Basic concepts: sets, relations, mappings, composition of mappings. Algebraic structures. Groups, rings, fields. Polynomials. Linear spaces (basis, dimension, Euclidean spaces). Matrices and Determinants. Linear systems: basic notions, solution techniques. Eigenvalues and eigenvectors (SVD, Jordan normal form). Linear mappings and transformations. Bilinear, quadratic and Hermitian forms. Cone sections.