Elements of categorial analysis

Course: Software engineering

Structural unit: Faculty of Computer Science and Cybernetics

Title
Elements of categorial analysis
Code
ОК.12
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
2 Semester
Number of ECTS credits allocated
3
Learning outcomes
PLO01. Know and systematically apply methods of analysis and modeling of the application area, identifying information needs and collecting source data for software design. PLO08. Conduct analytical research on the parameters of software systems for their validation and verification, as well as analyze the selected methods, tools for automated design and implementation of software. PLO13. Prepare research results in the form of articles in scientific journals and abstracts of reports at scientific and technical conferences
Form of study
Full-time form
Prerequisites and co-requisites
1. Know: basic concepts of discrete mathematics, mathematical logic and theory of algorithms. 2. Be able to: build recursive programs, build classes of equivalence relations, be able to perform algebraic transformations of logical expressions on the basis of logical identities.
Course content
The purpose of the discipline is to master the methods of solving problems in various subject areas by means of categorical mathematics. As a result of studying the discipline the student must: know the basic concepts of category theory and methods of proving statements in the internal language of categories; be able to solve problems of algorithm theory, discrete mathematics and mathematical logic by means of category theory, in particular, to build classes of relations of equivalence in categorical axiomatization, to give algebraic interpretation of inverse image, to calculate Boolean functions in topos.
Recommended or required reading and other learning resources/tools
1. Goldblatt R. Topoi. Categorical analysis of logic. – M. – Mir. – 1983. 2. Johnston P. The theory of topoi. – M. – Mir. –1978. 3. Kuts A.G. Topoi. Tasks and guidelines . - Omsk. University. – 1989.
Planned learning activities and teaching methods
Lectures, independent work (project), tests, homework, exam.
Assessment methods and criteria
1. Test 1: LO 1.1, LO1.2, LO2.1 - 10 points / 6 points. 2. Test 2: LO 1.2, LO1.3, LO2.1 - 10 points / 6 points. 3. Independent work 1: LO1.2, LO1.3, LO2.1, LO3.1 – 20 points /12 points. 4. Independent work 2: LO1.2, LO1.3, LO2.1, LO3.1 – 20 points /12 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

Departments

The following departments are involved in teaching the above discipline

Department of Intelligent Software Systems
Faculty of Computer Science and Cybernetics