CODE 90694 ACADEMIC YEAR 2020/2021 CREDITS 7 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 7 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 7 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/02 LANGUAGE Italian (English on demand) TEACHING LOCATION GENOVA SEMESTER 2° Semester TEACHING MATERIALS AULAWEB 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 ALDO CONCA Ricevimento: To be decided later on when the general timetable will be fixed. ANNA MARIA BIGATTI FRANCESCO VENEZIANO Exam Board 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) LESSONS LESSONS START The class will start according to the academic calendar. Class schedule BASICS OF HIGHER ALGEBRA EXAMS EXAM DESCRIPTION Oral and computer algebra project
