Syllabus
Ring, integral domain, 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.
Special types of algebraic equations.
Symmetric polynomials.
Annotation
The basic course focusing on polynomials. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.