Mathematics of Modern Technologies

Module aim

The goal is to introduce complex analysis, Fourier analysis, Laplace transform, vector differential calculus basics and to present their principal applications.

Module description

In this course students learn the concepts of complex numer and complex functions, complex integration, complex series, residues, Fourier series, integrals and tranfsorms, Laplace transform and its applications, vector differential calculus.

Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

Provide the information about DBMS, introduce a comparison of the differences, advantages and disadvantages; be able to create the database, use the SQL language, write queries, create GUI.

Module description

The course is designed to familiarize students with databases and database management systems concepts. Provides information on possible actions to databases, database users are presented, their possible rights working with databases and database security. Also course introduces the graphical user interface development as well as generating reports and its presentation.
Students must attend at least 80% of the time scheduled laboratory work and at least half of the lectures at the scheduled times.

Module aim

Provide a basic knowledge of stochastic nature of events and their mathematical models and the ability to apply this knowledge practically. To acquire the basic knowledge of mathematical statistics.

Module description

The module of study subject introduces the main concepts and definitions of Probability Theory – a random event, its probability, sum and multiplication of probabilities theorem, total-probability and Bayes formulas, the Normal and Poisson approximations to the Binomial probability. Random variables and their distribution analysis. Independence of random variables. The most common distribution laws of random variables (vectors), the analysis of numeric characteristics of random variables and their dependence are introduced. The empirical analogues of the theoretical distribution characteristics and the basic concepts of mathematical statistics are defined.

Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

To provide students with the comprehensive knowledge on copyrights and related rights, as one of the types of intellectual property while dealing with the legal framework in Lithuania and other countries, to acquire skills to analyze the theoretical and practical problems in the copyright law and to expand students’ capacity for self-absorption in this field.

Module description

The module involves the exploration of copyright rights and related rights among other types of intellectual properties, development of copyright law and its sources in Lithuania and other countries, the peculiarities of different types of copyrights and related rights, their subjects, objects, protection and the responsibility of copyright law infringements.
Students must attend at least 60 per cent of the seminars and at least half of the lectures at the scheduled times.

Module aim

Develop the capacity to design and develop projects in a wide range of fields, providing students with the knowledge and practical skills needed to implement a quality product development process and to control and manage project progress.

Module description

The purpose of the subject is to acquaint students with project management theories, methods and tools and to develop the practical ability to plan and dvelop project. The main study methods – interpretation, discussion, case analysis, analysis of practical tasks, project planning and execution. After completing the study subject, students will be able to analyze problems in the subject area and anticipate project implementation conditions and risks in real situations, using modern project management tools and financing instruments, recognized by science and practice. The course focuses on the Agile methodology. It explains how projects can be carried out in larger organisations with one or more teams and multiple departments involved.
Students must attend at least 80% of the time scheduled laboratory work and at least half of the lectures at the scheduled times.

Module aim

To introduce data structures, to present principles for development and implementation of algorithms, to show how the complexity of algorithms is analyzed, to solve sorting, search, combinatorial, graph problems.

Module description

Examples of algorithms. The main data structures and their implementation. Data search and sorting algorithms. Basic principles for development of algorithms. Complexity of algorithms. Greedy algorithms, dynamic programming. Algorithms for solution of graph problems.

Students must attend at least 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

Differential equations course is designed to provide knowledge Ordinary Differential Equations and their systems, relating it to the various application areas, to develop the ability to explore some real processes and to describe them using the differential equations, get the results, analyze and interpret them.

Module description

The Ordinary Differential Equations course consists of general theory of ordinary differential equations and their applications for modelling various real world processes. The basic topics: deffinitions, various first order differential equations (ODE) and their solutions, existence and uniqueness theorems, phase space, direction field, various higher order differential equations and their solutions, fundamental solutions system, systems of differential equations and analysis, a qualitative approach in the plane, the applications of differential equations and systems of differential equations (creating mathematical models, problem solving and analysis).

Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

The aim of the Applied Statistics subject is to master the basic principles of mathematical statistics and methods of multidimensional statistical analysis, to apply these methods effectively using a specialized statistical data analysis program, to formulate statistical conclusions and interpret the obtained results.

Module description

The module of study subject introduces parametric and nonparametric hypothesis testing tasks, statistical analysis of dependent observations, correlation analysis. Multivariate statistical analysis methods: regression analysis, factor analysis and classification procedures.

Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

Provide knowledge of cloud computing that will enable you to take advantage of any cloud service.

Module description

Cloud computing has taken over the market and overtaken the use of traditional data centers. Each of us uses cloud computing services on a daily basis without thinking about it. The services provided to the common user are easily accessible and intuitive to understand and are therefore perceived as everyday. In this course, you will learn about a wide range of cloud computing services and their providers. At the beginning of the course, the fundamental concepts and basic knowledge of the network and the web are provided to understand the principles of cloud computing. The course provides knowledge about the databases used in cloud computing, data centers, SOA (Service-oriented architecture) architecture, the basics of the NIST (National Institute of Standards and Technology, MD 20899-8930) standard, the concept of virtualization, hypervisors and containers, and the security of the provided services. In the course, we will devote time to the actual topic of artificial intelligence and its use in the clouds.
Students must attend at least 80% of the time scheduled laboratory work and at least half of the lectures at the scheduled times.

Module aim

Is to introduce to:
-the main types ant methods of machine learning to solve real problems;
-theoretical foundation of methods, their application possibilities (adventages and disadventages);
-Python (or R) software capabilities to solve these challenges.

Module description

Machine learning is an integral part of many commercial applications and research projects today, in areas ranging from medical diagnosis and treatment to finding your friends on social networks. In many cases this methodology facilitates the work of various organizations. In this course, we want to show you how easy it can be to build machine learning solutions with theoretical background yourself and how to do best it.

Students must attend at least 60% of the time scheduled practical works and 50% of the lectures.

Module aim

The course of Fuzzy Discrete Structures and Decision Making is designed to provide knowledge on some economic, management and other social sciences and practice models, create and analyze its to develop the ability to explore some processes and to describe them using the mathematical equations, analyze and interpret them.

Module description

The course of Fuzzy Discrete Structures and Decision Making consists of general theory for creating some economic, management and other social sciences and practice models and analysis. Fuzzy sets, fuzzy logics, fuzzy relations, its applications to mathematical modelling and problems of decision making are discussed.

Students must attend at least 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

Introduction to digital image algebra and its implementation in computerised systems. Practical skills of teamwork in designing, analysing and implementing the algorithms on simple image processing.

Module description

Digital image algebra and its implementation using MATLAB script and C++ programming language with special libraries are discussed in the course. The image enhancement, edge detection, thresholding, thinning and skeletonising techniques and morphological, linear and geometric transformations with image features and its classification are presented. Students must complete all scheduled laboratory work. Students must attend at least 80% of the course laboratory and at least half of the lectures according to the semester schedule.

Module aim

To familiarize students with the main decision making methods, work with electronic spreadsheets, to develop the ability to compile mathematical models of real processes, apply modern mathematical methods in decision making tasks.

Module description

Stages of decision-making. Data management. Working with electronic spreadsheets. Regression analysis. Forecasting. Optimization Models. Multi-criteria decision making. Decision making under uncertainty.

Students must attend at least 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

To give information on basic concepts and statements of general algebra.

Module description

Sets, functions and relations. Semigroups. Groups. Abelian groups. Rings, integral domains and fields. Modules and vector spaces. Linear operators. Characteristic equation. Eigenvalues and eigenvectors. Normal Jordan form of the matrix. Polynomial ring. Fundamental theorem of algebra. Elements of the coding theory. Applications of algebra in coding theory.

Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

The goal is to introduce the basic numerical methods and to learn how to apply these methods for solution of specific problems.

Module description

In this course students learn the concepts of computer arithmetic and stability of numerical algorithms, numerical methods for solution of nonlinear equations and systems of equations, direct and iterative methods for solution of linear systems of equations, interpolation and approximation, numerical methods for solution of eigenvalue and eigenfunction problems, optimization methods, and numerical integration methods.

Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

The aim of course is to provide the main knowledge about the big Data and the Big Data processing technologies.

Module description

The subject of the studies consists of the basics of big data, introduction to fundamental data processing programming models and technologies. During the studies, the fundamental concepts of big data are introduced. Challenges related to big data processing and system requirements necessary to solve them are overviewed. The course involves working with big data processing tools such as Hadoop and Spark. Various real-world use cases are also examined.

