Algebra and analytical geometry

1. Complex numbers.
2. Polynomials and algebraic equations.
3. Linear spaces – part 1.: linear independence, dimension, basis.
4. Matrix algebra.
5. Rank of matrix, systems of linear equations.
6. Determinants, inverse matrix, matrix equations.
7. Linear spaces – part 2: linear mapping, fundaments of spectral theory.
8. Linear, bilinear and quadratic forms.
9. Spaces with scalar product.
10. Vector algebra.
11. Analytical geometry of linear objects.
12. Classification of conics.
13. Quadric surfaces.