“Algebra and Geometry, Part I” - course 2800 rub. from MSU, training 15 weeks. (4 months), Date: November 30, 2023.
Miscellaneous / / December 02, 2023
The course is designed for university and university students studying in the specialties “Mathematics”, “Applied Mathematics”, “Computer Science”, “Physics”, “Economics”. Part I. Matrices, set-theoretic concepts, geometric vectors, linear spaces, systems of linear algebraic equations
Form of study
Correspondence courses using distance learning technologies
Chapter I. Basics of matrix theory
1. The concept of a matrix.
2. Operations on matrices.
3. Elementary transformations of a matrix and matrices of elementary transformations
4. Determinant of nth order. The simplest properties.
5. Minors and algebraic complements. Laplace's theorem
6. inverse matrix
Chapter II. Set-theoretic concepts
7. Multitudes. Cartesian product of sets
8. Binary relation. Equivalence relation
9. Display. Laws of composition
Chapter III. Geometric vectors
10. Directed Segments
11. Free vector. Linear operations on vectors
Chapter IV. Introduction to the theory of linear spaces
12. Real linear space. Definition and examples: geometric spaces, arithmetic spaces, polynomial spaces.
13. Linear dependence
14. Matrix rank. Basic Linear Dependence Theorem
15. Basis and dimension of linear space
16. Linear subspace
17. Linear affine variety
Chapter V Systems of linear algebraic equations
18. Main problems of the theory of solving systems
19. Systems with a square non-singular matrix
20. General systems. General solution of the system
21. Gauss method for studying and solving systems
Chapter VI. Geometric properties of solutions to a system of linear algebraic equations
21. Linear subspace of solutions of a homogeneous system. Fundamental system of solutions.
22. Linear manifold of solutions of an inhomogeneous system. General solution of the system.