Language: English
The goal of the course is the study of system of polynomial equations via Galois theory and using Groebner bases.
Teaching style: In presence+computational sections with the use of symbolic computation packages.
I - Rings, ideals and modules. Noetherian rings and the Hilbert basis theorem. Polynomials: The ring K [x_1, ..., x_n] of polynomials with coefficientsin a field. Grobner Bases and the Buchberger algorithm. Systems of polynomial equations and elimination theory.
II - Review of field extensions. Splitting fields of polynomials with coefficients in a field of characteristic 0, normal extensions and their basic properties. Fundamental Theorem of Galois theory. The Galois group of a polynomial. Applications: cyclotomic fields, solvability by radicals of algebraic equations.
Computational Commutative Algebra, Kreuzer, Robbiano, Springer, 2004.
Ricevimento: To be decided later on when the general timetable will be fixed.
ANNA MARIA BIGATTI (President)
ALDO CONCA (President)
STEFANO VIGNI (President)
The class will start according to the academic calendar.
BASICS OF HIGHER ALGEBRA
Oral and computer algebra project
