Universal algebra

Course: Software Engineering

Structural unit: Faculty of Computer Science and Cybernetics

Title
Universal algebra
Code
ННД.17
Module type
Обов’язкова дисципліна для ОП
Educational cycle
First
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
LO01. Analyze, purposefully search for and select the necessary information and reference resources and knowledge to solve professional problems, taking into account modern advances in science and technology.
Form of study
Full-time form
Prerequisites and co-requisites
Know the basics of discrete mathematics and the basic concepts of the linear algebra.
Course content
The purpose of the discipline is to acquire basic knowledge necessary for understanding groups, rings and fields, as well as their analysis; practical use of acquired knowledge to build algorithms based on the theory of groups, rings and fields. As a result of studying the discipline the student must: know the basic definitions, facts, theorems and statements of the theory of groups, rings, fields; definitions and elementary properties of elliptic curves; basic algorithms based on the application of group theory to problems of cryptography, complexity theory and number theory. be able to analyze finite groups, find extensions of groups, maximum subgroups; apply basic algorithms to problems of calculating discrete logarithm, cryptography based on elliptic curves, etc.
Recommended or required reading and other learning resources/tools
1. Fraleigh J. A First Course in Abstract Algebra, 3rd ed. Addison-Wesley Publishing, 1982. 2. Gilbert W.J., Nicholson W.K. Modern algebra with applications, 2ed., Wiley, 2004 347 с. 3. Washington L. C. Elliptic Curves: Number Theory and Cryptography, Second Edition (Discrete Mathematics and Its Applications) 2nd Edition, 2008, 531 с. 4. Van der Varden B.L. Algebra. – M.: Nauka, 1976. – 648 s. 5. Lidl R., Niderrajder G. Konechnye polya: v 2-h t. T. 1, M.:Mir, 1988. – 430 s. 6. Kurosh A.G. Lekcii po obshchej algebre. Izdanie 2-e, M.: Izd-vo "Nauka". 1973. – 400 s.
Planned learning activities and teaching methods
Lectures, practical classes, independent work, defense of laboratory work, exam.
Assessment methods and criteria
- semester assessment: 1. Test 1: LO 1.1, LO 1.2 - 20 points / 12 points. 2. Test work 2: LO 1.2, LO 1.3 - 20 points / 12 points. 3. Laboratory work 1 (project): LO1.2, LO1.3– 10 points / 6 points. 4. Laboratory work 2 (project): LO1.2, LO1.3 - 10 points / 6 points. - final assessment (in the form of an exam): - the maximum number of points that can be obtained by a student: 40 points; - learning outcomes that will be evaluated: LO1.1, LO1.2, LO1.3; - form and types of tasks: written. Types of tasks: 5 written tasks (Tasks for analysis and research of groups, rings and fields, each task costs 8 points)
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Yaroslav M. Linder
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