Students must attend at least 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

To teach students properly understanding of project management concept, as a view to modern method of management, to give theoretical and practical knowledge about types of projects, their purposes, cycle of project implementation, structure of business (activities) plan, to provide knowledge on the principles of project team formation, peculiarities of supervisor selection, business project control and changes performance management, project risk evaluation and management methodology, project m

Module description

This subject analyses projects as adequate form of office or enterprise management, the types of projects and management peculiarities of the separate projects. Students will be introduced with structure of separate parts of project, various project cycles Such management processes of projects are analysed as, for example, project activity and scope determination, project jobs and resources planning, project quality management, human resources management, communications management, risk management, project implementation control and regulation, changes management. The peculiarities of project management are discussed in order to achieve the EU financial support.

Module aim

To provide the fundamentals of economic knowledge and the skills to apply them in professional activities.

Module description

During the couse of Economic theory student study economic theory: micro and macroeconomics, economic issues and objectives. The measurement of individual markets: supply and demand balance and its elasticity. Analyzes the market competition models: perfect and imperfect competition. Study what the consumer and producer behavior in the market. There are discussed the costs and benefits, their calculation. Study, how measured by production volume – national product. Analysis of cyclical fluctuations, fiscal policy, monetary policy, unemployment and inflation, anti-inflation and stabilization policies.

Module aim

To introduce with the computer architecture and main elements including computer arithmetic and instruction sets, processor architecture, memory hierarchy, system bus and interruptions, input/output system, graphics and computing GPU, virtualization technologies.

Module description

Concepts of computer architecture, basic elements. Computer arithmetic and instructions. Processor architecture, instruction sets, pipelining principles, interrupts. Multicore processors, multiprocessors. RISC and CISC architectures. Memory hierarchy and layers. RAM and cache. Components of Input / output system. Module provides basic knowledge on computer network organization, computer network architecture, technological solutions, major protocols, including TCP/IP stack, computer network installation, administration and security questions are discussed.
Mandatory minimum attendance of module lectures – 50%.

Module aim

The Applied Econometrics course object is – to introduce students the regression analysis models, to teach them the practical application of these models for solving economic problems. Students must learn how to use econometric analysis software packages for creating econometric model and forecasting, they must be able to overcome raising difficulties and properly evaluate the results.

Module description

Applied Econometrics course consists of two variable regression model, multiple regression model, least squares estimates and their properties, analysis of model compatibility, forecasting, interpretation of results. Methods of solving problems examining regression models. Basics of time series.

Students must attend at least 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

Introduction to image segmentation and its implementation in computerised systems. Practical skills of teamwork in designing, analysing and implementing the algorithms on simple image processing.

Module description

Image segmentation and its implementation using MATLAB script and C++ programming language with special libraries are discussed in the course. Thresholding of colour and grayscale images, global and local image threshold, statistical pattern recognition, active surfaces, deformable models, Markov random field models and watershed methods are presented.
Students must complete all scheduled laboratory work. Students must attent at least 80% of the course laboratory and at least half of the lectures according to the semester schedule.

Module aim

Course objective – to acquaint students with the basic concepts of financial calculations, survival models, life insurance. To provide knowledge in solving practical problems.

Module description

Students are introduced to basics of financial calculations, the survival models, life insurance mathematical basics, various life annuities.
Students must attend at least 80 % of the time scheduled practical lectures.

Module aim

The aim of the course of Dynamical Systems and Chaos is the introduction of modern methods of investigation of dynamic systems and development of practical skills.

Module description

The course examines the qualitative research methods for dynamical systems. Students are introduced to the basic concepts of nonlinear dynamics – the phase space, fixed points, stability, bifurcation, limit cycles. Much attention is given to the continuous dynamical systems of the first and second order. Students are also introduced to the basic concepts of chaos theory limited to a detailed analysis of the continuous Lorenz system and discrete one-dimensional iterative maps.
This course is an introduction to the theory of dynamical chaos, which is being actively developed nowadays.

Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

To introduce to basic methods of mathematical modelling. Give basic information on the architecture of artificial neural networks and implementation of basic methods of ANN.

