The Department of Higher Mathematics is one of the oldest departments of our institute. 128 years ago, on 15 April 1885, the document “Regulations on HTI” was adopted, in which, in particular, §4 reads: “…the institute teaches the Law of God, higher mathematics, and descriptive geometry”. However, there was no department of higher mathematics in the structure of the institute at that time. Staff members of Kharkiv University were invited to teach higher mathematics courses.
For example, it is known that in the 1885/1886 academic year, K.O. Andreev, a professor at the university, taught analytical geometry at HTI , and M.O. Tikhomandrytskyi, an associate professor at the university, taught a course in differential and integral calculus. In 1887, O.M. Liapunov, a private associate professor of mathematics and analytical mechanics, was invited to teach higher mathematics courses at the institute. Later, together with V.A. Steklov, his student, Lyapunov developed a “methodology for teaching mathematics at HTI “. V.A. Steklov taught at HTI since 1893. At the same time, the name of Professor of Mathematics M.F. Kovalsky was mentioned. In the curricula of the 1902-1903 academic year, among the staff members of the HTI , there are Psheborskyi A.P., a collegiate adviser, Master of Pure Mathematics, and the hired teachers Lagutynskyi M.M., a private associate professor of the university who taught a course in analytical geometry at the HTI , and Alekseevskyi V.P., a private associate professor of the university, Master of Pure Mathematics, who taught a course in differential and integral calculus. Since 1909, the course of differential and integral calculus at HTI was taught by I.I. Belyankin.
It is probably known that in 1923 there was already a Department of Mathematics at the KhTi, and its first head was Vladimir Fomich Brzecka. He was 32 years old at the time. In 1916, he graduated from the Faculty of Physics and Mathematics of Kharkiv University, and in 1917, he taught mathematics in secondary schools in Kharkiv. In the autumn of 1920, he worked at the preparatory courses at the Kharkiv Institute of Technology, and in March 1921 he taught at the HTI .
Volodymyr Fomych headed the Department of Mathematics until his death (7 March 1954), first at the KhTi, since 1930 at the Mechanical Engineering Institute, and part-time at the Electrotechnical Institute, and since January 1950 (after the merger) at the KhPI. V.F. Brzeczka devoted a lot of time to educational and methodological work with young teachers of the department. For about 15 years, he was a researcher at the Mathematical Analysis Sector of the Institute of Mathematics at Kharkiv State University. Brzeczka wrote more than 30 scientific papers on the study of approximate methods of mathematical analysis, orthogonal polynomials, and extreme properties of polynomials.
Since 1954, for 10 years, the Head of the Department of Higher Mathematics of the KhPI was Kim Eng Van Insugovich (born in 1911) – Doctor of Physical and Mathematical Sciences, Professor. Since 1963, Kim Eng Van Insugovych has been a corresponding member of the Kazakh Academy of Sciences. His research interests include equations of mathematical physics. Since 1964, the department has been headed by Borys Melentyev (born in 1918), Candidate of Physical and Mathematical Sciences, Associate Professor.
And since 1971, Alisa Manuilova, Candidate of Physical and Mathematical Sciences, Associate Professor, became the Head of the Department of Higher Mathematics. Manuilova A.M. (born in 1927) has worked at the KhPI for 47 years, including 18 years as the head of the department. Alisa Mikhailovna is a graduate of the State Pedagogical University (Moscow), completed her postgraduate studies there and defended her PhD thesis in 1954. At that time, her research was limited to the equations of mathematical physics. However, since the early 70s, she has been seriously involved in the development of applied statistics, in particular, medical cybernetics. She has written two monographs and more than 70 scientific articles. A.M. Manuilova was the head of a number of economic contractual and state budgetary projects; many members of the department were involved in this work. The cooperation with the Research Institute of General and Emergency Surgery and the Ukrainian Research Institute of Clinical and Experimental Neurology and Psychiatry was particularly effective. In the 80s, the Department established links with the Institute of Heavy Engineering (Miskolc, Hungary). In 1984-1988, at the Kharkiv House of Scientists, she conducted the Republican Seminar “Application of Computers in Medicine”. A.M. Manuilova had postgraduate students, most of whom successfully defended their theses. The practical results of her research work include the creation of the automated information system (AIS) “Acute Abdomen”, which was tested and recommended for implementation by the Military Medical Academy (St. Petersburg) in a number of clinics in Ukraine and Russia, as well as the AIS “Depression”, whose task was to recognise manic-depressive psychosis and chronic stress conditions.
In July 1987, Yuri Levonovich Gevorgyan (born in 1945), Candidate of Physical and Mathematical Sciences, Professor, became the Head of the Department. Yurii Levonovych graduated from the Faculty of Mechanics and Mathematics of Gorky State University in 1968. Since the same year, he has been working as an assistant at the Department of Higher Mathematics of the Lenin Kharkiv Polytechnic Institute. In 1975, he defended his PhD thesis, and in 1979 he was awarded the academic title of associate professor, and in 2005 – the academic title of professor of the Department of Higher Mathematics.
His research interests include functional analysis and geometry of Banach spaces. For many years, he has been actively conducting research on mathematical modelling of physical processes using the equations of mathematical physics. He was a responsible executor in many contractual topics at the department, including the topics “Study of thermal deformations in powerful steam turbine units” (Central Boiler and Turbine Institute, St. Petersburg), “Study of electromagnetic wave propagation through inhomogeneous bodies” (UkrDUZT, Kharkiv), etc. In the course of one of the topics, the conditions for the application of mathematical models and methods for solving the 1st order Fredholm integral equations, taking into account the incorrectness of the problem, based on the study of regularisation methods by A.N. Tikhonov, were obtained.
