**General**

Studies in contemporary mathematics in Armenia date back to 1944, when a Section for Mathematics and Mechanics was created within the newly born Armenian Academy of Sciences. The section later developed into an Institute of Mathematics and Mechanics of Armenian Academy of Sciences whose first Director was Academician Artashes Shahinian well known for his results in complex analysis.

The Institute of Mathematics of Armenian Academy of Sciences separated from latter Institute in 1971. The bearers of the office of the Director of Institute have been Academician Mkhitar Djrbashian (1971-1989, 1989-1994 Honorary Director), Academician Norair Arakelian (1989-1991, 1997-2006), Academician Alexandr Talalyan (1991-1997), professor Bagrat Batikyan, coressponding member of NAS RA Valery Martirosian (2011-2012). The Academicians Sergei Mergelian, Raphayel Alexandrian, Ruben Ambartzumian and Anry Nersesyan also have greatly influence the formation of the scientific profile of the Institute.

In the early years the investigations carried out in the Institute concentrated on Function Theory. Gradually the sphere of investigations expanded and now includes Differential and Integral Equations, Functional Analysis, Probability Theory and Mathematical Statistics.

At present the Institute has about 25 main researchers as well as a number of associate researchers from Yerevan State University. The essential volume of the research results obtained in the Institute has been published in the Journal "Izvetija Academii Nauk Armenii, Matematika" of the Armenian Academy of Sciences. This journal was founded in 1966 and since 1979 the cover-to-cover translation of this journal named "Journal of Contemporary Mathematical Analysis" is published by Allerton Press Inc. in USA.

**Main Fields of Activity **

*Complex Analysis:* theory of approximations by analytic and harmonic functions, best approximations; applications of uniform and tangential approximations in various fields of complex analysis; investigation of problems of Weierstrass theory of analytic functions; Banach algebras of analytic functions; uniqueness problems of analytic and harmonic functions; value distribution theory of analytic and meromorphic functions; boundary value theory and boundary behavior of analytic, harmonic and subharmonic functions; integral transformations theory in complex domain; integral representations and classes of analytic and harmonic functions in multidimensional domains.

*Real Analysis: *trigonometric and general orthogonal series; bases in functional spaces; weighted functional spaces; differentiation of multidimensional integrals; representation and uniqueness for multiple Haar, Franklin, Walsh and trigonometric series; nonlinear approximation.

*Probability Theory: *integral and stochastic geometry; combinatorial integral geometry; point processes; sections of convex bodies by random planes and lines; measures generation by finite additive functionals; mathematical problems of statistical physics; limit theorems for random Gibbs processes and fields; statistics of stationary Gaussian processes.

*Differential and Integral Equations:* methods and algorithms for solution of equations; accelerating the convergence of decompositions by eigenfunctions of boundary problems and asymptotic estimates of the corresponding errors; computer realization of integral transforms and applications; parallelization of computations.

Mathematical Physics: methods of study and effective numerical-analytical solution of integral, integral-differential and other equations, arising in direct and inverse problems of radiative transfer, kinetic theory of gases, renewal stochastic processes, semi-Markov processes, filtration of stochastic processes, non-local interaction of waves; development of method of nonlinear factorization equations, Ambartzumian equation method; fixed point principles in the critical case.