NationMaster - Encyclopedia: Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров) (April 25, 1903 - October 20, 1987) was a Soviet mathematician who made major advances in different academic fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity). Kolmogorov is widely considered one of the prominent mathematicians of the 20^th century. Image File history File links No higher resolution available. ... April 25 is the 115th day of the year in the Gregorian calendar (116th in leap years). ... 1900 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Friday of the 13-day slower Julian calendar. ... Image:Tambov1781. ... Imperial Russia is the term used to cover the period of history from the expansion of Russia under Peter the Great, through the expansion of the Russian Empire from the Baltic Sea to the Pacific Ocean, to the deposal of Nicholas II of Russia, the last tsar, at the start... October 20 is the 293rd day of the year (294th in leap years) in the Gregorian calendar. ... 1987 (MCMLXXXVII) was a common year starting on Thursday of the Gregorian calendar. ... Position of Moscow in Europe Coordinates: Country District Subdivision Russia Central Federal District Federal City Government - Mayor Yuriy Luzhkov Area - City 1,081 kmÂ² (417. ... Image File history File links Flag_of_Russia_(bordered). ... Imperial Russia is the term used to cover the period of history from the expansion of Russia under Peter the Great, through the expansion of the Russian Empire from the Baltic Sea to the Pacific Ocean, to the deposal of Nicholas II of Russia, the last tsar, at the start... Image File history File links Flag_of_the_Soviet_Union. ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Moscow State University M.V. Lomonosov Moscow State University (Russian: ÐœÐ¾ÑÐºÐ¾Ð²ÑÐºÐ¸Ð¹ Ð³Ð¾ÑÑƒÐ´Ð°Ñ€ÑÑ‚Ð²ÐµÐ½Ð½Ñ‹Ð¹ ÑƒÐ½Ð¸Ð²ÐµÑ€ÑÐ¸Ñ‚ÐµÑ‚ Ð¸Ð¼ÐµÐ½Ð¸ Ðœ.Ð’.Ð›Ð¾Ð¼Ð¾Ð½Ð¾ÑÐ¾Ð²Ð°, often abbreviated ÐœÐ“Ð£, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... Moscow State University M.V. Lomonosov Moscow State University (Russian: ÐœÐ¾ÑÐºÐ¾Ð²ÑÐºÐ¸Ð¹ Ð³Ð¾ÑÑƒÐ´Ð°Ñ€ÑÑ‚Ð²ÐµÐ½Ð½Ñ‹Ð¹ ÑƒÐ½Ð¸Ð²ÐµÑ€ÑÐ¸Ñ‚ÐµÑ‚ Ð¸Ð¼ÐµÐ½Ð¸ Ðœ.Ð’.Ð›Ð¾Ð¼Ð¾Ð½Ð¾ÑÐ¾Ð²Ð°, often abbreviated ÐœÐ“Ð£, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... Nikolai N. Luzin. ... Vladimir I. Arnold (Moscow, December 2001). ... Roland Lvovich Dobrushin (Russian: Ð Ð¾Ð»Ð°Ð½Ð´ Ð›ÑŒÐ²Ð¾Ð²Ð¸Ñ‡ Ð”Ð¾Ð±Ñ€ÑƒÑˆÐ¸Ð½) (July 20, 1929, St Petersburg â€“ November 12, 1995, Moscow) was a Russian mathematician and probability theorist who made important contributions to probability theory, point process theory, mathematical physics, and information theory. ... Eugene Borisovich Dynkin (born May 11, 1924) is a Russian mathematician. ... Israel Moiseevich Gelfand (Ð˜Ð·Ñ€Ð°Ð¸Ð»ÑŒ ÐœÐ¾Ð¸ÑÐµÐµÐ²Ð¸Ñ‡ Ð“ÐµÐ»ÑŒÑ„Ð°Ð½Ð´) (born in 1913) is a prolific mathematician in the field of functional analysis, which he interprets in a broad sense as the mathematics of quantum mechanics. ... Leonid Levin (born November 2, 1948, USSR) is a computer scientist. ... Per Martin-LÃ¶f 2004 Per Martin-LÃ¶f is a Swedish logician, philosopher, and mathematician born in 1942. ... Yakov G. Sinai (1935-) is a Russian- American mathematician. ... Albert N. Shiryaev Albert Nikolayevich Shiryaev (ÐÐ»ÑŒÐ±ÐµÑ€Ñ‚ ÐÐ¸ÐºÐ¾Ð»Ð°ÐµÐ²Ð¸Ñ‡ Ð¨Ð¸Ñ€ÑÐµÐ², born October 12, 1934) is a well-known Russian Mathematician. ... Probability theory is a branch of mathematics concerned with analysis of random phenomena. ... A MÃ¶bius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... Analysis is the branch of mathematics most explicitly concerned with the notion of a limit, either the limit of a sequence or the limit of a function. ... Stalin Prize medal State Prize medal The USSR State Prize (Russian:Ð“Ð¾ÑÑƒÐ´Ð°ÌÑ€ÑÑ‚Ð²ÐµÐ½Ð½Ð°Ñ Ð¿Ñ€ÐµÌÐ¼Ð¸Ñ Ð¡Ð¡Ð¡Ð ) was the Soviet Unions highest civilian honour. ... The International Balzan Prize Foundation awards four annual monetary prizes to people or organisations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the brotherhood of man. ... Lenin Prize (Russian: Ле́нинская пре́мия) was one of the highest awards in the Soviet Union. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples . ... Lobachevsky Medal (Lobachevsky International Prize) is a medal awarded by Kazan State University in honor of Nikolai Ivanovich Lobachevsky, who was a professor there. ... April 25 is the 115th day of the year in the Gregorian calendar (116th in leap years). ... 1900 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Friday of the 13-day slower Julian calendar. ... October 20 is the 293rd day of the year (294th in leap years) in the Gregorian calendar. ... 1987 (MCMLXXXVII) was a common year starting on Thursday of the Gregorian calendar. ... Soviet redirects here. ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Probability theory is a branch of mathematics concerned with analysis of random phenomena. ... A MÃ¶bius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ...

