Mathematics

Due to the rapid increase in the use of technology in our daily lives, problems related to security and communication speed have emerged. Information must be stored securely and transmitted quickly and accurately.

Function theory, functional analysis, algebra, and Riemann surfaces are among the subjects of this field. Conformal domains in the complex plane or on Riemann surfaces, rings of analytic functions on these domains, maximal ideals, and the algebraic characterization of conformal domains constitute its main foundations.

Many scientific disciplines require the solution of systems of linear equations. Matrices play a crucial role in solving these systems. Determining characteristic structures of matrices—such as eigenvalues, eigenvectors, determinants, factorizations, and inverses—constitutes the foundation of matrix theory.

Combinatorial expressions arise in many contexts, ranging from counting problems to problems in linear algebra. These may include expressions such as binomial sums, linear or nonlinear recurrence relations, sums involving the terms of various number sequences, and calculations of generating functions. Moreover, the computation of the q-versions of such combinatorial expressions is among the fundamental topics of combinatorics today.

Approximation Theory examines the problem of how a function can be approximated by simpler functions (such as polynomials or operators). With the help of methods from Summability Theory, it is investigated how this approximation can be weakened. In particular, the “best approximation problem” is frequently studied not only in mathematics but also in physics and engineering.

The crises faced by global financial markets in recent years, along with the developments that followed, have once again demonstrated the need to develop mathematical models that can help us understand the dynamic structure of financial markets and produce solutions to the problems encountered. This field of study focuses on the development of mathematical models using deterministic and stochastic approaches.

Mathematical biology is an interdisciplinary field in which mathematics is applied to biology, medicine, and biotechnology. This area is one of the fastest-developing and most exciting fields where mathematics is applied today. This discipline relies on knowledge of a wide range of mathematical tools and the ability to model problems through strong analytical skills. Chaos, complexity, neuroscience, bifurcation, and stability are among the popular research topics in recent years.

This field is based on many-valued logic and encompasses interdisciplinary research. It provides more detailed insights in the modeling and solution of problems encountered in areas such as the solution of initial value and boundary value problems related to Differential Equations, Difference Equations, and Partial Differential Equations in mathematics, as well as in Oscillation Theory, Chaos Theory, Economics, Medicine, Engineering, Biology, and similar fields.