Absalamov Tolliboy

a.tolliboy@samdu.uz

Candidate of Physical and Mathematical Sciences, Associate Professor. Since 1981, he has been working in various positions at the Department of Mathematical Analysis of Samarkand State University. In 1984 he defended his Ph.D. thesis on the topic "Integral of the Cauchy Carrali type and a special integral with a continuous density function".

The scientist has published more than 70 scientific articles in domestic and foreign publications and is the author of more than 10 methodological and teaching aids.

Fayzullaeva Buvraziya

buvraziya_fayzullayeva@samdu.uz

Candidate of Physical and Mathematical Sciences, Associate Professor. Since 1977, he has been working in various positions at the Department of Mathematical Analysis of Samarkand State University. In 1994 she defended her Ph.D. thesis on "Multiple Special Integrals on Open Lines, Cauchy-Type Multiple Integrals and Their Applications". Author of more than 50 scientific and methodical works.

Arzikulov Abdikholik Ulashevich

a.arziqulov@samdu.uz 

Candidate of Physical and Mathematical Sciences, Associate Professor. Since 1983, he has been working in various positions at the Department of Mathematical Analysis of Samarkand State University. In 1992 he defended his Ph.D. thesis on the topic "Smoothness and spectral properties of the solution of boundary value problems with an elliptic boundary."

Abdikholik Arzikulov for his educational and scientific activities is one of the authors of more than 100 scientific and methodological articles and the universal textbook "Higher Mathematics" for almost all higher educational institutions. Published 5 manuals.

Nematov Akbarjon Begimkulovich

a.Nematov@samdu.uz

Candidate of Physical and Mathematical Sciences, Associate Professor. Since 1995 he has been working as an assistant, senior lecturer and associate professor of the Department of Mathematical Analysis of the Faculty of Mechanics and Mathematics of Samarkand State University. In 2005, he defended his Ph.D. thesis on the topic "Inverse problem of scattering theory for the Sturm-Liouville operator with a potential close to different potentials of the N-zone at different infinities."

Akbarjon Nematov published about 30 teaching aids and scientific articles prepared during his scientific and pedagogical activity.

Mamirov Berdiyor Ulugbekovich

b-mamirov@samdu.uz

Department assistant. Since 2013 he has been working as an assistant at the Department of Mathematical Analysis. In 2018, he defended his Ph.D. thesis in physical and mathematical sciences on the topic "Excitation of eigenvalues of a two-particle Schrödinger operator on a lattice."

Berdiyor Mamirov is the author of more than 30 scientific articles and abstracts, 2 study guides.

Usmanov Salim Eshimovich

   u.salim@samdu.uz

Department assistant. Since 2019, she has been working as an assistant at the Department of Mathematical Analysis. In 2019, he defended his Ph.D. thesis in physical and mathematical sciences on the topic “The problem of boundedness of maximum operators associated with elastic hypersurfaces”. The researcher conducts research on Fourier transforms related to hypersurfaces and problems of boundedness of maximum operators. In his research, he studies the existence of a consistent coordinate system for elastic hypersurfaces, the smooth computation of the Fourier transform of measures embodied on such surfaces, the boundedness of the maximum operators associated with elastic hypersurfaces in the space of compact functions.

HISTORY OF THE DEPARTMENT OF MATHEMATICAL ANALYSIS

The Department of Mathematical Analysis is one of the first departments created at Samarkand State University, it was founded in 1934. The head of the first department was Associate Professor V.P. Soloviev.

After the restoration of the university in 1944, the department was headed by associate professor M.S. Sobirov in 1945-1961. In 1961-1966, associate professor Kh. A. Abdullaev, in 1966-1972 honored worker of science of Uzbekistan M. S. Sobirov, in 1972-1984 associate professor A. N. Nazarov, in 1984-1985 associate professor A. Mamatkulov, in 1985-1994 headed by Associate Professor U.E. Mamirovlar.

In 1994-1996, the Departments of Mathematical Analysis and Theory of Functions of the Faculty of Mechanics and Mathematics were merged and received the name "Functional Theory and Functional Analysis", which was headed by Academician S.N. Lakaev.

In 1996, the Department of Mathematical Analysis was reorganized and until 2001 it was headed by Associate Professor U. E. Mamirov. In 2001-2020, the department was headed by Professor Ikramov I.A.

The following professors worked at the department in different years: Ibragimova S.G., Goziev A., Nazarov A., Kutmatov Sh., Mamashev S., Bubnov E.A., Roziev J., Matniyazov B., Asrorov Ya., Nurimov T., Gabulov R., Khamroev K., Rabbimov A.S., Mamatkulov A., Soliev A., Ashurov R., Musaev A., Aimatov K., Otakulov S., Lakaev S.N. Abdukadyrov E., Mamatkulov H., Ochilov P.I., Islamov I., Kornienko V.V., Begmatov A.Kh., Jalilov A.A., Tursunkulov B.M., Muyasarov A., Sunnatov H.M. ., Bokiev K., Pozdniyakova N.S., Mamatov Sh.

Each head of the department, who has worked in leadership positions, has rendered a worthy service in increasing the potential of the department, establishing relations with foreign universities and attracting young people to scientific work.

