**History** of the "Higher Mathematics" department of Peter the Great Saint-Petersburg Polytechnic University starts from the origins of the St. Petersburg Polytechnic Institute. The draft law on the establishment of the St. Petersburg Polytechnic Institute was finally taken up by the State Council on February 4, 1902 and its state and workforce was approved on May 2, 1902 by Nicholas II. Thus, May 2, 1902 should be considered as the starting date of the formation of the "Higher Mathematics" department.

Higher Mathematics was one of the first subjects taught in the newly opened institute. The first professor and head of the department was Ivan Ivanov (1862 – 1939) until 1935. He was elected as a corresponding member of the Academy of Sciences of the USSR in 1924 and he was awarded the honorary title of Honored Scientist of the RSFSR (Russian Soviet Federative Socialist Republic) in 1933. Ivanov expertly gathered a team and tactfully led them; he directed his colleagues, among who there were many outstanding mathematicians.

Ivanov (1862 – 1939)

Since its foundation and until 1927 mathematics was taught by Professor Adamov (1972 - 1927), from 1906 to 1924 by Professor Bilibin (1879 - 1935). Professors Adamov and Gunter participated in the creation of the “collection of problems” and this work has been reprinted 13 times over the next 50 years.

Gunter (1871 - 1941)

Vinogradov (1891 - 1983) had a significant influence on the development of the department; he was an eminent scientist and educator who has worked here since 1920. He graduated from St. Petersburg University in 1914, since 1929 he was a member of the USSR Academy of Sciences, honorary member of the 15 foreign academies and scientific societies, twice Hero of Socialist Labor, laureate of Lenin Prize. The main works of Vinogradov, related to the field of use of the method for estimating trigonometric sums in number theory, created by him in 1934, was highly appreciated. Through this method, he was able to solve the famous weak (or ternary) Goldbach conjecture in 1937. Corresponding Member of the USSR Academy of Sciences, Honored Scientist of the RSFSR Gunter (1871 - 1941) joined the institute's team of mathematicians in 1926. Gunter put forward original ideas in mathematical physics, and the publication of works on this subject started in 1923. He has written many articles on the hydrodynamics of an ideal fluid and in the process of writing the classical potential theory were carried out.

Professor Kuzmin (1891 - 1949), corresponding member of the Academy of Sciences of the USSR since 1946, came to the department in 1922, managed it from 1945 to 1949. His scientific heritage was very diverse: works on algebra, number theory, probability theory, the constructive theory of functions and the theory of elasticity. In his work "On an arithmetic property of algebraic functions" (1927), he offers a simple proof of the famous theorem of Hilbert (a theorem of zeros).

Kuzmin (1891 - 1949)

Professor Amosov (1891 - 1969), worked at the department from 1928 to 1969 and from 1949 to 1951 directed it. His research interests extend to the field of applied mathematics. Thus, examining the thermal conductivity of the welding process he solve the plane problem of heat conduction with a moving heat source; in his work "Changing the insulating capacity of plate by incisions", containing the solution of the problem posed by shipbuilders, he proposed a method for solving some complex transcendental equations with elliptic integrals.

Amosov (1891 - 1969)

Professor Lappo-Danilevsky (1896 - 1931), he was a corresponding member of Academy of Sciences of the USSR since 1931; he came to the department in 1929. At the end of the 20s he published a series of papers on the analytic theory of linear differential equations.

Seven departments were formed during the reorganization of the Polytechnic Institute in 1930. Each department was a part of the Higher Mathematics department and they were headed by prominent scientists and mathematicians. For example, the Department of Metallurgical Institute was headed by Academic Vinogradov, Electromechanical by Ivanov, hydraulic institute by Kuzmin, Physical and mechanical by Gavrilov, Mechanical Engineering by Havre.

In 1934 there was the unification of industrial institutes in the Leningrad Industrial Institute. Professor Bernstein (1880-1968) was the head of the Higher Mathematics department from 1935 to 1941. He was a member of the USSR Academy of Sciences from 1929. Having decided in 1903 nineteenth and in 1908 twentieth Hilbert's theorem, he boldly entered into science. The solution for the nineteenth theorem was carried out by the team of scientists; this team included outstanding mathematics as Adamar, Picard, Poincaré. Bernstein was awarded the degree of doctor of science after this work. A large part of his further research was devoted to the theory of functions, and, mainly, to the theory of approximation of functions by polynomials. This work marked the beginning of a new field of theory of functions that Bernstein called "constructive" theory of functions. Also great interest has his work on probability theory. He the first constructed axiomatics of probability theory and received the general results of limit theorems for dependent and independent random variables.

