1 
Name of the course 
Algebra 

2 
Year of study, speciality 
1, Mathematics (ScienceDesign Activity) 

3 
Semester of study 
2 

4 
Credits 
4 

5 
Lecturer 
Bondarenko A.A. 

6 
Course objectives 
To acquaint students with fundamental methods of general and linear 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: – perform operations with complex numbers in algebraic and trigonometric form, to extract roots of complex numbers, use de Moivre formula; – calculate determinants; – perform operations on matrices; – solve systems of linear equations; – find the basis of a vector space, of a sum and intersection of subspaces, coordinates of a vector in a given basis, find the rank of the matrix and vector systems; – find eigenvalues and eigenvectors of a matrix and a linear operator; – reduce the quadratic form to the canonical form; – reduce the orthogonal operator to the canonical form; – – find an orthonormal basis, an orthogonal complement to the subspace. 

7 
Prerequisites 
Algebra (part 1) 

8 
Contents 


9 
RecommendedLiterature



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

11 
Language of teaching 
Russian 

12 
Conditions (requirements), current control 
– check of individual tasks, – tests. examinations marks are given taking into account: 40% – semester work, 60% – oral answer in an examination 

13 
Form of current assessment 
an examination, control test 