Andrey Markov
Encyclopedia
Andrey Andreyevich Markov (June 14, 1856 N.S. – July 20, 1922) was a Russia
n mathematician
. He is best known for his work on theory of stochastic process
es. A primary subject of his research later became known as Markov chain
s.
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 on constructive mathematics and recursive function
theory.
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.
's excommunication from the Russian Orthodox Church
, requested that he himself be excommunicated. In response, the Church formally excommunicated him.
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is best known for his work on theory of stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es. A primary subject of his research later became known as Markov chain
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...
s.
He and his younger brother Vladimir Andreevich Markov
Vladimir Andreevich Markov
Vladimir Andreevich Markov was a Russian mathematician, brother of Andrey Markov. He died of tuberculosis at the age of 25.- External links :*...
(1871–1897) proved Markov brothers' inequality
Markov brothers' inequality
In mathematics, the Markov brothers' inequality is an inequality proved by Andrey Markov and Vladimir Markov. This inequality bounds the maximum of the derivatives of a polynomial on an interval in terms of the maximum of the polynomial. For k = 1 it was proved by Andrey Markov, and for k = 2,3,.....
.
His son, another Andrey Andreevich Markov
Andrey Markov (Soviet mathematician)
Andrey Andreyevich Markov Jr. was a Soviet mathematician, the son of the great Russian mathematician Andrey Andreyevich Markov Sr, and one of the key founders of the Russian school of constructive mathematics and logic...
(1903–1979), was also a notable mathematician, making contributions on constructive mathematics and recursive function
Recursive function
Recursive function may refer to:*Recursion , a procedure or subroutine, implemented in a programming language, whose implementation references itself*A total computable function, a function which is defined for all possible inputs...
theory.
Biography
Andrey Andreyevich Markov was born in RyazanRyazan
Ryazan is a city and the administrative center of Ryazan Oblast, Russia. It is located on the Oka River southeast of Moscow. Population: The strategic bomber base Dyagilevo is just west of the city, and the air base of Alexandrovo is to the southeast as is the Ryazan Turlatovo Airport...
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
Viktor Bunyakovsky
Viktor Yakovlevich Bunyakovsky was a Russian mathematician, member and later vice president of the Petersburg Academy of Sciences.He worked in theoretical mechanics and number theory , and is credited with an early discovery of the Cauchy-Schwarz inequality, proving it for the infinite dimensional...
, Korkin
Aleksandr Korkin
Aleksandr Nikolayevich Korkin was a Russian mathematician. He made contribution to the development of partial differential equations. After Chebyshev, Korkin was the most important initiator of the formation of the Saint Petersburg Mathematical School....
and Yegor Zolotarev
Yegor Ivanovich Zolotarev
Yegor Ivanovich Zolotarev was a Russian mathematician.- Biography :...
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
Saint Petersburg State University
Saint Petersburg State University is a Russian federal state-owned higher education institution based in Saint Petersburg and one of the oldest and largest universities in Russia....
.
Among his teachers were Yulian Sokhotski
Yulian Vasilievich Sokhotski
Julian Karol Sochocki was a Polish mathematician....
(differential calculus, higher algebra), Konstantin Posse (analytic geometry), Yegor Zolotarev (integral calculus), Pafnuty Chebyshev
Pafnuty Chebyshev
Pafnuty Lvovich Chebyshev was a Russian mathematician. His name can be alternatively transliterated as Chebychev, Chebysheff, Chebyshov, Tschebyshev, Tchebycheff, or Tschebyscheff .-Early years:One of nine children, Chebyshev was born in the village of Okatovo in the district of Borovsk,...
(number theory, probability theory), Aleksandr Korkin
Aleksandr Korkin
Aleksandr Nikolayevich Korkin was a Russian mathematician. He made contribution to the development of partial differential equations. After Chebyshev, Korkin was the most important initiator of the formation of the Saint Petersburg Mathematical School....
(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
Pedagogy
Pedagogy is the study of being a teacher or the process of teaching. The term generally refers to strategies of instruction, or a style of instruction....
work began after the defense of his Master's thesis in autumn 1880. As a privatdozent
Privatdozent
Privatdozent or Private lecturer is a title conferred in some European university systems, especially in German-speaking countries, for someone who pursues an academic career and holds all formal qualifications to become a tenured university professor...
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 TolstoyLeo Tolstoy
Lev Nikolayevich Tolstoy was a Russian writer who primarily wrote novels and short stories. Later in life, he also wrote plays and essays. His two most famous works, the novels War and Peace and Anna Karenina, are acknowledged as two of the greatest novels of all time and a pinnacle of realist...
's excommunication from the Russian Orthodox Church
Russian Orthodox Church
The Russian Orthodox Church or, alternatively, the Moscow Patriarchate The ROC is often said to be the largest of the Eastern Orthodox churches in the world; including all the autocephalous churches under its umbrella, its adherents number over 150 million worldwide—about half of the 300 million...
, requested that he himself be excommunicated. In response, the Church formally excommunicated him.