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