Cartesian products, Relations, Algebraic structures, Tables, Matrix operations, Reverse Matrix, Inverse Matrix. Determinants and their properties, Linear systems, Gauss method, Gauss - Jordan method, Systems solved with the use of inverse matrix, Cramer method, Vector spaces, Kernel and Image of linear mappings, Eigenvalues and eigenvectors, Matrix diagonalization, Applications in Informatics.

Sampling theory, Random samples, Random numbers. Description of statistical data with arrays and graphics, Frequency array, Histogram. Analysis of Variance. Correlation coefficient. Confidence intervals, Statistical hypothesis-testing process. Regression. Statistical software.

Dynamical systems. Theoretical models and modeling strategies. Evolution in time and space. Scale effects and multi-scale modeling. Explicit models for computer science and natural hazards. Queueing Theory. Fundamental Concepts of Queueing. TheoryThe M/M/1 Queue. The powerfulness of Simulation. Simulation strategies. Effective simulation codes for explicit theoretical models. Simulation of deterministic and stochastic dynamic systems. Analysis of simulation results and evaluation.

The Internet expansion and especially the extensive post content on the Web have stimulated the development of technologies for creating dynamic applications that enable the implementation of complex interactive environments and easy content management. Advanced applications, such as content management platforms, distance education digital systems, and social networking sites are included, among others, in the wide range of dynamic Internet applications that have a direct impact on the ways of content publication and distribution. In the course, PHP language for creating applications is taught, and insights into the MySQL database management system for storing and retrieving content are provided, the main educational objective being the capacity for developing, managing and evaluating dynamic applications that run in the Web environment.

Basic Sets, Real Numbers - Axioms of Real numbers - Euclidean spaces, Sequences, Monotony, Subsequence, Convergence, Numerical Series, Convergence Criteria: Absolute and Relative Convergence, Telescopic Series, Limit, Continuity, Derivative, Basic Theorems of Differential Calculus, Convexity, Taylor Theorem, Taylor Series, Power series, Integral, Beta and Gamma Functions, Applications of Integrals, Differential Equations, Functions of several Variables, Limit and Continuity - Partial Derivative, Extrema, Completion, Multiple Integration, Change of Variables, Fourier Theory, FFT.