Syllabus
1. Abstract theory of division - number domains, polynomial domains, fundamental theorem of arithmetics for general domains, Euclid's algorithm, principal ideals 2.
Algebra of polynomials - multiple roots, multivariate polynomials, symmetric polynomials, splitting fields, the fundametal theorem of algebra 3. Field extensions - finite extensions, algebraic extensions, degree, constructions with ruler and compass
Annotation
Introductory course for the second year students of mathematics.
Introduction to the theory of groups and commutative algebra.