CODE 25905 ACADEMIC YEAR 2023/2024 CREDITS 8 cfu anno 2 MATEMATICA 8760 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/02 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW Language Italian AIMS AND CONTENT LEARNING OUTCOMES Second corse in Algebra devoted to the formal introduction to the basic notoon of groups and rings. AIMS AND LEARNING OUTCOMES At the end of the class students will have gained algebraic notions such as the action of a group on a set, fields, domains, reduced rings, ideals (radical, prime and maximal) of a (commutative) ring, euclidean, principal ideal, and unique factorization domains, field extensions, algebraic elements, minimal polynomials and splitting fields. TEACHING METHODS Standard. SYLLABUS/CONTENT Groups, homomorphisms of groups, subgroups and quotient groups. Linear groups, permutation groups, finite groups of low order. Group actions on sets. Rings, subrings and ideals. Euclidean rings and factorial rings. Polynomials rings. Filed extensions. Modules. Structure theorem of fg modules over PID RECOMMENDED READING/BIBLIOGRAPHY M. Artin, Algebra, Bollati Boringhieri; Lindsay N. Childs, "Algebra, un'introduzione concreta", (traduzione di Carlo Traverso), ETS Editrice Pisa, 1989. D.Dikranjan, M.Lucido, Aritmetica ed Algebra, Liguori Eds. TEACHERS AND EXAM BOARD MATTEO VARBARO ALDO CONCA Ricevimento: Office hours will be fixed at the beginning of the semester and comunicated via alulaweb. Exam Board MATTEO VARBARO (President) ALDO CONCA LESSONS LESSONS START The class will start according to the academic calendar. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written and oral ASSESSMENT METHODS If each of the intermediates written exams has been overcome with a grade >=16/30, and the average grade is at least 18/30, it is not necessary to take the written exam. The written exam consists in exercises related to concepts seen during the lectures. Similar exercises are often done during the exercise-lectures. The oral exams will concern concepts seen during the lectures, with the purpose to verify if the student has gained the necessary knowledge Exam schedule Data appello Orario Luogo Degree type Note 09/01/2024 10:00 GENOVA Scritto 13/02/2024 10:00 GENOVA Scritto 11/06/2024 10:00 GENOVA Scritto 09/07/2024 14:00 GENOVA Scritto 17/09/2024 10:00 GENOVA Scritto FURTHER INFORMATION Intermediete written tests. Agenda 2030 - Sustainable Development Goals Quality education Gender equality