##### Department of Mathematical Analysis, Business Analysis and Statistics

The Department of Mathematical Analysis, Business Analysis and Statistics was formed in 1953 as a result of dividing the Department of Mathematics. At that time it was called “The Department of Higher Mathematics”, and in 1970 it was renamed into the Department of Mathematical Analysis. In 2013 the Department of Algebra and Geometry was formed at the Faculty of Physics and Mathematics, to which the algebraic disciplines were transferred.

Throughout its history, the department was headed by:

- 1953–1964 — Associate Professor, PhD (Physics and Mathematics) B. Khatset, Honored Educator of the USSR, author of more than 30 works, including several books that were published and republished as textbooks for Higher Pedagogical Institutions of Ukraine and teacher manuals. B. Khatset was the first to form the department staff, hiring the best graduates of the Faculty of Physics and Mathematics.
- 1964–1970 — Associate Professor, PhD (Physics and Mathematics) P. Karpenko.
- 1970–1976 — Associate Professor, PhD (Physics and Mathematics) H. Kysylevskyi, author of more than 30 works covering the results of academic research and dealing with methodology of teaching.
- 1976–1985 — Associate Professor, PhD (Physics and Mathematics) L. Tarhonskyi, Honored Educator of the USSR, author of more than 40 works covering the results of academic research and dealing with methodology of teaching.
- 1985–2021 — Associate Professor, PhD (Physics and Mathematics) O. Herus, author of more than 60 works covering the results of academic research and dealing with methodology of teaching.

Since September 2021 the department has been headed by Doctor of Sciences (Physics and Mathematics), senior researcher E. Sevost’yanov, author of 163 articles in specialized journals and two monographs, including 118 articles in the Scopus database.

In 1949–1951 the outstanding mathematician H. Katz, known for his theory of ring groups, which was later renamed “Katz algebras”, taught at the department. V. Kostarchuk, Yu. Shmulian, A. Nesterchuk, A. Martyniuk, V. Rudakov, O. Androshchuk, H. Kysylevskyi, A. Merzheievskyi, A. Baranivska, D. Merzheievskyi, T. Didkivska, I. Sverchevska, O. Kolomiitsev also taught at the department. In particular, it is worth mentioning the development of problems of functional analysis made by H. Kysylevskyi, whose research is related to Odessa scientific school, which is well-known in the scientific world. However, O. Androshchuk’s scientific interests were connected with Kyiv scientific school.

The significant scientific results were obtained by Professor M. Osadchyi in the 70s. He solved the problems that lay on the border between the theory of functions and functional analysis. At the same time Associate Professor L. Targonskyi worked on series summation problems, Associate Professor T. Didkivska worked on the problems of applied mathematics, and Associate Professor A. Nesterchuk worked on the problems related to approximate solutions of differential equations.

The problems of hypercomplex analysis were investigated by S. Plaksa, S. Hryshchuk and V. Shpakivskyi who began their scientific research as the students of the Faculty of Physics and Mathematics under the scientific supervision of O. Herus. At present they work as scientists at the Institute of Mathematics of the National Academy of Sciences of Ukraine. M. Tkachuk studied the properties of convex sets in multidimensional spaces.

Since 2014 Doctor of Sciences (Physics and Mathematics) Evgeny Sevost’yanov is working at the department. Under his guidance a scientific school on the theory of mappings began its work. Besides, he is a guarantor of the postgraduate course Mathematical Analysis in the specialty 111 Mathematics. Evgeny Sevost’yanov, together with his students Sergei Skvortsov and Olexander Dovhopiatyi, developed the theory of local and boundary behavior of mappings with the direct and inverse Poletsky inequality. In particular, they obtained existence theorems for continuous solutions of the Beltrami equations, as well as the corresponding applications to the Dirichlet problem for this equation. Evgeny Sevost’yanov also proved analogues of the well-known theorems of Sokhotsky-Weierstrass, Liouville, Picard, Iversen, Montel for mappings with non-bounded characteristic (ring Q-mappings). He is the author of two monographs in the publishing house “Naukova Dumka”:

- Kovtonyuk D., Salimov R. and Sevost’yanov E., To the theory of the mappings of Sobolev and Orlicz-Sobolev classes. — Kiev: Naukova Dumka, 2013, 304 p.
- Sevost’yanov E., Investigation of space mappings by geometric method. — Kiev: Naukova Dumka, 2014, 304 p.

Evgeny Sevostyanov some time ago was, and is also currently the head of the following scientific projects:

- 2013: The method of moduli, theory of local and boundary behavior of some classes of space mappings with unbounded quasiconformality characteristic, RC 0113U001632
- 2017–2027: Local and asymptotic behavior of reflections with finite distortion, RC0117U004570
- 2018–2020: Geometric and topological problems of the modern theory of mappings, RC0118U000098
- 2022–2024: Modern problems of the geometric theory of functions and mappings, RC0122U000821.

