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Nikolai Bugaev

( Honored ordinary professor of mathematics at Moscow University)

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Biography Nikolai Bugaev
photo Nikolai Bugaev
Born in 1837. in Dusheti (Tiflis province), where he received his early education, and in 1847, Mr.. been sent by his father, a military doctor Caucasian troops, in the 2 nd Moscow gymnasium. At the end of her course with a gold medal, he entered the Physics and Mathematics Faculty of Moscow University, where he studied under the guidance of professors, Zernova Brashman, David, and others. After completing the course in 1859, Mr.. was left at the university to prepare for a professorship, but, . Wishing to get as applied mathematics, . enrolled in engineering school, . after, . production of officers, . in Nikolaev engineering academy, . where he attended lectures Ostrogradskii,
. In 1861, on the occasion of the temporary closure of the academy, Bugaev was seconded to the 5 th Battalion, but soon came out of retirement, he returned to Moscow University, where he passed the MA exam in 1863. defended his thesis for a master's degree "Convergence of infinite series in their appearance". In the same year, the Ministry sent abroad, where he spent about 2 1 / 2 years. Upon his return in 1866. defended his thesis for a doctorate in pure mathematics, numerical identity, which are in connection with the properties of the symbol E. From 1887 to 1891. was dean of the Faculty. Help of an erudite and literary activities Bugaev began in 1861,. in the Journal of Mathematical Sciences "Guseva, . where he placed the following articles: "Proof of Cauchy's theorem," "Proof of Wilson's theorem," "Notes on a single article of higher algebra, Serre", "Rational functions, . expressing the two roots of the cubic equation to the third,
. A new way to solve this equation "," Graphic method of tangents to the curves on the plane, "" The solution of 4-th degree "," Integration of rational fractions without the aid of decomposition, "" Notes on the theory of equal roots ". Most scientists work Bugaeva placed in "Matematicheskii Sbornik", namely: "The numerical identities, which are in connection with the properties of the symbol E" ( "Matematicheskii Sbornik", t. I); "The general theorem in number theory with one arbitrary function" ( "Matematicheskii Sbornik", t. II); "As to the rules of convergence Pommer (" Matematicheskii Sbornik ", t. II); "Euler's theorem on polyhedra, geometric properties of planar networks" (ibid.); "Some special theorems for numerical functions" ( "Matematicheskii Sbornik", t. III); "Differential Equations 1-th order" (ibid.); "Mathematics as an instrument of scientific and pedagogical" (ibid.); "Integrable differential equations of the form 1-th order" ( "Matematicheskii Sbornik", t. IV); "The doctrine of the numerical derivatives (" Matematicheskii Sbornik ", t. V and VI); "Some problems of numerical algebra" ( "Matematicheskii Sbornik", t. VII); "The numerical equation of degree 2" (Mathematical Collection, "t. VIII); "the theory of the divisibility of numbers" (ibid.); "the theory of functional equations" (ibid.); "The solution of a chess problem by numerical functions" ( "Matematicheskii Sbornik", t. IX); "Some properties of the residue and the numerical sum" ( "Mathematical Sbornik", t. X), "The solution of equations of degree 2 in the module is simply" (ibid.), "Rational functions, . are in connection with the theory of approximate square root "(ibid.)," Some applications of the theory of elliptic functions to the theory of discontinuous functions "(" Mathematical Sbornik ", . t,
. XI and XII); "A common law theory of partition of numbers" ( "Matematicheskii Sbornik", t. XII); "General Principles of calculating E. .. (x) with one independent variable" ( "Matematicheskii Sbornik", t. XII and XIII); "Properties of a numerical integral over the divider and its application. Logarithmic numerical functions "(" Matematicheskii Sbornik ", t. XIII); "Common methods of calculating the numerical integrals of divisors. Natural classification of integers and discontinuous functions "(" Mathematical Sbornik ", t. XIV); "total transformation of numerical integrals and dividers (" Matematicheskii Sbornik ", t. XIV); "the theory of convergence of the series" (ibid.), "Geometry of random variables" (ibid.), "Various applications of the beginning of the largest and lowest for the theory of algebraic functions" (ibid.), "A general theorem of the theory of algebraic curves of higher order "(" Mathematical Sbornik ", . t,
