1 
Name of the course 
Additional chapters of algebra 

2 
Year of study, speciality 
2, Mathematics (ScienceIndustrial Activity) 

3 
Semester of study 
4 

4 
Credits 
3 

5 
Lecturer 
BenyashKrivets V.V. 

6 
Course objectives 
To acquaint students with fundamental methods of general algebra, with basic algebraic structures – groups, rings and fields; to create a base for studying basic concepts and methods of modern mathematics; to form mathematical thinking among students; to acquaint with methods of mathematical proofs; to study algorithms for solving specific mathematical problems. To instill in students the ability to independently study educational and scientific literature in the field of mathematics. As a result of studying the course, a student should be able to:
– determine whether a given subset is a subgroup in a group, a subring or an ideal in a ring, a subfield in a field; – to perform calculations in a quotient group, quotient ring; – build finite fields of a given order and perform calculations in them; – apply the most important theoretical results to solving computational problems related to groups, rings and fields. 

7 
Prerequisites 


8 
Contents 


9 
RecommendedLiterature

1. Milovanov M.V, Tyshkevich R.I, Fedenko A.S. Algebra and analytic geometry. V. 1. Minsk: Amalfeya, 2001. 2. Milovanov M.V, Tolkachev M.M, Tyshkevich R.I, Fedenko A.S. Algebra and analytic geometry. V. 2. Minsk: Amalfeya, 2001. 3. Burdun A.A, Murashko E.A, Tolkachev M.M, Fedenko A.S. A collection of problems on algebra and analytic geometry. Minsk: Universitetskoe, 1999. 4. Monakhov V.S, Buzlanov A.V. Algebra and Number Theory: Workshop. Minsk: Izd. center of BSU, 2007. 5. Proskuryakov I.V. Problems in linear algebra. Moscow: Nauka, 1978. 6. Faddeev D.K, Sominsky I.S. Collection of problems on higher algebra. Moscow: Nauka, 1977. 7. Barkovich O.A. Algebra: problems for practical studies and independent work. Part 1. Introduction to algebra. Minsk: BSPU, 2005. 8. Barkovich O.A. Algebra: problems for practical studies and independent work. Part 2. Linear algebra. Minsk: BSPU, 2006. 9. Kostrikin A.I. Introduction to Algebra. V. 13. Moscow: Phys.Math. literature, 20002001. 10. Gelfand I.M. Lectures on linear algebra. Moscow: MTsNMO, 1998. 11. Kurosh A.G. The course of higher algebra. Moscow: Nauka, 1965 (and later editions). 12. Maltsev I.M. Fundamentals of linear algebra. Moscow: Nauka, 1970. 13. Faddeev D.K. Lectures on algebra. Moscow: Nauka, 1984. 14. Vinberg E.B. Course of algebra. Moscow: Factorialpress, 2001. 15. Vinogradov I.M. Fundamentals of number theory. Moscow: Nauka, 1976. Advanced reading: 16. Ireland K., Rosen M. Classical introduction to the modern theory of numbers. Moscow: Mir, 1987. 17. Van der Waerden B. L. Algebra. Moscow: Nauka, 1976. 18. Kostrikin A.I, Manin Yu.I. Linear Algebra and Geometry. Moscow: Nauka, 1983. 19. Kargapolov M.I, Merzlyakov Yu.I. Fundamentals of group theory. Moscow: Nauka, 1972. 20. Lang S. Algebra. Moscow: Mir, 1968. 21. Collection of problems in algebra. Ed. A.I. Kostrikin. Moscow: Nauka, 1987. 

10 
Teaching methods 
Verbal, visual, problembased, practical, dialogbased and heuristic. 

11 
Language of teaching 
Russian 

12 
Conditions (requirements), current control 
– check of individual tasks, – control work, – test. 

13 
Form of current assessment 
control test 