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