Module description

Basic methods of mathematical modelling and main mathematical techniques. Simple examples showing the wide range of applications. Models based on first oder differential equations and systems of such equations.. Systems of ODEs of the second order. Introduction into Artificial Neural Networks. Multi-layer feed-forward networks and networks with back-propagation. Convolution networks. Gradient descent methods.
Students must attend at least 60% of the time scheduled practical works, 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

Learning of an advanced topics in the artificial inteligence and its information systems related applications

Module description

The role of AI in IS, knowledge representation and reasoning, application of knowledge-based systems in IS, problem solving and agents, planning, simple planning
agents, application of software agents in IS, distributed AI and agents societies, swarm intelligence and its application in IS, learning, application of learning in IS,
other modern AI methods and their application in IS.
Mandatory minimum attendance of module lectures – 50%.

Module aim

Financial engineering and modelling course is designed to provide knowledge on stable distributions theory basic concepts as well as stable modelling aplications in finance engineering, to develop the ability to explore economic processes and to describe them using stable laws, analyze and interpret these models.

Module description

Stable laws have a wide sphere of application: probability theory, physics, electronics, economics, sociology. They play an especially important role in financial mathematics, since classical models of financial markets based on the hypothesis of normality often become inadequate. This course consists of general theory of a-stable laws, their properties and applications in finance engineering.

Students must attend at least 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

The primary objective of the module is to introduce main concepts of software systems engineering, principles and methods.

Module description

The module introduces what is software systems engineering. It is explained what is the activity of software systems development. It views the similarities and differences of Art, Craft, Science and Engineering. The main attention is paid to the concepts of system, system engineering, software, software systems, software systems engineering, information system, and business system. Students are familiarized with possible enterprise information systems and their software. The concept of a software’s chronic crisis and its manifestation are introduced during lectures. The following topics are covered during the lectures also: software systems engineering processes, basic principles and paradigms of software systems engineering. Students are taught to begin creating software systems that meet the needs of customers. The module is also taught how to write technical reports and other technical documents.
Mandatory minimum attendance of module lectures – 50%.

Module aim

The aim of the course is to provide the knowledge about parallel programming and distributed memory/heterogeneous systems to implement it, to introduce the construction principles of parallel algorithms, to teach to work with parallel programming tools such as MPI and CUDA.

Module description

The course covers the main concepts parallel programming and principles of parallel algorithms construction. The course is oriented to programming on systems with distributed memory and introduces the programming in heterogeneous systems.

Students must attend at least 80% of the time scheduled laboratory works and 50% of the lectures.

Module aim

The aim is to introduce the main classes of equations of mathematical physics, define important concepts of partial differential equations and to present methods for solutions of such equations.

Module description

Main concepts. First order partial differential equations. Classification of partial differential equations. Main types of equations and problems of mathematical physics. The wave equation, initial and initial-boundary value problems. The heat conduction equation, initial and initial-boundary value problems. The existence and uniqueness of a solution. Solving methods. Boundary value problems for the Laplace equation in simple regions.

Module aim

Obtain basic software testing theoretical and practical knownledge.

Module description

The practical and theoretical knowledge is presented in this module. The testing methods and tools are presented. The tools are uesed practically during lab works. The tests generation and execution algorithms and tools are presented and used by the students during course.

Module aim

Introduction to linear transforms, image features, and its implementation in computerised systems. Practical skills of teamwork in designing, analysing and implementing the algorithms on simple image processing.

Module description

Linear transforms and image features and its implementation using MATLAB script and C++ programming language with special libraries are discussed in the course. Fourier, cosine, Walsh, Wavelet transforms and extraction of image features are presented. Students must complete all scheduled laboratory work. Students must attend at least 80% of the course laboratory and at least half of the lectures according to the semester Lecture schedule.

Module aim

To educate the skills of self-sufficient research, to form the ability to solve complex problems of applied mathematics. After preparing tasks of this course a student should be able to understand formulation of the final work and to prepare schedule.

Module description

A student obtains a description of mathematical model. Mathematical models are based on classical mathematical problems studied before. Concrete cases can be provided by various parameters and by initial or boundary conditions of various types. A student must be able to perform numerical experiments, to prepare visualization of the results, to explain the process of this research and to do right conclusions. To prepare the report with LaTeX.

Module aim

The aim of the course – to provide students with knowledge on information security needs, possible threats and abilities to select suitable countermeasures or prevention mechanisms against it.