Evgeny Sevost’yanov is also a laureate of the following state prizes and awards:

- 2010 Bonus of Verkhovna Rada of Ukraine, for a serious of the works “The investigations in the theory of mappings with finite distortion and approximation of functions in the quasi-norm spaces”. Decision of Verkhovna Rada of Ukraine from February, 2, of 2010, minutes no. 1847 — VI.
- 2011 Bonus of the Cabinet of Ministers of Ukraine “For outstanding achievements of young people in the construction of Ukraine”. The decision of the Cabinet of Ministers of Ukraine from June 15, 2011 536-p“, diploma number 24.
- 2014 The Award of the President of Ukraine for 2014 (2015), Presidential Decree no. 936/2014 of 16 December 2014, laureate certificate no. 748.

The courses covered by the department are mathematical analysis, complex analysis, differential equations, differential and integral equations, calculus of variations, basics of economics and business, applied statistics, packages of applied programs and statistical data analysis, modules of families of curves and quasiconformal mappings, quasiconformal analysis.

The department staff has developed training guidelines for all courses they provide training in. The European credit system has been introduced in student training and assessing. The staff has published a number of handbooks and tutorials for secondary school pupils and university students:

- Tarhonskyi L. P., Osadchyi M. M., Herus O. F., Baranivska A. F. Mathematical Analysis. Functions of One Variable. — Zhytomyr, 2002.
- Herus. O. F., Lenchuk I. H., Sarana O. A. Entrance Examination in Mathematics at Zhytomyr Ivan Franko State University: Methodical manual. — Zhytomyr, 2002.
- Sarana O. A. Elements of the Theory of Harmonic and Subharmonic Functions: Methodical manual. — Zhytomyr, 2002, 2011.
- Tarhonskyi L. P., Osadchyi M. M., Baranivska A. F. Mathematical Analysis. Functions of Many Variables. — Zhytomyr, 2003.
- Sarana O. A. Competitions in Mathematics: Combining the Simple and the Complex. — Kyiv, 2004, 2011.
- Sarana O. A., Yasinskyi V. V. Advanced Competition Mathematical Problems. — Kyiv, 2005.
- Sarana O. A., Semenets S. P. Non-standard Geometric Problems: Educational and methodological manual. — Zhytomyr, 2007.
- Sverchevska I. A., Prus A. V. Test Problems in Stereometry. — Zhytomyr, 2008.
- Sarana O. A. Combinatorics. Elements of Probability Theory. — Kyiv, 2009.
- Sverchevska I. A. Linear Algebra. Algebra and Theory of Numbers: Tutorial. — Zhytomyr, 2010.
- Osadchyi M. M., Tarhonskyi L. P., Tarhonskyi A. L., Podvysotskyi R. V. Complex Analysis: Tutorial.— Zhytomyr, 2011.
- Sverchevska I. A. Structuring the Content and Methods of Forming the Concepts of the Topic “Geometric Bodies” in a Secondary School. — Zhytomyr, 2018.
- Sarana O. A. Collection of Topical and Trial Tests in Mathematics. — Ternopil, publishing house “Navchalna knyha — Bohdan”, 2019.
- Sevost’yanov E. O. Elements of the Theory of Measure and Integral: Educational and methodological manual. — Zhytomyr, 2015.
- Sevost’yanov E. O. Moduli of Families of Curves and Quasiconformal Mappings: Educational and methodological manual. — Zhytomyr, 2015.
- Sevost’yanov E. O., Tarhonskyi A. L., Skvortsov S. O. Elements of the Theory of Functions of a Real Variable: Educational and methodological manual. — Zhytomyr, 2018.
- Sevost’yanov E. O., Ilkevych N. S. Differential and Integral Equations. Part I: Educational and methodological manual. — Zhytomyr, 2020.
- Sevost’yanov E. O. Quasiconformal Analysis: Educational and methodological manual. — Zhytomyr, 2021.
- Dovhopiatyi, O. P., Sevost’yanov, E. O., Tarhonskyi, A. L. Mathematical Analysis. Part I. — Zhytomyr, 2022.

In 2004–2020 a number of PhD theses were defended: 2004 (D. A. Merzheievskyi), 2006 (A. L. Tarhonskyi), 2007 (I. A. Sverchevska), 2008 (M. V. Tkachuk and S. V. Hryshchuk), 2011 (V. S. Shpakivskyi), 2021 (S. O. Skvortsov).

In 2007–2009 the department staff carried out a research project entitled “Monogenous and Hyperholomorphic Functions in Finite-dimensional Algebras and Their Application to Boundary Value Problems of Mathematical Physics”. In 2016–2018 the project “Monogenous Functions in Banach Algebras and Boundary Value Problems of Analysis and Mathematical Physics” was carried out. In 2018–2020 the department staff worked on the project “Geometric and Topological Problems of Modern Mapping Theory”. Within the framework of these projects joint scientific research has been developed with the Institute of Mathematics of the National Academy of Sciences of Ukraine, scientific institutions of Mexico, Cuba, Israel, Italy, Belgium and Serbia. The results of the research were presented at international conferences and seminars in Ukraine and abroad.

There is a permanent exhibition of scientific works, tutorials, educational and methodological manuals published by the lecturers of the department.