Faculty of Economics and Business

Department of Mathematics

სურათი

Department of Mathematics

Head of Department – Prof. V. BALADZE

Prof. V.  Baladze authored over 60 research papers and has been extensively published nationally and internationally, including such well-known magazines such as Topology and its Applications (2004 sec., 2009.). Dr. Baladze presented his papers at over twenty international Math forums. His former students and no fellow professors, Dr. V. Abuseridze, Dr. A. Beridze, Dr.L. Turmanidze, Dr. G. Ivanadze, Dr. M. Dzadzamia have been further developing the study area.

Historical Overview

 The Department of Mathematics has a long history of one of the best National Math schools. It also is one of the most distinguished research centers. 

Development of Mathematics reflects an interesting history in Georgia, and Adjara has always had an excellent research reputation.  Foundation fathers of the Georgian Math School, famous Georgian Mathematicians . Razmadze, N. Muskhelishvili, a. Kharadze, G. Nikoladze used to work here who significantly contributed to the progressive, demanding programs and research directions.  

Advanced mathematical research in Math started in 1935 with the foundation of Batumi Teachers' College. It further developed in 1945, when the Pedagogical Institute was established.  The main centers of research were the Kathedras of algebra-geometry, mathematical analysis and mathematics.

Wave of reforms at the Shota Rustaveli State University in 2005 founded Department of Mathematics. Since 2008 the department has been headed by V. Baladze.

Department of Mathematics administers academic and scientific processes at the Faculty of  Mathematics and Computer Sciences  and offers study programs at BA, MA and PhD students.

Department of Mathematics develops three programmatic areas: geometry-topology, algebra- number theory and mathematical logic, mathematical analysis, statistics) leads educational courses and research programs in various fields of classical and modern mathematics.

Professors of the Department of Mathematics have a tradition of carrying out mission of University Rectors, Vice Rectors, Vice-Chancellors etc. which started since the Pedagogical Institute was established.

D. Baladze – Rector of Batumi State Pedagogical Institute (1977-1990) and Batumi State University (1990-1991).

V. Baladze – Rector of Shota Rustaveli State University (2006-2007), Vice Rector, Director of the University’s Academic Department (2005-2006).

A. Beradze Batumi State Pedagogical Institute and the Vice-Chancellor for Research Training (1957-1962)

Y. Diasamidze - Shota Rustaveli State University Academic Council member since 2006.

L. Turmanidze - Shota Rustaveli State University, Head of Quality Assurance since 2007.

Sh. Makharadze -shota Rustaveli State University in Acting (2008), a member of the University Senate, 2006-present.

N. Rokva - member of the Senate since 2009, Shota Rustaveli State University

N. Suramnidze Shota Rustaveli State University Academic Council (2006-2008), Nead of the Center for testing and skills assessment from 2008 to the present day.

G. Khukhunaishvili -Vice Rector of Batumi Pedagogical Institute Training and Research (1971-1979).

Cooperation:

Department of Mathematics strives to develop and maintain connections outside the university with the international mathematical centers of excellence.

 Batumi has always been favourite venue for national and international Math forums, conferences and symposia. Fruitful cooperation in Batumi mathematicians. The Department retains close cooperation with partner institutions: Tbilisi State University, Tbilisi A. Razmadze Mathematical Institute, N. Muskhelishvili Institute of Computational Mathematics, I. Vekua Institute of Applied Mathematics and other international schools in Kiev, Riga, Moscow, St. Petersburg.

Distinguished Contributors:

Georgian academician G. Chogoshvili, founder of Georgian mathematical school did an exceptional merit to the establishment second Georgian University in Batumi. He along with his fellow outstanding national professors have assessed and predicted the prospective role that a new University could play in Batumi and throughout Adjara. The actions he took were the real basis for the establishment of the university.  

Academician G. Tchoghoshvili’s scientific school has raised in our university many generations of mathematicians. His constant attention and support to students of Batumi University who were assigned to study at different times in our country and foreign educational institution is worth of special emphasis.    

Research priorities

The Department of Mathematics is dedicated to mathematical education with the important contributions to the development and research of many mathematical problems and general development of the study area. The Department is s home of highly ranked undergraduate, graduate and PHD programs.

Topology studies ranks as a priority for the Department. The evolution of the topology studies started with the research works carried out by G. Khukhunaishvili and G. Kirtadze.  G. khukhunaishvilis studied the Hilbert space of continuous reflections. His research deliverable is finding of necessary and sufficient conditions which the metric space should meet in order to be continuous reflection of the Hilbert space. Based on these results he studied the set of topological features which may continuously reflect Hilbert space.

 

Professor V. Baladze’s scientific interests are the general topology, algebraic topology and geometric topology. His studies completed new directions in Topology: theory of topological class module dimension of spaces, the theory of shapes, Fiber shape theory, Pre-compact shape theory, theory and co-shape and Compactification (co) homology theory.

 

The first cycle of Prof. Baladze’s works refers to the theory of module measurement of the spaces class. He examined a small induction, large induction and covering modular dimensions, which represent the dimension of the type of functions and play an important role in the theory of classical dimension of the emerging research problems. Prof. Baladze established their basic features and relations with classical inductive and Lebesgue measures, continuous reflection dimension and multiples, and his research deliverables were large inductive dimension axiomatic characterization, generalized moritas theorem on spaces Lebesgue dimensions and continuous reflection dimension, surveyed spaces with increment dimensions and combinatorial properties, and space and approximate and factorization theorems of space and reflection.

