**Teaching**is performed during the

**first two years of study**, while the

**third year**is entirely for the

**work on doctoral thesis**.

**In the first year of study**, student chooses

**three courses from the first year of their chosen domain (Applied mathematics)**.

**In the second year**, student chooses

**three courses from the group of all elective courses**at second year of doctoral academic studies, regardless of the elective domain the course belongs to.

## 1. YEAR

##### Elective Block (3 out of 6)

**The name of the course:**Approximation Theory

**Code:**3DЕА1I01

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Polynomials in scientific computing and industrial applications. Representations of polynomials. Univariate polynomials: vector space, algebraic and analytic properties. Root-finding techniques. Interpolation and data fitting. Rational functions. Iteration of rational functions. Rational interpolation and Data fitting. Polynomials in several variables. Numerical factorization. Applications with the use of software.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Numerical Linear Algebra

**Code:**3DЕА1I02

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Introduction to MATLAB. Introduction to LaTex. Errors. Vector and matrix norm. Perturbation, conditioning, stability. Matrix transformations and applications. Dimension reduction. Least squares problems.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Stastistics

**Code:**3DЕА1I03

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS: **10

**Course outline:**

Statistical methodology. Descriptive analysis. Arranging and displaying data. Descriptive measures. Measures of central tendency and dispersion. Distribution of discrete and continuous random variables. Sample and sample statistics. Statistical testing methods. Hypothesis testing. T-test, Analysis of variance with one and two factors. Pearson's chi-squared test. Simple linear regression and correlation. Multiple regression and correlation. Factor analysis. Taxonomic analysis. Discrimination analysis. Non-parametric methods. Index numbers, Analysis of time series. Working in the SPSS program package.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Numerical Mathematics

**Code:**3DЕА1I04

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Arithmetic of finite length and numerical processes. General theory of iterative processes. Application to operator equations. Nonlinear equations and systems. Quadrature processes and convergence. Cauchy’s problems and contour problems for ordinary dferential equations. Grid method for partial diferential equations. Symbolic computation and algorithms. Implementation of algorithms using the Mathematica package.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Discrete structures and combinatorics

**Code:**3DЕА1I05

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Special number sequences. Stirling numers. Bell numbers. Catalan numbers. Euler numbers. Bernouli numbers. Applications in combinatorial mathematics. Extremal problems. Combinatorial block schemes. Special matrices: Binary, Hadamard, Stohastics, Permutation matrices. Combinatorial distribution and counting problems. Spectral matrices and graph theory. Graph invariants. Energy of matrices and graphs. Directed graphs. Mapping of directed coordinated graphs on plane and line.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Special functions

**Code:**3DЕА1I06

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Hypergeometric functions: definition, recursive and transformation formulas, differential equation. Functions defined by integrals: Gamma function, Beta function, Bessel functions. Orthogonality in Hilbert space. Orthogonal polynomials: zeros, differential equation, three-term recurrence relation, generating function, hypergeometric representation. Construction of orthogonal polynomials. Classical orthogonal polynomials. Orthogonal polynomials with non-classical weights. Elements of fractional calculus. Fractional integral. Fractional derivative of Riemann-Liouville and Caputo type. Mittag-Leffler function.

Specification for the book of courses

Specification for the book of courses

##### Obligatory

**The name of the course:**Scientific and Research Work 1

**Code:**3DNIR1

**Number of classes per week:**

- Study and research work: 11

**ECTS:** 30

**Course outline:**

Formed individually in accordance with the needs of the scientific or seminar work, its complexity and structure. Lecturer assigns the specific task to a student. Student studies professional and scientific papers dealing with similar topics, makes research in order to find solutions for the assigned task, or to carry out certain experiments in the laboratory. The work also includes computer simulations, statistical analyzes,and participation in writing research papers in the specific scientific field.

Specification for the book of courses

Specification for the book of courses

## 3. YEAR

##### Obligatory

**The name of the course:**Scientific and Research Work 3

**Code:**3DNIR2

**Number of classes per week:**

- Study and research work: 11

**ECTS:** 30

**Course outline:**

Formed individually in accordance with the needs of the scientific or seminar work, its complexity and structure. Lecturer assigns the specific task to a student. Student studies professional and scientific papers dealing with similar topics, makes research in order to find solutions for the assigned task, or to carry out certain experiments in the laboratory. The work also includes computer simulations, statistical analyzes,and participation in writing research papers in the specific scientific field.

