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Elements of categorial analysis

ОК.12

Обов’язкова дисципліна для ОП

Second

2023/2024

2 Semester

3

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

Full-time form

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.

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.

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.

Lectures, independent work (project), tests, homework, exam.

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.

Ukrainian