 

Associate Professor L. Turmanidze works on the shape theory developed in the same region of space.  Her works explained the equal reflection concept of the pre-compact space and designed its Cech reversed system. She has proved theorems of the homologous pro-groups long exact sequence and pre-compact spaces’ equal reflections’ long exact homologous sequences reflection. Dr. Turmanidze determined co-relations between F. Bauer’s topological strong shape and equally strong shape theories. Her findings reflect that equal shape pairs and their endings have the same equal shapes. Dr. Turmanidze constructed equally strong shape invariant and incessant continuums of the ANRU spaces, pre-compact ANRU spaces and finite dimensional equal polyhedral subcategories’ finate co-variant and contra variant functors’ of Cech type. The constructions identify that the finate continuums of the functors get the same meaning for the equal space pairs and their endings.     

 

Assistant Professor M. Dzadzamias works on the Geometric theory of compact transformation groups. She studied topological spaces with continuous action of the topological groups with the terms of retracts and shape theories. Assist. Prof. Dzadzamia explained absolute retracts and extensors towards various classes of spaces and found their basic properties. Applications of her research deliverables include characterizations for the equi-variant shape retracts and fibrations,  constructions of  I. M. Smirnov’s  metric and compact equi-variant shape theories  extensions of theories and studies for any G- spaces Pairs category.

Associate Professor A. Beridze’s study focuses on the determination and axiomatic survey of the varieties of Alexander–Spanier’s cohomological functor, the so called finitely dimensional Alexander–Spanier’s cohomological functor, compact carriers finitely dimensional Alexander–Spanier’s  cohomological functor, partially continuous finitely dimensional Alexander–Spanier’s  cohomological functor; The study has established different qualities of the constructed functors and has found correlations between them and the classic cohomological functors in the axioms and isomorph terms by Eilenberg –Steenrod. Dr. Beridze’s studies surveyed expansion theory problems of V. Baladze and I.M. Smirnov.  In particular, the study found necessary and sufficient conditions, for which the real compactification increment of the regular space has isomprphic Alexander–Spanier’s  type cohomological group for the given group. 

Professor  O. Surmanidze studies  problems of Topological algebra and group theory.  Important results have been gained in regards of transition of discrete groups of well-known classical results onto a commutative topological groups, so that they still remain well-known classical results. Prof. Surmanidze has proved analogous theorems to  the  locally compact commutative groups constructed by Pontryagin for the theory of characteristics and classical duality.  In particular, weakly compact linear topological commutative groups duality classical theory is generalized with consideration of the mentioned groups class without topology totally include compact commutative groups  class without topology.  The application of topological compact linear algebraic groups survey resulted in obtaining Topological properties and characteristics of the theory of discrete linear groups. Prof. Surmanidze surveyed locally compact commutative groups with different topological structures.

Recent grants:

The project (co) homologous punctures of topological spaces and continuous reflection (Co) and functions and applications of their dimension will be carried out under the supervision of Professor Vladimir Baladze.  

The project is a winner of Shota Rustaveli National Science Foundation grant in 2014  (FR / 233 / 5-103 / 14)

Great contributors:

Today Batumi is rightly considered a well-known mathematical center, with the support and significant contribution to the scientific center by mathematics P. Alexandrov, S. Bakhvalov, N. Berikashvili, A. Bogomolov, V. Boltianski, T. Gegelia, A. Glagolev, N. Efimov, N. Vakhania, N. Vekua, I. Kighuradze, V. Kupradze, V. Kokilashvili, A. Kurosh, E. Liapin, L. Zambakhidze, P. Zeragia, Kh. Inasaridze, Gv. Mania, L. Mdzinarashvili, E. Nadaraia , I. Nikolsky, B. Plotkin, I. Smirnov, V. Tarieladze, A. Shirshov, S. Chernikov, E. Tsitlanadze, V. Chelidze, C. Chogoshvili, A. Kharadze, B. Khvedelidze, l. Zhizhiashvili and others ).

The largest contributors, the first generation of Batumi Pedagogical Institute have had their successors, the present vital force of the Department of Mathematics, professors in Algebraic studies: Zebur Avaliani, Rezo Asatiani, Omar Givradze, Khemidz Devadze, Yasha Diasamidze, Shota Makharadze, Nino Rokva, Rezo Katamadze, Shota Kemkhadze, Aslan Khakhutaishvili; professors of Geometric studies: Emzar Baladze, Alexander Beradze, Selim Nizharadze, George Ruseishvili; professors in Topology studies: Dursun Baladze, Vladimir Baladze, Shalva Bakhtadze, Anzor Beridze, Lela Turmanidze, George Kirtadze, Onise  Suramnidze, Maya Dzadzamia, Givi Khukhunaishvili; professors in Mathematical analysis and its application: Johnny Babilodze, Mzevinar Bakuridze, Andro Begiashvili, Mikhail Gadakhabadze, Jumber Davitadze, Temur Kokobinadze, Nicholoz Lomjaria, Dali Makharadze, Givi Nogaideli, Nino Svanidze, Akaki Tsivadze, Merab Khabazi; educators who contributed to the establishment of Math teaching - Mary Gordeladze, Mikheil Gokhidze, Silovan Dadunasvili, David Ishkhnelidze, Eter Takidze, Tamaz Tsulukidze, Vladimir Khalvashi. 

 


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