Bernstein (1880-1968)

The greatest scientific and pedagogical achievements of the Department occurred in 1934-1941. During this time here worked such scientists as Bernstein, Ivanov, Kuzmin, Gunther, Gernet, Frank and Amosov. Truly obsessed with science, they created around themselves an atmosphere of creativity and mutual understanding.

Professor Gernet (1877 - 1943) graduated from higher education courses for women established in St. Petersburg (Bestuzhev courses) in 1898 and then continued to study mathematics at the University of Gottingen under the guidance of the Professor Hilbert. In 1901 she defended her doctoral thesis and after that, she taught at the Bestuzhev courses, after defending her master's thesis in 1915 – as a professor. She was the second female mathematician who received a degree in a Russian university. Gernet has worked at the department from 1930, until death from starvation in besieged Leningrad. Some scientific results obtained by her, entered the variations calculations textbooks. Professor Franck (1878 -1942), worked at the department from 1930 to 1941. His main works related to two areas: the geometry and applied mathematics. From his geometric works, it is necessary to underline his original study of unilateral surfaces, which he reported to the Congress of Mathematicians in 1934.

Gernet (1877 - 1943)

Professor Erugin (1907-1990), worked for the department in the 30s. He was a member of the USSR Academy of Sciences, Gunter's pupil. The success of his works on the theory of differential equations was provided by connection Lappo- Danilevsky method, which he freely owned, with ideas of Lyapunov, that made it possible to create a general theory of reducible system. Erugin made a great contribution to the qualitative theory of differential equations and the theory of sustainability.

A significant contribution to the development of mathematics and the teaching made such Professors, as Voronovskaya (1898-1972), Popov (1899-1973), Filippov (1876-1941), Besicovich (1886-1958), Koyalovich (1867-1941), Lebedev (1911-1994).

Great Patriotic war constitutes a tragic page in the history of the department. Many employees left for the front. Among them was Assistant Professor Shakno (1909-1995), who worked at the department from 1930 to 1984 year. He was the author of 13 textbooks on elementary and higher mathematics. During the Siege of Leningrad died Gernet, Gelbke, Nikonov, Yeletsky. Part of the department staff was evacuated along with the institute first in Pyatigorsk, then in Tashkent, the part could not withstand the harsh of a military. In Pyatigorsk talented mathematics Pancakes and Rozenson were shot by the Germans.

Kuzmin was the head of department after re-evacuation, then he was replaced by Amosov. Professor Janelidze (1916-1964) was the chairman of the department of mathematics from 1952 to 1954, his scientific work relates to theories of elasticity and plasticity of hesitation.

From 1945 to 1974, at the Higher Mathematics department worked Gorshkov (1916-1978), who directed it from 1954 to 1974. After the wounded at the front and prolonged treatment, he returned to Kazan University, from which he graduated in 1941, and enrolled in the Graduate School of the Leningrad office of Institute of Mathematics to the Professor Faddeev. In 1954 Gorshkov defended his thesis for the academic council of Leningrad national institute, which recommended this thesis work as a Doctorate Degree. In 1957 he received the degree of Doctor of Physical and Mathematical Sciences, in 1963 – an academic status of a professor was appropriated to him. The most significant works of Gorshkov are his researches of problems of Markov about a range of arithmetic minima of uncertain binary square forms with material coefficients.

*Gorshkov (1916-1978)*

From 1945 to 1959, the department was actively working on the redaction and the new edition of the famous three-volume collection of problems in higher mathematics, edited by Gunther and firstly published in 1911. Among its 10 minute drafters were 3 professors of Polytechnic University - Adamov, Gunter and Friedman. In the future, the number of authors (in connection with the expansion of subjects) was added by Polytechnic professors: Kuzmin, Bernstein, Amosov and Gernet. After the war, under the leadership of Kuzmin, Dzhanelidze and Amosov the whole team of professors of the department of 15 people worked on the re-release of this book. Last 14th edition was published in 1959.

From 1972 to 1985 the department of the higher mathematics was divided into two – No. 1 and No. 2. Professors Aksenov, Gorshkov, Srebryansky, Ryzhakov and Kalinin managed them. After the association in 1985 Ozerov was the chairman of the department, and then from 1987 to 2003 – professor Hvatov. Since 2003, the department is headed by Professor Antonov.

