Discrete Mathematics

Major: Computer Science (Design and programming of intelligent systems and devices)
Code of subject: 6.122.12.O.004
Credits: 6.00
Department: Computer-Aided Design
Lecturer: Professor of CAD department, DSc, Senior Researcher Olena Stankevych
Semester: 1 семестр
Mode of study: денна
Мета вивчення дисципліни: The purpose of the course is to acquaint students with the basic concepts, ideas, and methods of logical analysis, to teach them to use them when solving specific practical problems, to prepare students for the study of special disciplines and independent study of mathematical and scientific and technical literature, to form an integral system of theoretical knowledge, necessary for the professional activity of a competent specialist in the field of information technologies, to develop the skills of analytical thinking and the skills of applying mathematical apparatus to the formalization of real processes and phenomena.
Завдання: The study of an educational discipline involves the formation of competencies in students of education: 1. The ability to solve complex specialized tasks and practical problems in the field of computer science or in the learning process, which involves the application of theories and methods of information technologies and is characterized by the complexity and uncertainty of conditions. 2. Ability to abstract thinking, analysis and synthesis. 3. Ability to apply knowledge in practical situations. 4. Knowledge and understanding of the subject area and understanding of professional activity. 5. Ability to communicate in the national language both orally and in writing. 6. Ability to communicate in a foreign language. 7. Ability to learn and master modern knowledge. 8. The ability to be critical and self-critical. 9. Ability to evaluate and ensure the quality of the work performed. 10. Ability to act on the basis of ethical considerations. 11. The ability to realize one's rights and responsibilities as a member of society, to realize the values ??of a civil (free democratic) society and the need for its sustainable development, the rule of law, and the rights and freedoms of a person and a citizen in Ukraine. professional competences: 1. The ability to mathematically formulate and investigate continuous and discrete mathematical models, and justify the choice of methods and approaches for solving theoretical and applied problems in the field of computer science, analysis, and interpretation. 2. The ability to think logically, draw logical conclusions, use formal languages ??and models of algorithmic calculations, design, develop and analyze algorithms, evaluate their effectiveness and complexity, solvability and unsolvability of algorithmic problems for adequate modeling of subject areas, and creation of software and information systems.
Learning outcomes: Learning results: 1. To use the modern mathematical apparatus of continuous and discrete analysis, linear algebra, and analytical geometry, in professional activities to solve problems of theoretical and applied nature in the design and implementation of information objects. 2. The ability to choose methods and tools of modern information technologies for the automated design of microsystems. 3. The ability to develop mathematical models for components of microsystems, considering the technological processes of their manufacture. 4. The ability to use modern methods and means of engineering design of complex systems and objects and carry out their adaptation for the automated design of microsystems. Teaching and learning methods: explanatory and illustrative method; problem execution method; visual methods: demonstration and illustration, presentation at lectures; reproductive method; semi-research and research methods; method of group work (brainstorming) for developing models of applied problems. Methods of assessing the level of achievement of learning outcomes: assessment of practical works; assessment of laboratory works; assessment of calculation and graphic work; tests.
Required prior and related subjects: prerequisites: algebra, geometry; prerequisites: object-oriented programming, organization of databases and knowledge, computer circuitry and architecture of computer systems, algorithmization and programming.
Summary of the subject: The proposed course will provide students with in-depth theoretical and practical knowledge, skills, and understanding of set theory and mathematical logic, graph theory, and Boolean function theory. The scheme of presentation of the material makes it possible to structure the study of the subject according to increasing complexity. For each topic, sets of practical and laboratory tasks have been carefully selected. Practical and laboratory material makes up about 50% of the total volume of the discipline and is divided into two types: exercises for consolidating and deepening the understanding of theoretical provisions in practical classes and tasks for the implementation of computer projects in laboratory works. A significant part of them expands the introduced concepts, enables a deeper understanding of the rationale, or provides insight into the practical application of the material in various fields of knowledge, including artificial intelligence, mathematical linguistics, programming, operations research, system analysis, decision-making theory, etc. The educational discipline is an instrumental basis for performing the analytical part of further disciplines, as well as coursework.
Опис: Basic concepts of the theory of sets and relations. Relationship of sets. Properties of relations. Elements of graph theory. Ways of specifying graphs. Operations on graphs. Hamiltonian and Euler graphs. Finding minimal paths on graphs. Transport network and flows in it. Fundamentals of mathematical logic. Normal forms. Boolean functions. Minimization of Boolean functions. Basic concepts of automata theory.
Assessment methods and criteria: Current control: Practical work - analysis of the report in accordance with the established requirements, written survey Laboratory work - analysis of the report in accordance with the established requirements, written survey. Calculation-graphic work - analysis for compliance with the task, independence of execution, design in accordance with established requirements. Semester control: Testing in the VNS, oral examination.
Критерії оцінювання результатів навчання: Assessment methods and criteria: - Current control (45%): written reports on practical and laboratory work, report on the execution of computational and graphic work, oral survey - Final control (55%, examination control): testing (45%), oral component (10%).
Recommended books: 1. Балога С. І. Дискретна математика : навч. посіб. – Ужгород: ПП «АУТДОР-ШАРК», 2021. – 124 с. 2. Журавчак Л. М. Дискретна математика для програмістів : навч. посіб. – Львів : Львівська політехніка, 2019. – 420 с. 3. Гвоздьова Є. В., Гірник М. О. Дискретна математика : навч. посіб. для студентів напрямів підгот. «Комп'ютерні науки» та «Економічна кібернетика» / Укоопспілка, Львів. комерц. акад. – Львів : Вид-во Львів. комерц. акад., 2015. – 123 c. 4. Кривий С. Л. Дискретна математика. – К.: Букрек, 2017. – 568 с. 5. Висоцька В. А., Литвин В. В., Лозинська О. В. Дискретна математика : практикум (Збірник задач з дискретної математики) : навч. посіб. – Львів: Вид-во «Новий Світ – 2000», 2020. – 575 с. 6. Johnsonbaugh R. Discrete mathematics. Pearson, 2022. 7. Rosen K. Discrete Mathematics and its Applications. Discrete Mathematics and Its Applications Sixth Edition 2006 Kenneth Rosen.pdf - Google Диск 8. Lewis H., Zax R. Essential Discrete Mathematics for Computer Science. Princeton University Press, 2019.