BASICS OF HIGHER ALGEBRA
7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA
OVERVIEW
Language: English
AIMS AND CONTENT
LEARNING OUTCOMES
The goal of the course is the study of system of polynomial equations via Galois theory and using Groebner bases.
Teaching methods
Teaching style: In presence+computational sections with the use of symbolic computation packages.
SYLLABUS/CONTENT
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.
RECOMMENDED READING/BIBLIOGRAPHY
Computational Commutative Algebra, Kreuzer, Robbiano, Springer, 2004.
TEACHERS AND EXAM BOARD
Ricevimento: To be decided later on when the general timetable will be fixed.
Exam Board
ALDO CONCA (President)
FRANCESCO VENEZIANO
MATTEO VARBARO (President Substitute)
MARIA EVELINA ROSSI (President Substitute)
ALESSANDRO DE STEFANI (President Substitute)
EMANUELA DE NEGRI (President Substitute)
ANNA MARIA BIGATTI (President Substitute)
LESSONS
Teaching methods
Teaching style: In presence+computational sections with the use of symbolic computation packages.
LESSONS START
The class will start according to the academic calendar.
ORARI
EXAMS
Exam description
Oral and computer algebra project