. XV); "On the equations of the fifth degree, be solved by radicals" (with Lakhtin, ibid.); "Discontinuous geometry" (ibid.); "Getting Maximum and minimum rates in the theory of differential equations. Entire particular integrals "(" Mathematical Sbornik ", t. XVI). In addition, the report of the University for 1887: "SA. Usov (bio) and in "Proceedings of the Psychological Society" for 1889: "On freedom of faith". Then at different times Bugaev published a number of pedagogical works: "Introduction to the Theory of Numbers" (Studies of the University of Moscow ")," A Guide to arithmetic ";" book of problems to arithmetic ";" Initial algebra ";" Questions to algebra ";" Initial geometry,
. Bugaev published a series of articles critical-bibliographic content in the "Bulletin des sciences mathematiques et astronomiques", published by Darboux, and several articles in the "Comptes rendus" of the Paris Academy of Sciences. Professor Bugaev was not only an active member of the Moscow Mathematical Society, but for a long time belonged to the composition of his office, fulfilling the first duty of the Secretary and then Vice-President of the society. At present, he was elected its chairman at the same time he was an honorary member of the public dissemination of technical knowledge, an indispensable member of the Society of Natural Sciences and member of Society for the Psychological and naturalists. Almost all universities in Russia are a math professor, a former student Bugaev; in Moscow - Nekrasov, in Kharkov - Andreev, in Warsaw - Sonin and Anisimov, in Kazan - Nazim, in Kiev - Pokrovsky, in Odessa - Transfiguration. In addition to these scientists became more famous deceased Baskakov and Liventsev. Scientists study Bugaeva very diverse, but most of them belong to the theory of discontinuous functions and to analyze. In studies on the theory of discontinuous functions (so-called theory of numbers), the author proceeded from the idea that pure mathematics is divided into two equal divisions: the analysis or the theory of continuous functions and the theory of discontinuous functions. These two divisions, the author believes, are fully consistent. Indeterminate analysis and theory of forms, or so-called theory of numbers correspond to the algebra of discontinuous function. In the "numerical identities etc.", "The Doctrine of the numerical derivatives" and other articles Bugaev gives for the first time a systematic exposition of the theory of discontinuous functions and specifies methods for their study. Many of the results of the author many years later, scientists confirmed Cesaro, Hermite, Gegenbauer, and other. With the help he found in the writings of the results spoken Bugaev could study the theory of some applications of elliptic functions to number theory in a very special way, . and he not only proved many unproven Liouville theorem, . but beyond that found a more complex theorems, . which can hardly have been able to withdraw without the methods of numerical analysis, these studies are in the essay "Some applications of the theory of elliptic functions",
. Work on the analysis applies his master's thesis on the convergence of the series, which provides an opportunity to get an infinite number of signs of convergence, based on the idea of conjugate series. In his work "General Principles of calculating E. .. (x) etc." Bugaev proposes a new calculus, which is in the same relation to the analysis in which the calculation of E (x) stands for the theory of numbers. Here Bugaev shows that the differential calculus, finite differences, derivational are special cases of this calculus. Solving the many new questions and giving new relations, the author gives the opportunity in previous issues to get faster solutions. In the article "Rational functions etc." given the opportunity to express the expansion of the square root of the polynomial rational functions with any desired approximation. In the writings of Education Bugaev draws attention among other things, the literary language processing, . in Taskbook Bugaev long warned specify the famous British psychologist Ben, . choosing the specific facts of many tasks, . describing various aspects of natural phenomena, . history and life,
. D. Bobylev.

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