| CODE | 90694 |
|---|---|
| ACADEMIC YEAR | 2020/2021 |
| CREDITS |
7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA
7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA |
| SCIENTIFIC DISCIPLINARY SECTOR | MAT/02 |
| LANGUAGE | Italian (English on demand) |
| TEACHING LOCATION | GENOVA (Mathematics) |
| SEMESTER | 2° Semester |
| TEACHING MATERIALS | AULAWEB |
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.
Office hours: To be decided later on when the general timetable will be fixed.
ALDO CONCA (President)
FRANCESCO VENEZIANO
ANNA MARIA BIGATTI (President Substitute)
EMANUELA DE NEGRI (President Substitute)
ALESSANDRO DE STEFANI (President Substitute)
MARIA EVELINA ROSSI (President Substitute)
MATTEO VARBARO (President Substitute)
Teaching style: In presence+computational sections with the use of symbolic computation packages.
The class will start according to the academic calendar.
Oral and computer algebra project