The Faculty of Mathematics and Informatics has almost formed two scientific schools.

**1. “Nonlinear Analysis”**

The Department of Mathematical and Functional Analysis has working scientific school “Nonlinear Analysis” under the direction of Doctor of Mathematics and Phisics, Professor Andrii Zagorodniuk. The main directions of scientific research school are:

• Algebra of the analytic functions, the theory of Banach spaces.

• Approximation of functions (continuous function) on normalized (Banach) spaces.

• Polynomials and analytic functions on Banach spaces.

• Spectra of algebra of analytic functions on Banach spaces and Frechet spaces.

• Spectral properties and hypercicles of composition operators on spaces of analytic functions of Banach space.

• Global linearization of nonlinear mappings on topological vector spaces.

• Research of algebra of block-symmetric analytic functions and their spectrum.

• Homomorphisms and differentiation of Banach algebras of analytic functions of an infinite number of variables.

• Homomorphisms and differentiation on the symmetric products of topological algebras.

• The structure set of homomorphisms of some algebras of analytic functions on Banach spaces.

• Homomorphisms and ideals in the algebras of analytical differentiable functions on Banach spaces.

• Operators in the space of analytic functions on Banach manifolds, linear subspaces in the nuclei of polynomials on Banach spaces.

• Properties of spectrum of algebras generated symmetric (p,q)-polynomials on spaces with symmetric structure.

**2. “Research and development of theoretical and methodological foundations of creation of a vertical information technology”**

At the Department of Informatics the Scientific School “Research and development of theoretical and methodological foundations of creation of a vertical information technology” is formed under the supervision of Doctor of Technics, Professor Lubomyr Petryshyn. Followers of school are Maria Lavriv, Natalia Prevysokova, Yurii Ilyash, Volodymyr Monasteretskyy.

Scientific school focuses on developing theoretical and methodological foundations for realization of vertical information technology using coding message by Galois sequences, development hardware platform of RISC architecture, analysis and design of methods for adaptive reduce of redundancy of continuous information flows and so on.