Early life

Kolmogorov was born at Tambov in 1903. His mother died in childbirth and he was raised by his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a wealthy nobleman. His father, an agronomist by trade, was deported from Saint-Petersburg for participation in the revolutionary movement. He went missing in the Russian Civil War. Image:Tambov1781. ... Tunoshna (also Tunoshnoye, or Tunoschna) (Russian: ) (IATA: IAR, ICAO: UUDL) is an airport in Yaroslavl Oblast, Russia located 18 km southeast of Yaroslavl. ... Yaroslavl (Russian: ) is a city in Russia, the administrative center of Yaroslavl Oblast, located 250 km north-east of Moscow at . ... An Estate comprises the houses and outbuildings and supporting farmland and woods that surround the gardens and grounds of a very large property, such as a country house or mansion. ... Agricultural science (also called agronomy) is a broad multidisciplinary field that encompasses the parts of exact, natural, economic, and social sciences that are used in the practice and understanding of agriculture. ... â€œLeningradâ€ redirects here. ... Combatants Red Army Latvian Riflemen White Army (Monarchists) Ukrainian Peoples Republic Green Army (Cossacks) Black Army (Anarchists) Blue Army (Peasants) Czechoslovak Legion Allied intervention Other anti-Bolshevik forces Commanders Leon Trotsky, Mikhail Tukhachevsky, Sergei Kamenev, Semyon Budyonny, Mikhail Frunze Alexander Antonov, Anton Denikin, Alexander Kolchak, Lavr Kornilov, Pyotr Wrangel...

Kolmogorov was educated in his aunts' village school, and his earliest literary efforts and mathematical papers were printed in the school newspaper. As an adolescent he designed perpetual motion machines, concealing their defects so cleverly that his secondary-school teachers could not discover them. In 1910 his aunt adopted him and they moved to Moscow, where he went to a gymnasium (the equivalent of a United States high school), graduating from it in 1920. This article or section should include material from Parallel Path See also Perpetuum mobile as a musical term Perpetual motion machines (the Latin term perpetuum mobile is not uncommon) are a class of hypothetical machines which would produce useful energy in a way science cannot explain (yet). ... Position of Moscow in Europe Coordinates: Country District Subdivision Russia Central Federal District Federal City Government - Mayor Yuriy Luzhkov Area - City 1,081 kmÂ² (417. ...