In particular, from 1965 to the present, graduates of the department have defended more than 10 doctoral and more than 40 master's theses, they work in high positions in various higher educational institutions of our republic. In addition, the graduates of the department have performed and are performing the duties of the district head of public education, directors of the KHK and AL, employees of the internal affairs bodies and directors of secondary schools in public administration organizations.

Those who attended special courses at the department and defended their doctoral dissertations: Abdualimov B., Khudoynazarov Kh., Khodjayorov B., Lakaev S.N., Safarov T., Begmatov A.Kh., Karnienko V.V., Ikromov I.A., Jalilov A.A., Kasimov Sh.G., Rozikov O., Abdullaev Zh.I., Imamkulov S.A., Yakhshiboev M., Kuliev K.

The current staff of the department: d.p.m.s. Khasanov G.A., head of the department, Ph.D. Prof. Ikromov I.A., associate professors of Ph.D. Doctors of Philosophy (PhD): Usmanov S.E., Mamirov B.U., Muranov Sh., assistants: Mardonov Zh., Eshbekov R.U. the scientific potential of the department is 89 percent.

Scientific circles and seminars operating at the department:

The department conducts scientific research on the theory of oscillating integrals and the theory and methodology of teaching mathematical analysis.

Today there is a scientific seminar "Theory of special features and its applications" under the guidance of Professor Ikromov I.A.

G. A. Khasanov, one of the participants of this seminar, successfully defended his PhD thesis in 2004 on the topic “Estimation of smooth phase oscillating integrals”. In 2010 D.D. Turakulov successfully defended his Ph.D. thesis on the topic "On the evaluation of the Fourier transforms of smooth measures embedded in convex hypersurfaces".

A.R. Safarov defended his dissertation for the degree of Doctor of Philosophy in mathematical analysis in 2017 on the topic “Flat estimates of vibrational integrals and their applications”, S. Usmanov - in 2019 on the topic “The problem of limits of maximum operators associated with diffuse hypersurfaces”, Sh Muranov - in 2020 on the topic “Estimates of vibrational integrals with a quenching multiplier” received PhD degrees, and K. Kuliev received a Doctor of Physical and Mathematical Sciences (DSC) degree in mathematical analysis in 2022 on the topic “Hardy type inequalities and their applications to nonlinear Sturm-Louville problems".

At the same time, the scientific and methodological seminar "Problems of teaching mathematical analysis" regularly works at the department under the guidance of G.A. Khasanov and A. Arzikulov.

Scientific cooperation carried out by members of the department: The department conducts activities in cooperation with higher educational institutions and research institutes of a number of countries near and far abroad. Including ISTF (Italy), Kiel University (Germany), Putra University (Malaysia), Moscow State University (MSU), Novosibirsk State University (NSU), Novosibirsk Institute of Mathematics. S.L. Sobolev, International Kazakh-Turkish University. Yassavi (Scientific research is carried out jointly with the Republic of Kazakhstan).

As a result, trips were made to foreign countries: Ikromov I.A. (Italy, Germany, Turkey, South Korea), Mardiev R. (France), Arziklov A.U. (England, Turkey), Khasanov G.A. (Italy, Malaysia), S. Usmanov (Turkey).

Employees of the department are laureates of the following international and national grants: Prof. I.A. Ikromov. - Grant of the DFG Foundation (number USB-486) of the University of Kiel in Germany (2001-2019), grant of the International Center for Theoretical Physics in Trieste, Italy (2002-2003), NARUz FTKK Fund of the Republic of Uzbekistan 70-06 2005 From 2001 to the present I.A. Ikromov conducts research jointly with Professor D. Müller of the University of Kiel, Germany, on the basis of a grant from the DFG Foundation. In 1996-2004 and 2007-2013 he was a member of the Italian International Scientific Center for Theoretical Physics named after Abdus Salam. OT-F4-69 "Harmonic analysis, level geometry and their application to problems of mathematical physics" (2017, Uzbekistan)

Prof. A. Jalilov. - Grant of the International Center for Theoretical Physics in Trieste, Italy (2002), German scientific grant DAAD (2004). Scientific grant from the University of Lille, France (2005), scientific grant from the Royal Society of England (2004-2006).

The department has a master's degree, basic doctoral studies (PhD), doctoral studies (DSc).

Directions of education taught by the department: "5130100 - Mathematics", "5110100 - Mathematics and Informatics", "5130300 - Mathematical Engineering", "5140300 - Mechanics and Mathematical Modeling" of the Faculty of Mathematics. "5130200 - Applied Mathematics", "5330100 - Informatics and Programming Technologies" of the Faculty of Digital Technologies and "5140200 - Physics", "5110200 - Physics and Astronomy" for courses of the Faculty of Physics and students of the Faculty of International Educational Programs.

Disciplines conducted at the department:

BACHELOR:

• Fundamentals of mathematics;
• Mathematical analysis
• Separate chapters of analysis;
• Asymptotic methods of analysis;
• Improper integrals depending on the parameter and their applications;
• The content of general education textbooks.

MASTER:

• Additional chapters of mathematical analysis;
• Theory of singular integral equations;
• Theory of distributions;
• Oscillating integrals and their asymptotics;
• Theory of maximal operators;
• Methods of teaching special subjects.