Ring, domain of integrity, field.

Algebraic and functional definitions of a polynomial.

Divisibility of polynomials, reducible and irreducible plynomials.

Substituting into a polynomial, roots, decomposition into prime factors.

Algebraic equation (with one unknown), solutions and solvability.

Greatest common divisor of polynomials, Euclidean algorithm.

Derivative of a polynomial, simple and multiple roots. Numerical methods for finding real roots.

Approximation of a function by a polynomial, Lagrange interpolation polynomial

The basic course focusing on polynomials. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.