In 1920 Kolmogorov began to study at Moscow University and the Chemistry Technological Institute. Kolmogorov gained a reputation for his wide-ranging erudition. As an undergraduate, he participated in the seminar of Russian historian S.V. Bachrushin and published his first research paper on landholding practices in the Novgorod Republic in the fifteenth and sixteenth centuries.^[1] A the same time (1921-1922), Kolmogorov obtained several results in set theory and the theory of trigonometrical series. Moscow State University M.V. Lomonosov Moscow State University (Russian: ÐœÐ¾ÑÐºÐ¾Ð²ÑÐºÐ¸Ð¹ Ð³Ð¾ÑÑƒÐ´Ð°Ñ€ÑÑ‚Ð²ÐµÐ½Ð½Ñ‹Ð¹ ÑƒÐ½Ð¸Ð²ÐµÑ€ÑÐ¸Ñ‚ÐµÑ‚ Ð¸Ð¼ÐµÐ½Ð¸ Ðœ.Ð’.Ð›Ð¾Ð¼Ð¾Ð½Ð¾ÑÐ¾Ð²Ð°, often abbreviated ÐœÐ“Ð£, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... An historian is someone who writes history, a written accounting of the past. ... Landowner or Landholder is a holder of the estate in land with considerable rights of ownership or, simply put, an owner of land. ... Velikiy Novgorod (Russian: ) is the foremost historic city of North-Western Russia, situated on the M10(E95) federal highway connecting Moscow and St. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... The Fourier series is a mathematical tool used for analyzing periodic functions by decomposing such a function into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. ...

Maturity

In 1922 Kolmogorov constructed a Fourier series that diverges almost everywhere, gaining international recognition. Around this time he decided to devote his life to mathematics. In 1925 Kolmogorov graduated from Moscow State University, and began to study under the supervision of Nikolai Luzin. He made lifelong friends with Pavel Alexandrov who involved Kolmogorov in 1936 in an ugly political persecution of their mutual teacher, the so-called Luzin case or Luzin affair. Kolmogorov (together with A. Khinchin) became interested in probability theory. Also in 1925, he published his famous work in intuitionistic logic - On the principle of the excluded middle. In 1929 Kolmogorov earned his Ph.D. at Moscow State University. Year 1922 (MCMXXII) was a common year starting on Sunday (link will display full calendar). ... The Fourier series is a mathematical tool used for analyzing periodic functions by decomposing such a function into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. ... In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a limit. ... In measure theory (a branch of mathematical analysis), one says that a property holds almost everywhere if the set of elements for which the property does not hold is a null set, i. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Year 1925 (MCMXXV) was a common year starting on Thursday (link will display the full calendar) of the Gregorian calendar. ... Moscow State University M.V. Lomonosov Moscow State University (Russian: ÐœÐ¾ÑÐºÐ¾Ð²ÑÐºÐ¸Ð¹ Ð³Ð¾ÑÑƒÐ´Ð°Ñ€ÑÑ‚Ð²ÐµÐ½Ð½Ñ‹Ð¹ ÑƒÐ½Ð¸Ð²ÐµÑ€ÑÐ¸Ñ‚ÐµÑ‚ Ð¸Ð¼ÐµÐ½Ð¸ Ðœ.Ð’.Ð›Ð¾Ð¼Ð¾Ð½Ð¾ÑÐ¾Ð²Ð°, often abbreviated ÐœÐ“Ð£, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... Nikolai N. Luzin. ... Pavel Sergeevich Alexandrov (Па́вел Серге́евич Алекса́ндров, sometimes romanized Alexandroff or Aleksandrov) (born May 7, 1896 - died November 16, 1982) was a Russian mathematician. ... Aleksandr Ya. ... Probability theory is a branch of mathematics concerned with analysis of random phenomena. ... Year 1925 (MCMXXV) was a common year starting on Thursday (link will display the full calendar) of the Gregorian calendar. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... 1929 (MCMXXIX) was a common year starting on Tuesday (link will take you to calendar). ... Doctor of Philosophy (Ph. ... Moscow State University M.V. Lomonosov Moscow State University (Russian: ÐœÐ¾ÑÐºÐ¾Ð²ÑÐºÐ¸Ð¹ Ð³Ð¾ÑÑƒÐ´Ð°Ñ€ÑÑ‚Ð²ÐµÐ½Ð½Ñ‹Ð¹ ÑƒÐ½Ð¸Ð²ÐµÑ€ÑÐ¸Ñ‚ÐµÑ‚ Ð¸Ð¼ÐµÐ½Ð¸ Ðœ.Ð’.Ð›Ð¾Ð¼Ð¾Ð½Ð¾ÑÐ¾Ð²Ð°, often abbreviated ÐœÐ“Ð£, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ...

