| 1 | Transformations, some algebraic structures, permutations and polynomials |
| 2 | To teach matrices and introduce various types of matrices |
| 3 | To explain some important special points of special matrices |
| 4 | To teach elementary row and column operations and to find inverse of a square matrix by using these operations |
| 5 | To teach definition of determinant and its related operations and calculations |
| 6 | To teach linear system of equations |
| 7 | To teach the conditions of existence of a solution for linear equation systems |
| 8 | To teach vector spaces and give related definitions for further calculations |
| 9 | To define and teach eigenvalue and eigenfunctions and by using them to teach the solutions of a system of linear equations |