PART 1.- Introductory notions.

Chapter 1.- Sets and Functions. Sets, correspondences and functions.

Chapter 2.- Combinatorics. Variations, permutations and combinations.

PART 2.- Matrices and determinants.

Chapter 1.- Matrices. Basic definitions. Operations with matrices. Special matrices.

Chapter 2.- Determinants. Basic notions about permutations. Determinant of a square matrix: definition and properties. Cofactor expansion of a determinant. Rank of a matrix. Inverse of a matrix.

Chapter 3.- Equivalence and congruence of matrices. Elementary transformations. Row equivalence of matrices. Column equivalence of matrices. Matrix equivalence. Congruence.

Chapter 4.- Systems of linear equations.  Cramer's Rule. Rouche-Frobenius Theorem. Gaussian elimination method.

Chapter 1.- Vector spaces and vector subspaces. Definition and properties. Vector subspaces.

Chapter 2.- Spanning sets. Linear independence. Bases. Linear combinations of vectors. Linear dependence and linear independence. Bases, dimension and coordinates. Rank of a set of vectors. Change of basis. Equations of the subspaces. Dimension of a sum of subspaces.

Chapter 3.- Linear maps. Definition and properties. Matrix representation of a linear map. Change of basis. Kernel and image of a linear map. Composition of homomorphisms.

Chapter 4.- Endomorphisms. Introduction. Eigenvalues and eigenvectors. Diagonalization and similarity. Triangularization and similarity. Jordan forms.