Module description

The subject introduces students with definition of information security, ways to assure the security (CIA triad) and possible threats. What is, what types of cryptography exist, how it can be used to assure security is analyzed. Students get know the principles of some symmetrical, asymmetrical cryptography and hash function algorithms. Different type of security threats are analyzed in the subject. Students find out the basics of malware programming code, attacks against web systems, computer networks, personal computers and persons as well as understands possible solutions to prevent it.
Students must attend at least 80% of the time scheduled laboratory work.
Students must attend at least 60% of the time scheduled practical lectures.
Mandatory minimum attendance of module lectures – 50%.

Module aim

The aim is to introduce the students to optimization theory and its interaction with applications, fostering abilities to efficiently solve practical optimization problems developing, implementing and applying proper optimization methods and algorithms.

Module description

Formulation of optimization problem, classification of optimization problems. Nonlinear optimization without constraints: necessary and sufficient optimality conditions, gradient descent and non-gradient methods. Global optimization. Nonlinear programming: optimality conditions, duality, methods. Linear programming: formulation, simplex algorithm, ellipsoid and interior point methods. Combinatorial optimization: classes of problems, enumeration, branch and bound method, metaheuristics.

Module aim

To choose the assigment for the final thesis and to find out the appropriate mathematical models for it; to select appropriate algorithms and to define the required data structures and informatics tools

Module description

The first final thesis’ preparation stage

Module aim

To introduce a student with the peculiarities of the scientific style, the requirements for the terms, the principles of terms regulation, the regularities of Professional language, To teach to write and edit a scientific text.

Module description

The understanding of standard language and its functional styles are discussed. Public and non-public language is examined. Terms and basics of profesional language is analyzed in detail. Structural characteristics and parameters of a scientific text, as well as its compostion, is discussed.compostion, is discussed.

Module aim

Acquaint with philosophical ethics and fundamental ethical problems and concepts. Transmit a knowledge of ethical foundations, principles and systems. Foster critical judgement and the capacity for logical, reasoned discussion. Encourage a sense of values.

Module description

Students learn about basic ethical schools and systems, fundamental issues of deontological and teleological ethic. Historical developement of ethical thought, periods such as Early Asian, Greece and Romain, medievvial, Reneissance, New Age and modernism. The main ethical issues are discussed: good and evil, principle of morality and free will, person as a goal in itself, notion of dignity, conscience, norm and morality, grounding morals in athority and discourse, notion of virtue, happiness and meaning of life and etc. Analyzed texts and philosophic al arguments os themost significant scholars of the field (Plato, Aristotle, Kant).
Students must attend at least 60 percent of the seminars and at least half of the lectures at the scheduled times

Module aim

Course of Optimization in economics is designed to introduce concepts and models of economic processes and basics of optimizations and of control of them.

Module description

Study course consists of a static optimization, variational calculus, linear programming, control theory, dynamic programming basics and is focused on their application in a modeling and optimization of economic processes.

Module aim

Introduction to image processing in medical diagnostics and its implementation in computerised systems. Practical skills of teamwork in designing, analysing and implementing the algorithms on simple image processing.

Module description

Image processing in medical diagnostics and its implementation using MATLAB script and C++ programming language with special libraries are discussed in the course. Medical image coding, filtering, segmentation, registration and visualisation are presented. Students must complete all scheduled laboratory work.
Students must attend at least 80% of the course laboratory and at least half of the lectures according to the semester Lecture schedule.

Module aim

The aim of the course is to introduce the theoretical and practical aspects, issues and applications of public communication.

Module description

Public Communication course aims to introduce personal branding, corporate communication, communication with clients and internal communication, the students who have chosen studies of engineering sciences, computer sciences, technology sciences, mathematics sciences. Students learn how to present themselves and their ideas, better speak in public, to make good and convincing points, to better use the internet and social media for their professional goals, also to understand cross-cultural communication. The importance of media channels, messages and communication to target audiences are also introduced in the course. Through practical tasks for personal branding, students will learn how to adopt public ethics, protocol standards. In this course an approach of learning by doing is combined with theoretical analysis and students’ self-reflection. The practical part of the course consists of active participation in discussions during different exercises, case studies as well as preparation and presentation of public speeches and presentations.
Participation in at least 60% of the scheduled exercises is mandatory. Lecture attendance is at least 50%

Module aim

For a given problem: investigate the chosen/created mathematical model and algorithm, implement and test it.

Module description

The second final thesis’ preparation stage

Module aim

To learn employing theoretical knowledge in practical work

Module description

Consolidation and application in practical work of knowledge acquired during studies in the fields of mathematics, informatics and technical sciences