|SCIENTIFIC DISCIPLINARY SECTOR||MAT/02|
The goal of the course is to introduce fundamental and computational aspect of commutative algebra.
The aim is to introduce the basic notions of commutative algebra as, e.g., noethrerian ringsand modules, and their computational aspects via the introduction of Groebner bases.
Basic algegra (groups and rings).
Teaching style: In presence+computational sections with the use of symbolic computation packages.
1) - 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.
2) Grobner Bases and the Buchberger algorithm. Systems of polynomial equations and elimination theory. Syzygies and intersection of ideals.
3) Computations with system of Symbolic computations.
Computational Commutative Algebra, Kreuzer, Robbiano, Springer, 2004.
Office hours: Reception hours: before and after lessons, or upon request by email/Teams.
Office hours: To be decided later on when the general timetable will be fixed.
Office hours: By appointment
ALDO CONCA (President)
ANNA MARIA BIGATTI (President Substitute)
EMANUELA DE NEGRI (President Substitute)
ALESSANDRO DE STEFANI (President Substitute)
MARIA EVELINA ROSSI (President Substitute)
MATTEO VARBARO (President Substitute)
The class will start according to the academic calendar.
Oral exam and computer algebra project
Discussion concerning the theoretical results and the algorithms presented. The student is expected to be able to reproduce the proofs of the main results discussed.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the office Settore Servizi di supporto alla disabilità e agli studenti con DSA and the teachers at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools. Good afternoon !