The active organisational and methodological work of Prof. Gevorgyan contributed to the defence of dissertations by the staff of the department. Over the past 20 years, Olshansky V.P., Batygin Y.V., Pirotti E.L., Grigoriev O.L., Oleksenko V.M. PhD theses were defended by Polianska T.S, Chikina N.O., Spivak O.V., Balaka M.E., Cheremska N.V., Marchenko T.M., Pershyna Y.V., Potanina T.V., Kulyk S.I., Dukhopelnikov S.V., Antonova I.V.
As the Head of the Department, Yurii L. Gevorgyan leads the work on improving the educational process and its methodological support in order to improve the methods of teaching higher mathematics. He pays great attention to the development of modern educational and methodological literature. He has prepared and published more than 30 educational and methodological works, including 16 textbooks, 11 teaching aids and 3 textbooks, including 10 textbooks with the stamp of the Ministry of Higher Education of Ukraine. Today, these are basic textbooks that reflect modern views in pedagogy on the issues of fundamental mathematical training of engineers.
Y.L. Gevorgyan pays much attention to the introduction of modern teaching technologies, modern forms of independent work of students, including the use of WEB technologies. Currently, a new concept of higher education is being formed in higher education, designed to expand access to quality information at any stage of education. The use of computer technologies in the educational process opens up fundamentally new opportunities for enhancing learning, including independent work of students. In addition, such systems enable learning at an individual pace at a time convenient for the student, in accordance with his or her level of training. New information technologies significantly change the forms of interaction between students and teachers in the learning process, but the goal is not to destroy the old traditions in education.
Since 2008, the department has been organising the Higher Mathematics Olympiad for 1st and 2nd year students of NTU “KPI”. The popularity of this Olympiad is growing every year. Already in 2013, 112 students from 8 faculties took part in it.
Since February 2022, Yulia Pershyna, Doctor of Physical and Mathematical Sciences, has been the Head of the Department.
In 2000, Yulia Ihorivna graduated with honours from the Faculty of Mechanics and Mathematics of V. N. Karazin Kharkiv National University and received a degree in mathematics, teacher of mathematics and computer science. Since 2006, she has been working at the Department of Higher Mathematics. She participates in the implementation of state budget and contractual research works in the field of mathematical modelling in computed tomography. In 2007, she defended her thesis on “Mathematical modelling in computed tomography using function interleaving”. In 2008, she won the Third Regional Competition “The Best Young Scientist of Kharkiv Region” in the nomination “Mathematics and Computer Science”. In 2009 and 2012, she received grants from the President of Ukraine to support the research of young scientists.
Yulia Pershyna is active in organisational, methodological and scientific work. Laureate of the Cabinet of Ministers Award for Special Achievements of Youth in the Development of Ukraine (Resolution of the Cabinet of Ministers of 15 June 2011, No. 536-r). Scholar of the Cabinet of Ministers of Ukraine for young scientists for 2012-2013 (Resolution No. 5 of the Presidium of the Committee on State Prizes of Ukraine in Science and Technology of 07 November 2011). Diploma of the National Academy of Sciences of Ukraine for the series of works “Solving three-dimensional and four-dimensional problems of computed tomography using interleaving and mixed approximation operators” (Resolution of the Presidium of the National Academy of Sciences of Ukraine No. 36 of 15.02.2012).
Since 2012 – Associate Professor of the Department of Higher Mathematics. In 2015, she defended her doctoral thesis. Acknowledgement of the Ministry of Education and Science of Ukraine (2016). International grant for participation in the 7th European Congress of Mathematics, July 18 – 22, 2016 (Berlin, 2016). Diploma of the Ministry of Education and Science of Ukraine (2018). International grant for participation in the International Congress of Mathematicians – ICM2018, held at Riocentro Convention Centre, Rio de Janeiro, RJ, Brazil, from August 1-9, 2018. Winner of the competition “Higher School of Kharkiv Region – the Best Names” in the nomination “Teacher of Fundamental Disciplines” (2018). International grant for participation in the 8th European Congress of Mathematics, July 5 – 11, 2020 (Portorož, Slovenia, 2020).
The staff of the department are actively engaged in research activities, participate in international scientific conferences, and exchange of research experience.
The main areas of research of the department’s staff:
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theory of measure,
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group theory,
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automation of control processes,
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multi-criteria optimisation problems,
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fundamental problems of mechanics and hydrodynamics,
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mechanics of deformable solids,
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mathematical logic and formal algorithmic languages,
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mathematical models in economics, medicine and ecology,
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modelling of technological processes in mechanical engineering, shipbuilding, railway and urban transport, etc.
Over the past 30 years, the department’s staff has received 24 copyright certificates and patents for inventions, 18 acts of implementation of scientific developments.
The highly professional staff of the department devotes a lot of effort and energy to improving the mathematical training of students of NTU “KPI”, improving the quality and efficiency of the educational process. Every year, the department’s teachers teach higher mathematics to more than 2 thousand students. In recent years, the department has prepared and published more than 70 methodological developments, more than 30 textbooks and teaching aids, including 10 with the stamp of the Ministry of Education of Ukraine, 5 textbooks and 6 monographs.