Infopaket

Universal algebra

ННД.17

Обов’язкова дисципліна для ОП

First

2022/2023

4 Semester

5

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.

Full-time form

Know the basics of discrete mathematics and the basic concepts of the linear algebra.

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.

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.

Lectures, practical classes, independent work, defense of laboratory work, exam.

- 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)

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