Specification for the book of courses

**The name of the course:**Doctoral Thesis

**Code:**3DZR

**Number of classes per week:**

- Lectures: 0
- Exercises: 0

**ECTS:** 30

## 2. YEAR

##### Elective Block (3 out of 82)

##### Courses from the chosen domain (Applied Mathematics)

**The name of the course:**Mathematical Methods of Optimization

**Code:**3DЕА3I02

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Elements of convex analysis. Convex sets and convex functions. Subgradients and generalization of convexity. Optimality and regularity conditions. Lagrange function and duality. Linear programming and simplex method. Nonlinear programming. Quadratic programming. Algorithms and convergence. Unconstrained optimization. Constrained optimization. Interior point method. Multiobjective optimization. Elements of calculus of variations. Variational methods.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Analysis of Numerical Algorithms

**Code:**3DЕА3I03

**Number of classes per week:**

- Lectures:3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Problems of linear algebra. Direct and iterative methods for solving a system of linear equations, matrix inversion , and the finding matrix eigenvalues. Ill-conditioned systems. Nonlinear equations and systems. Newton and other methods. Method of Newton - Kantorovich. Algebraic equations. Bernoulli's method. Simultaneous method. Gauss - Seidel's approach. Approximation of functions. Interpolation. Problem of the best approximations. Differentiation and integration. Newton - Cotes and Gaussian quadrature formulas. Acceleration methods: convergence of sequences and series, matrix multiplication. Aitken method. Euler - Abel transformation. Fast Fourier Transformation (FFT).

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Spectral graph theory

**Code:**3DЕА3I04

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Topological indices of the graph based on the degrees of vertices and edges (Zagreb indices, Randić indices, geometric-arithmetic topological index, ABC topological index, ISI, SDD, ...). Basic characteristics of topological indices, bounds, values on concrete graphs.Matrices associated with the graph (adjacency matrix, adjacency matrix by edges, incident matrix, Laplacian matrix, normalized Laplacian matrix, Randic matrix, signless Laplacian matrix, ...). Graph spectrums and basic properties.Energy of matrices and graphs. Kirchhoff indices.Operations with graphs and spectra.Regular graphs. Measures of irregularity of graphs.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Highly Efficient Iterative Methods

**Code:**3DЕА3I05

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Basic characteristics of iterative methods. Convergence analysis, order of convergence, R-order of convergence. Initial values problem and stability of methods. High precision iterative methods for determining the zeroes of the analytic function and the zeroes of polynomial.Iterative methods for determining the solution of the linear equations system (the Krilov space, Arnoldi iteration, GMRS method).Application of mathematical software tools in realization of the mentioned methods.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Simulation of Industrial Systems

**Code:**3DЕА3I06

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

The concept of simulation and methods. Design of simulation models. Simulation tools. The mathematical foundation of digital simulation. Numerical methods implemented in simulation tools. Simulation of systems with distributed parameters. Simulation of systems with discontinuities. Errors in the simulation and methods for overcoming them. The application of simulation in the identification, design and optimization of automatic control systems. Real-time simulation, hardware and software aspects, algorithms for numerical integration. Simulation of industrial systems. Simulation of complex systems. Modern trends in the simulation of industrial systems.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Mathematical Models in Industry

**Code:**3DЕА3I07

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Models of dynamical systems. The classification of the models. Abstract models. Principles of mathematical modeling. Types of mathematical models. Examples of mathematical models. The mathematical modeling of technical systems (mechanical, hydraulic, thermal, chemical and technological). Simplification of mathematical models. Validation and verification of the model. Mathematical modeling of disturbance. Modelling of industrial systems. Modeling of complex systems. Current trends in modeling of industrial systems. Modeling using orthogonal functions. Applications of genetic algorithms, fuzzy logic and neural network in the mathematical modeling in the industry. Commercial software for the modeling of industrial systems.

