Syllabus
Ring, integral domain, field.
Algebraic and functional definitions of a polynomial.
Divisibility of polynomials, reducible and irreducible polynomials.
Roots of polynomials.
Algebraic equation (in one variable).
Greatest common divisor and least common multiple of polynomials, Euclidean algorithm.
Derivative of a polynomial, multiplicity of roots.
Numerical methods for real roots.
Polynomial approximation of a function.
Annotation
The basic course focusing on polynomials and their properties. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.