Andrey Markov
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Andrei Andreevich Markov
(1856–1922; b. Ryazan, Russia; d. St Petersburg, Russia) Russian mathematician. Markov was educated at St Petersburg U (where one teacher was Chebyshev). On graduation, he joined the staff and specialized in probability. Markov's outstanding contribution was the idea underlying Markov processes. He is also remembered for his contribution to the mathematics of linear models through the Gauss–Markov theorem. A lunar crater is named after him.
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Andrey Andreyevich Markov
Russian mathematician (1856–1922)
Born at Ryazan in Russia, Markov studied at the University of St. Petersburg and later held a variety of teaching posts at the same university, eventually becoming a professor in 1893. He was an extremely enthusiastic and effective teacher. His mathematical interests were very wide, ranging over number theory, the theory of continued fractions, and differential equations. It was, however, his work in probability theory that constituted his most profound and enduring contribution to mathematics.
Among Markov's teachers was the eminent Russian mathematician Pafnuti Chebyshev, whose central interest was in probability. One of Markov's first pieces of important research centered on a key theorem of Chebyshev's – ‘the central limit theorem’. He was able to show that Chebyshev's supposed proof of this result was erroneous, and to provide his own, correct, proof of a version of the theorem of much greater generality than that attempted by Chebyshev. In 1900 Markov published his important and influential textbook Probability Calculus, and by 1906 he had arrived at the fundamentally new concept of a Markov chain. A sequence of random variables is a Markov chain if the two probabilities conditioned on different amounts of information about the early part of the sequence are the same. This aspect of Markov's work gave a major impetus to the subject of stochastic processes.
The great importance of Markov's work was that it enabled probability theory to be applied to a very much wider range of physical phenomena than had previously been possible. As a result of his work a whole range of subjects, among them genetics and such statistical phenomena as the behavior of molecules, became amenable to mathematical probabilistic treatment.
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Andrey Markov
For other people named Andrey Markov, see Andrey Markov (disambiguation).
| Andrey (Andrei) Andreyevich Markov | |
|---|---|
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| Born | 14 June 1856 N.S. Ryazan, Russian Empire |
| Died | 20 July 1922 (aged 66) Petrograd, Russian SFSR |
| Residence | Russia |
| Nationality | Russian |
| Fields | Mathematician |
| Institutions | St Petersburg University |
| Alma mater | St Petersburg University |
| Doctoral advisor | Pafnuty Chebyshev |
| Doctoral students | |
| Known for | Markov chains; Markov processes |
Andrey (Andrei) Andreyevich Markov (Russian: Андре́й Андре́евич Ма́рков) (14 June 1856 N.S. – 20 July 1922) was a Russian mathematician. He is best known for his work on theory of stochastic processes. A primary subject of his research later became known as Markov chains.
He and his younger brother Vladimir Andreevich Markov (1871–1897) proved Markov brothers' inequality. His son, another Andrey Andreevich Markov (1903–1979), was also a notable mathematician, making contributions to constructive mathematics and recursive function theory.
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Biography
Andrey Andreyevich Markov was born in Ryazan as the son of the secretary of the public forest management of Ryazan, Andrey Grigorevich Markov, and his first wife Nadezhda Petrovna Markova.
In the beginning of the 1860s Andrey Grigorevich moved to St. Petersburg to become an asset manager of the princess Ekaterina Aleksandrovna Valvatyeva.
In 1866, Andrey Andreevich's school life began with his entrance into St. Petersburg's fifth grammar school. Already during his school time Andrey was intensely engaged in higher mathematics. As a 17-year-old grammar school student, he informed Bunyakovsky, Korkin, and Yegor Zolotarev about an apparently new method to solve linear ordinary differential equations and was invited to the so-called Korkin Saturdays, where Korkin's students regularly met. In 1874, he finished the school and began his studies at the physico-mathematical faculty of St. Petersburg University.
Among his teachers were Yulian Sokhotski (differential calculus, higher algebra), Konstantin Posse (analytic geometry), Yegor Zolotarev (integral calculus), Pafnuty Chebyshev (number theory, probability theory), Aleksandr Korkin (ordinary and partial differential equations), Okatov (mechanism theory), Osip Somov (mechanics), and Budaev (descriptive and higher geometry).
In 1877, he was awarded the gold medal for his outstanding solution of the problem "About Integration of Differential Equations by Continuous Fractions with an Application to the Equation 
". In the following year, he passed the candidate examinations and remained at the university to prepare for the lecturer's position.
In April 1880, Markov defended his Master's thesis "About Binary Quadratic Forms with Positive Determinant", which was encouraged by Aleksandr Korkin and Yegor Zolotarev.
Five years later, in January 1885, there followed his doctoral thesis "About Some Applications of Algebraic Continuous Fractions".
His pedagogical work began after the defense of his Master's thesis in autumn 1880. As a privatdozent he lectured on differential and integral calculus. Later he lectured alternately on "introduction to analysis", probability theory (succeeding Chebyshev who had left the university in 1882) and calculus of differences. From 1895/96 until 1905 he also lectured on differential calculus.
One year after the defense of his doctoral thesis, he was appointed extraordinary professor (1886) and in the same year he was elected adjunct to the Academy of Sciences. In 1890, after the death of Viktor Bunyakovsky, Markov became an extraordinary member of the academy. His promotion to an ordinary professor of St Petersburg University followed in autumn 1894.
In 1896, he was elected an ordinary member of the academy as the successor of Chebyshev. In 1905, he was appointed merited professor and was granted the right to retire, which he did immediately. Until 1910, however, he continued to lecture on the calculus of differences.
In connection with student riots in 1908, professors and lecturers of St. Petersburg University were ordered to monitor their students. Markov refused to accept this decree and wrote an explanation in which he declined to be an "agent of the governance". Markov was rejected from further teaching activity at St. Petersburg University, and he eventually decided to retire from the university.
In 1913, the council of St. Petersburg elected nine scientists honorary members of the university. Markov was among them, but his election was not affirmed by the minister of education. The affirmation only occurred four years later, after the February revolution in 1917. Markov then resumed his teaching activities and lectured on probability theory and the calculus of differences until his death in 1922.
Excommunication from the Russian Orthodox Church
In 1912, Markov, protesting Leo Tolstoy's excommunication from the Russian Orthodox Church, requested that he himself be excommunicated. In response, the Church formally excommunicated him.[1]
See also
- Markov chain Monte Carlo
- Gauss-Markov theorem
- Gauss–Markov process
- Hidden Markov model
- Markov information source
- Markov number
- Markov property
- Markov's inequality
- Markov process
- Markov blanket
- Markov network
- Markov decision process
- Chebyshev–Markov–Stieltjes inequalities
- Markov algorithm
- Subjunctive possibility
Notes
- ^ G.P. Basharin, A.N. Langville, and V.A. Naumov The Life and work of A.A. Markov.
References
- А. А. Марков. "Распространение закона больших чисел на величины, зависящие друг от друга". "Известия Физико-математического общества при Казанском университете", 2-я серия, том 15, ст. 135–156, 1906.
- A.A. Markov. "Extension of the limit theorems of probability theory to a sum of variables connected in a chain". reprinted in Appendix B of: R. Howard. Dynamic Probabilistic Systems, volume 1: Markov Chains. John Wiley and Sons, 1971.
External links
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Wikimedia Commons has media related to: Andrey Markov |
- Andrey Markov at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Andrey Markov", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Markov.html.
- Biography of A.A. Markov by his son, A.A. Markov-jnr (Russian)
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