In 1930 Kolmogorov went on his first long trip abroad, traveling to Göttingen, Munich, and then to Paris. His pioneering work About the Analytical Methods of Probability Theory was published (in German) in 1931, the same year he became a professor at Moscow University. In 1933 Kolmogorov published Foundations of the Theory of Probability, laying the modern foundations of probability theory and establishing his reputation as one of the world's experts in this field. In 1935, Kolmogorov became the first chair of probability theory at the Faculty of Mathematics and Mechanics of Moscow State University. In 1939 he was elected a full member (academician) of the USSR Academy of Sciences. In a 1938 paper he "established the basic theorems for smoothing and predicting stationary stochastic processes"^[2] — a paper that would have major military applications during the Cold War to come. Year 1930 (MCMXXX) was a common year starting on Wednesday (link will display 1930 calendar) of the Gregorian calendar. ... GÃ¶ttingen marketplace with old city hall, GÃ¤nseliesel fountain and pedestrian zone GÃ¶ttingen ( ) is a city in Lower Saxony, Germany. ... Munich (German: , pronounced ; Austro-Bavarian: Minga [1]) is the capital of the German Federal State of Bavaria. ... City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) Paris Eiffel tower as seen from the esplanade du TrocadÃ©ro. ... 1931 (MCMXXXI) was a common year starting on Thursday (link is to a full 1931 calendar). ... 1933 (MCMXXXIII) was a common year starting on Sunday. ... It has been suggested that this article or section be merged with Probability theory. ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will display full calendar). ... // Although lectures in mathematics have been delivered since Moscow State University was founded in 1755, the separate mathematical and physical department was founded only in 1804. ... Moscow State University M.V. Lomonosov Moscow State University (Russian: ÐœÐ¾ÑÐºÐ¾Ð²ÑÐºÐ¸Ð¹ Ð³Ð¾ÑÑƒÐ´Ð°Ñ€ÑÑ‚Ð²ÐµÐ½Ð½Ñ‹Ð¹ ÑƒÐ½Ð¸Ð²ÐµÑ€ÑÐ¸Ñ‚ÐµÑ‚ Ð¸Ð¼ÐµÐ½Ð¸ Ðœ.Ð’.Ð›Ð¾Ð¼Ð¾Ð½Ð¾ÑÐ¾Ð²Ð°, often abbreviated ÐœÐ“Ð£, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... 1939 (MCMXXXIX) was a common year starting on Sunday (link will display full year calendar). ... Russian Academy of Sciences: main building Russian Academy of Sciences (Ð Ð¾ÑÑÐ¸ÌÐ¹ÑÐºÐ°Ñ ÐÐºÐ°Ð´ÐµÌÐ¼Ð¸Ñ ÐÐ°ÑƒÌÐº) is the national academy of Russia. ... In the mathematics of probability, a stochastic process can be thought of as a random function. ... For other uses, see Cold War (disambiguation). ...

