CODE 90694 ACADEMIC YEAR 2022/2023 CREDITS 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 7 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/02 TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW Language: English AIMS AND CONTENT LEARNING OUTCOMES The goal of the course is to introduce fundamental and computational aspect of commutative algebra. AIMS AND LEARNING OUTCOMES 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. PREREQUISITES Basic algegra (groups and rings). TEACHING METHODS Teaching style: In presence+computational sections with the use of symbolic computation packages. SYLLABUS/CONTENT 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. RECOMMENDED READING/BIBLIOGRAPHY Computational Commutative Algebra, Kreuzer, Robbiano, Springer, 2004. TEACHERS AND EXAM BOARD ANNA MARIA BIGATTI Ricevimento: Reception hours: before and after lessons, or upon request by email/Teams. ALDO CONCA Ricevimento: To be decided later on when the general timetable will be fixed. ALESSANDRO DE STEFANI Ricevimento: By appointment 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 ALGEBRA 3 EXAMS EXAM DESCRIPTION Oral exam and computer algebra project ASSESSMENT METHODS 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. FURTHER INFORMATION 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 !