Specification for the book of courses

Specification for the book of courses

**The name of the course:**Mathematical Foundations of Statistical Learning and Applications

**Code:**3DЕА3I08

**Number of classes per week:**

- Lectures: 3
- Exercises: 0

**ECTS:** 10

**Course outline:**

Point estimates, confidence intervals. Nonparametric methods for distribution hypothesis testing. Maximal likelihood method. Linear regression, dependence between two random variables, regression line, dependence between random and control variable. Nonlinear regression, piecewise linear regression, logistic regression. Time series analysis, linear and nonlinear prediction. AR processes, MA processes and ARMA processes. Training alghorithms based on statiatical learning. Algorithms

Specification for the book of courses

Specification for the book of courses

##### Groups of courses from all other domains

Electrical power engineering offers 7 elective courses in the second year of doctoral academic studies:

- Electrical Machines and Transformes - Selected Chapters
- Electrical Machines and Power Converters for Renewable Energy Sources
- Digital Control of Electrical Drives and Power Converters
- Computation of Lightning Overvoltages
- Power Cable Engineering
- Power Quality in Distribution Networks
- Active Distribution Networks and Microgrids

Electronics offers 11 elective courses in the second year of doctoral academic studies:

- Digital Processing of Audio Signal
- Digital Circuits and Systems Design
- Embedded Systems Design
- System-on-Chip Design
- DSP Architectures and Algorithms
- Electronic Circuits Testing
- Reconfigurable Systems Synthesis of Filters
- RF Systems Architectures
- Computer Vision
- Ultrasonic Technique

Metrology and measurement technique offers 4 elective courses in the second year of doctoral academic studies:

- Measurement and Acquisition Systems
- Industrial Measurement and Information Systems
- Measurement and Information Technologies
- Medical and Bioelectronic Measurement Technique

Nanotechnologies and microsystems offers 10 elective courses in the second year of doctoral academic studies:

- Power Devices and Circuits
- Microsensors
- Reliability of Electronic Devices and Microsystems
- Prognosis of the Material Properties
- Advanced Electronic Ceramic Materials
- Software Engineering in Microelectronics
- Solar Systems, Technologies and Devices
- Technology, Design and Characterization of Microsystems
- Reliability Modeling of MOS Devices
- Influence of Radiation on Microelectronic Devices

Applied physics offers 5 elective courses in the second year of doctoral academic studies:

- Devices of Vacuum and Gas Electronics
- Medical Physics
- Semiconductor Devices and Technologies
- Sensors and Actuators
- Technological Processes in Gasses and Vacuum

Computing science and informatics offers 12 elective courses in the second year of doctoral academic studies:

- Design and Analysis of Parallel Algorithms
- Advanced Topics in Fault Tolerant System Design
- Bioinformatics
- Medical Informatics
- Applications of Spectral Techniques for Digital Devices Design
- Advanced Topics in Mobile and Ubiquitous Computing
- Advanced Topics in Computer Graphics
- Advanced Topic in Intelligent Systems
- Advanced Topics in Specialized Information Systems
- Mathematical Fundament of the Game Theory
- Advanced Topics in E-Learning Technologies
- Web Mining and Information Retrieval

Communications and information technologies offers 17 elective courses in the second year of doctoral academic studies:

- Audio Communications
- Antennas and Propagation
- Applications of Neural Networks in Telecommunications
- Satellite Communication Systems
- RF and Microwave Amplifiers
- Electromagnetic Compatibility and Signal Integrity
- Detection of Signals in Noise
- Communication Algorithms and Applications
- 5G and 6G Mobile Communications
- Information Theory and Source Coding
- Statistical Signal Processing
- Digital Communications Over Fading Channel
- Coherent Optical Telecommunication Systems
- Theory and Applications of Software Radio
- Advanced Modeling Techniques for RF Applications
- Free-space Optical Telecommunications
- Advanced Signal and Data Processing

Theoretical electrical engineering offers 3 elective courses in the second year of doctoral academic studies:

- Methods for Steady-state Electromagnetic Fields Calculation
- Inverse problems in Electromagnetics
- Bounday Element Method in Electromagnetics

Control systems offers 6 elective courses in the second year of doctoral academic studies:

- Digital Control Techniques
- Optimal Control
- Variable Structure Systems
- Distributed Computer Control
- Predictive Control
- Adaptive Control Systems

##### Obligatory

**The name of the course:**Scientific and Research Work 2

**Code:**3DNIR2

**Number of classes per week:**

- Study and research work: 11

**ECTS:** 30

**Course outline:**

Formed individually in accordance with the needs of the scientific or seminar work, its complexity and structure. Lecturer assigns the specific task to a student. Student studies professional and scientific papers dealing with similar topics, makes research in order to find solutions for the assigned task, or to carry out certain experiments in the laboratory. The work also includes computer simulations, statistical analyzes,and participation in writing research papers in the specific scientific field.

Specification for the book of courses

Specification for the book of courses

Doctor of Science in electrical engineering and computing

0

ECTS

0

Years