Theory of algorithms and mathematical logic

Course: Software Engineering

Structural unit: Faculty of Computer Science and Cybernetics

Title
Theory of algorithms and mathematical logic
Code
ННД.13
Module type
Обов’язкова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2023/2024
Semester/trimester when the component is delivered
4 Semester
Number of ECTS credits allocated
5
Learning outcomes
PLO05. Know and apply relevant mathematical concepts, methods of domain, system and object-oriented analysis and mathematical modeling for software development. PLO06. Ability to select and use appropriate software development methodology. PLO13. Know and apply methods of algorithm development, software design and data and knowledge structures. PLO27.1. Analyze, evaluate and select tools and computing tools, technologies, algorithmic and software solutions to solve software engineering problems. PLO28.1. Know and have the skills to implement basic algorithms and data structures of programming.
Form of study
Distance form
Prerequisites and co-requisites
1. Know: basics of discrete mathematics, some chapters of mathematical analysis, algebra and programming. 2. Be able to: solve equations and systems of linear algebraic equations over a field of natural numbers. 3. Have skills: algorithmic processes in programming.
Course content
The purpose of the discipline is to master the theoretical issues of algorithmization, the main methods of solving logical problems, means of building logical models of problems in different subject areas. As a result of studying the discipline the student must: know the basic algorithmic systems, information on algorithmically unsolvable problems, fundamental results of the theory of computability, basic logical systems and fundamental results on incompleteness, methods of solving logical problems; be able to build logical models of problems, to investigate the issues of algorithmization within algorithmic systems, to prove the correctness of logical formulas by means of syntactic and semantic logical systems.
Recommended or required reading and other learning resources/tools
1. A.I. Maltsev. Algorithms and recursive functions. – Kyiv. – Naukova dumka. – 2017. 2. O.I. Provota. Concrete algorithmics. – M. – Nauka. – 2017. 3. R. Smalyan. Theory of formal systems. – M. – Nauka. – 1981. 4. C. Chen, R. Lee. Mathematical logic and automatical proof of theorems. – M. – Nauka. – 1983. 5. G. P. Gavrilov. Collection of problems in discrete mathematics. – M. – Nauka. – 1977. 6. Y .V. Chromoj. Collection of exercises and problems in mathematical logic. – Kyiv. – Vyshcha shkola. – 1978. 7. O.I. Provotar, O.S. Shkilnyak. Examples and problems in the theory of algorithms and mathematical logic. – Kyiv. – VPC "Kyiv University". – 2012.
Planned learning activities and teaching methods
Lectures, practical classes, independent work, tests, homework, exam.
Assessment methods and criteria
1. Test 1: LO 1.1, LO1.2 - 20 points. 2. Test 2: LO1.3 - 20 points. 3. Test 3: LO 1.1, LO1.2, LO2.1 - 20 points. 1. Test 1: LO 1.3, LO2.1 - 20 points. Final assessment (in the form of an exam): - maximum number of points: 40 points; - learning outcomes which shall be assessed: LO1.1, LO1.2, LO1.3, LO2.1: - form of examination and types of tasks: written work, 4 written assignments.
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Oleksandr I. Provotar
Department of Intelligent Software Systems
Faculty of Computer Science and Cybernetics
Oksana S. Shkilniak
Department of Intelligent Software Systems
Faculty of Computer Science and Cybernetics