schools or republics. Each contest could have 2-3 parts. For instance, the Republican round of University Olympiads on physics could have three parts: theory, lab and computer modeling. All students were given the same set of problems to solve. They would work on solutions strictly individually - no teamwork was allowed - and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Academy Of Sciences
The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such as libraries, publishing units, and hospitals. Peter the Great established the Academy (then the St. Petersburg Academy of Sciences) in 1724 with guidance from Gottfried Leibniz. From its establishment, the Academy benefitted from a slate of foreign scholars as professors; the Academy then gained its first clear set of goals from the 1747 Charter. The Academy functioned as a university and research center throughout the mid-18th century until the university was dissolved, leaving research as the main pillar of the institution. The rest of the 18th century continuing on through the 19th century consisted of many published academic works from Academy scholars and a few Ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the '' variety of groups''. History Before the nineteenth century, alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Engineering
Software engineering is a systematic engineering approach to software development. A software engineer is a person who applies the principles of software engineering to design, develop, maintain, test, and evaluate computer software. The term '' programmer'' is sometimes used as a synonym, but may also lack connotations of engineering education or skills. Engineering techniques are used to inform the software development process which involves the definition, implementation, assessment, measurement, management, change, and improvement of the software life cycle process itself. It heavily uses software configuration management which is about systematically controlling changes to the configuration, and maintaining the integrity and traceability of the configuration and code throughout the system life cycle. Modern processes use software versioning. History Beginning in the 1960s, software engineering was seen as its own type of engineering. Additionally, the development of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
