Infopaket

Theory of algorithms and mathematical logic

ННД.13

Обов’язкова дисципліна для ОП

Second

2021/2022

4 Semester

5

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.

Full-time form

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.

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.

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.

Lectures, practical classes, independent work, tests, homework, exam.

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.

Ukrainian