Later on, Kolmogorov switched his research interests to the area of turbulence, where his 1941 works has significant influence on the field. In classical mechanics he is best known for the KAM theory (first presented in 1954 in Amsterdam, during the International Congress of Mathematicians). In 1957 he solved Hilbert's thirteenth problem (a joint work with his student V. I. Arnold). He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time. Image File history File links Size of this preview: 800 Ã— 539 pixels Full resolution (1398 Ã— 942 pixel, file size: 88 KB, MIME type: image/jpeg) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Andrey Kolmogorov ... Image File history File links Size of this preview: 800 Ã— 539 pixels Full resolution (1398 Ã— 942 pixel, file size: 88 KB, MIME type: image/jpeg) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Andrey Kolmogorov ... County Harju County Mayor JÃ¼ri Ratas Area 159. ... State motto: KÃµigi maade proletaarlased, Ã¼hinege (Translated: Workers of the world, unite!) Official language Estonian, Russian (de facto) Capital Tallinn Chairman of the Supreme Council Arnold RÃ¼Ã¼tel (at the time of regaining independence) Established In the USSR: - Since - Until July 21, 1940 August 6, 1940 August 20, 1991... Image File history File links Size of this preview: 800 Ã— 557 pixels Full resolution (1302 Ã— 906 pixel, file size: 73 KB, MIME type: image/jpeg) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Andrey Kolmogorov ... Image File history File links Size of this preview: 800 Ã— 557 pixels Full resolution (1302 Ã— 906 pixel, file size: 73 KB, MIME type: image/jpeg) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Andrey Kolmogorov ... County Harju County Mayor JÃ¼ri Ratas Area 159. ... State motto: KÃµigi maade proletaarlased, Ã¼hinege (Translated: Workers of the world, unite!) Official language Estonian, Russian (de facto) Capital Tallinn Chairman of the Supreme Council Arnold RÃ¼Ã¼tel (at the time of regaining independence) Established In the USSR: - Since - Until July 21, 1940 August 6, 1940 August 20, 1991... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... For the movie, see 1941 (film). ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... The Kolmogorovâ€“Arnoldâ€“Moser theorem is a result in dynamical systems about the persistence of quasi-periodic motions under small perturbations. ... Year 1954 (MCMLIV) was a common year starting on Friday (link will display full calendar) of the Gregorian calendar. ... Nickname: Motto: Heldhaftig, Vastberaden, Barmhartig (Valiant, Determined, Compassionate) Location of Amsterdam Coordinates: Country Netherlands Province North Holland Government - Mayor Job Cohen (PvdA) - Aldermen Lodewijk Asscher Hennah Buyne Carolien Gehrels Tjeerd Herrema Maarten van Poelgeest Marijke Vos - Secretary Erik Gerritsen Area [1][2] - City 219 kmÂ² (84. ... The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... 1957 (MCMLVII) was a common year starting on Tuesday of the Gregorian calendar. ... 21. ... Vladimir I. Arnold (Moscow, December 2001). ... Algorithmic information theory is a field of study which attempts to capture the concept of complexity by using tools from theoretical computer science. ... In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. ...

Kolmogorov married Anna Dmitrievna Egorova in 1942. He pursued a vigorous teaching routine throughout his life, not only at the university level but also with younger children, as he was actively involved in developing a pedagogy for gifted children, in literature and music as well as mathematics. At the University, he occupied different positions, including the head of several departments (probability, statistics and random processes, mathematical logic) and also served as dean of the Faculty of Mechanics and Mathematics. Gifted children are those considered by educational systems to have significantly higher than normal levels of one or more forms of intelligence. ... Old book bindings at the Merton College library. ... For other uses, see Music (disambiguation). ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Probability is the chance that something is likely to happen or be the case. ... A graph of a Normal bell curve showing statistics used in educational assessment and comparing various grading methods. ... In the mathematics of probability, a stochastic process can be thought of as a random function. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... // Although lectures in mathematics have been delivered since Moscow State University was founded in 1755, the separate mathematical and physical department was founded only in 1804. ...

In 1971 he joined an oceanographic expedition aboard the research vessel Dmitri Mendeleev. He wrote a number of articles for the Great Soviet Encyclopedia. In his later years he devoted much of his effort to the mathematical and philosophical relationship between probability theory in abstract and applied areas.^[3] Thermohaline circulation Oceanography (from Ocean + Greek Î³ÏÎ¬Ï†ÎµÎ¹Î½ = write), also called oceanology or marine science, is the branch of Earth Sciences that studies the Earths oceans and seas. ... Title page of the 3rd ed. ... Probability theory is a branch of mathematics concerned with analysis of random phenomena. ...