* Заведующий кафедрой Валерий Иванович Антоно*

Professor Antonov – head of the department

In 2010, in the Higher Mathematics department were 135 teachers, among them 19 professors and more than 60 candidates of Sciences. Scientific research is conducted in several directions: algebra, optimization theory, graph theory, approximation theory, the theory of ordinary differential equations and partial differential equations, functional analysis, probability theory and mathematical statistics, programming, numerical methods, mathematical modelling, including neural network (by professors Tarkhov, Vasilyev).

Teachers of the department constantly conduct a lot of work in the direction of a search of the most effective methods of training, preparation of scientific and methodical aids, usage of computers in the educational process, actively participates in the programs "The Higher School of Russia". Professors Maximov and Hvatov published two books of the methodical direction "The basis of the Higher Mathematics Discipline" and "The Structured Program".

The Department actively introduces modern technologies of control in teaching the higher mathematics – written examinations, two-level examinations, test control of knowledge. These technologies provide an objective assessment of the quality of learning, the possibility of a better understanding of the necessary level of assimilation of varying themes (knowledge, skills) and have an impact on the content of courses, on understanding by the teacher the need of their processing. The department developed the principles of construction of tests, their uses, and the assessment of the validity of the difficulties. For general technical and economic specialities has created packages of tests that are widely used in the educational process. At the same time, the teachers create a tasks bank for the higher and elementary mathematics, which are developed on the basis of test generators. The bank of tasks was created in the standard MS Word format, which makes the bank easily accessible to any user.

The Department pays a lot of attention to the preparation of textbooks and manuals. Professor Nogin is one of the authors of the book "Bases of the theory of optimization". Professor Vassiliev is one of the authors of the monograph "Undifferentiated optimization".

In 1995, the Department has won the tender announced by the Ministry of Education of the Russian Federation on the establishment of a textbook on mathematics for undergraduate technical directions. The textbook consists of 6 volumes. In 1999, was published the 1st volume "Common areas of mathematics", in 2001 - 6 th volume - "Probabilistic branches of mathematics." In 1999 the textbook on mathematics for humanitarian specialities appeared in publishing house “Special Literature”. Employees of department Maximov, Romanov and Yastrebov together with the department of sociology and right of SPbSTU wrote the monograph "Mathematical Methods of Modelling of Management Processes in the Social Sphere". The book was published in the publishing house "Nestor" in 1999 and can also be used in the training process for the preparation of bachelors and masters-sociologists. The same can be used and the monograph "mathematical methods and models in ecology", republished with supplements 3 times. In its preparation were attended Professors Romanov and Maksimov. Professor Aksyonov published 4-volume textbook on mathematics for students of the Faculty of Physics and Mechanics. Professor Ryzhakov prepared, published and periodically reissued editions of the mathematics that provide teaching in the Faculty of Radio Physics.

In collaboration with the Technical University of Dresden in 1986, was published, and in 1992 reprinted the book "Introduction to queueing theory". In writing were participated Professor Maksimov and Associate Professor Amosova.

In 2007 professor Maximov published the monograph "New methods of the correlative and determination analysis", and in the period of 2008 – 2010 he published 3 manuals on probabilistic subject – "The theory of probability and stochastic processes", "Theory and practice in mathematical statistics. Notes to the theory of probability "," Random processes. Theory and problems. "

A new kind of tutorial was created by Department - supporting notes for all sections of the course of mathematics. They released 9 pieces. They are very popular and reissued periodically. The Moscow publishing house "exposé" interested in supporting notes and issued the first transcript and prepares to publish the rest. In the supporting notes the material is presented in a logical sequence with illustrations and examples; secondary issues and difficult evidence omitted, small are given.

Organizationally, the department is divided into sections according to the number of departments served. Sections are headed by professors and associate professors. The Head of the department has 3 deputy - on study (Professor of Transfiguration), by a technique (Professor Maximov), on scientific work (Professor Halidov). The head of the department, his deputies and heads of sections, the labor union organizer make a council of the department which systematically gathers and discusses the main questions of work.

Since 2007, the department began to turn-out specialists in the field of "Applied Mathematics and Informatics". The main emphasis in the training of future scientists placed on the development of an analytical way of thinking with the further implementation of mathematical models on modern computers.