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See also

The probability of some event (denoted ) is defined with respect to a universe or sample space of all possible elementary events in such a way that must satisfy the Kolmogorov axioms. ... The Kolmogorov backward equation (KBE) and its adjoint the Kolmogorov forward equation (KFE) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. ... The Fokker-Planck equation (named after Adriaan Fokker and Max Planck; also known as the Kolmogorov Forward equation) describes the time evolution of the probability density function of position and velocity of a particle, but it can be generalized to any other observable, too. ... In fractal geometry, the Minkowski-Bouligand dimension or Minkowski dimension is a way of determining the fractal dimension of a set S in a Euclidean space , or more generally of a metric space (X,d). ... In fractal geometry, the Minkowski-Bouligand dimension or Minkowski dimension is a way of determining the fractal dimension of a set S in a Euclidean space , or more generally of a metric space (X,d). ... In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. ... In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constrains on the moments of its increments will be continuous (or, more precisely, have a continuous version). It is credited to the Soviet mathematician Andrey Nikolaevich Kolmogorov. ... In mathematics, the Kolmogorov extension theorem is a theorem that guarantees that a suitably consistent collection of finite-dimensional distributions will define a stochastic process. ... In probability theory, Kolmogorovs inequality is a so-called maximal inequality that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. ... Landau-Kolmogorov inequality is an inequality between different derivatives of a function. ... There are very few or no other articles that link to this one. ... In topology and related branches of mathematics, the T0 spaces or Kolmogorov spaces, named after Andrey Kolmogorov, form a broad class of well-behaved topological spaces. ... In statistics, the Kolmogorov-Smirnov test (often called the K-S test) is used to determine whether two underlying probability distributions differ, or whether an underlying probability distribution differs from a hypothesized distribution, in either case based on finite samples. ... The Kolmogorov-Arnold-Moser theorem is a theorem in non-linear dynamics that solves the small-divisor problem in classical perturbation theory. ... In probability theory, Kolmogorovs zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a tail event, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one. ... Borels paradox (sometimes known as the Borel-Kolmogorov paradox) is a paradox of probability theory relating to conditional probability density functions. ... In mathematics, specifically in probability theory, and yet more specifically in the theory of stochastic processes, the Chapman-Kolmogorov equation is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process. ... Chaitin-Kolmogorov randomness defines a string (usually of bits) as being random if and only if it is shorter than any computer program that can produce that string. ... In mathematics, the Hahn-Kolmogorov theorem characterizes when a finitely additive function with non-negative (possibly infinite) values can be extended to a bona fide measure. ... Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ...

Bibliography

A bibliography of his works appeared in The Annals of Probability, 17(3): 945--964 (July 1989). Satellite image of part of the Rhine-Meuse delta, showing the Island of Dordrecht and the eponymous city (7) Dordrecht (population 119,649 (2004)), or in English: Dort, is a city in the Dutch province of South Holland, the third largest city of the province. ... Wolters Kluwer N.V. (Euronext: WKL) is one of the worlds leading publishers and providers of information products and services. ... Jean van Heijenoort (prounounced highenort) (July 23, 1912, Creil France - March 29, 1986, Mexico City) was a pioneer historian of mathematical logic. ...

External links

The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... The Mathematics Genealogy Project is a web-based database that gives an academic genealogy based on dissertation supervision relations. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ...

References

Categories: 20th century mathematicians | 1903 births | 1987 deaths | Alumni and faculty of Moscow State University | Erdős number 2 | Heroes of Socialist Labor | Members of the Russian Academy of Sciences | Probability theorists | Russian mathematicians | Soviet mathematicians | Stalin Prize winners | Wolf Prize recipients The premises of The Royal Society in London (first four properties only). ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... April 25 is the 115th day of the year in the Gregorian calendar (116th in leap years). ... 1900 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Friday of the 13-day slower Julian calendar. ... Image:Tambov1781. ... Imperial Russia is the term used to cover the period of history from the expansion of Russia under Peter the Great, through the expansion of the Russian Empire from the Baltic Sea to the Pacific Ocean, to the deposal of Nicholas II of Russia, the last tsar, at the start... October 20 is the 293rd day of the year (294th in leap years) in the Gregorian calendar. ... 1987 (MCMLXXXVII) was a common year starting on Thursday of the Gregorian calendar. ... Position of Moscow in Europe Coordinates: Country District Subdivision Russia Central Federal District Federal City Government - Mayor Yuriy Luzhkov Area - City 1,081 kmÂ² (417. ...

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