CODE 25897 ACADEMIC YEAR 2022/2023 CREDITS 9 cfu anno 1 MATEMATICA 8760 (L-35) - GENOVA 9 cfu anno 1 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI 8766 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/02 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW In this course we present to the first year student of the degree course in Mathematics the basic mathematical language and a first introduction to abstract algebraic structures through the preliminary analysis of the algebraic structures of the set of integers and of the set of polynomials a coefficients in a field. AIMS AND CONTENT LEARNING OUTCOMES Provide basic mathematical language. Introduction to abstract algebraic notions by studying the algebra of integers, polynomials in a rational, real, complex or finite fileds coefficient variable and their quotients. First introduction to abstract group theory. AIMS AND LEARNING OUTCOMES By attending and partecipating to the activities (lectures both theretical and exercises, guided exercises, tutoring sessions, etc.) the student will - Become familiar with the basic mathematical language and improve formalization skills. - Become familiar with algebraic structures, first through the study of already known objects (integers, polynomials), then with an abstraction towards more theoretical notions (groups, quotients, homomorphisms etc.). TEACHING METHODS Standard blackboard lectures with studentes and teachers in presence. SYLLABUS/CONTENT Introduction to the basic notions: sets, maps, surjectiive, , injective and bijective. - Binary operation and their properties. Equivalence relations and induced quotients. - Cardinality: countsble and uncountable sets. Permutations. Induction. Newton binomial formula. - The integers: Euclidean algorithm and its applications. Prime numbers and unique factorization. The integers mod n. - Complex numbers. - Polinomials: in one variable and coefficients in the rational numbers, real numbers, complex numbers and finite fields. . Unique factorization property for polynomials. Irreducibility criteria. Quotients and their properties: zero-divisors, nilpotents and invertible elements. - Introduction to algebraic structures. Groups, perionds, subgroups, homomorphisms and quotients. RECOMMENDED READING/BIBLIOGRAPHY Luca Barbieri-Viale, "Che cosa e' un numero?", Cortina Ed. 2013. Lindsay N. Childs, "Algebra, un'introduzione concreta", (traduzione di Carlo Traverso), ETS Editrice Pisa, 1989. M. Artin, Algebra, Bollati Boringhieri I. N. Herstein, Algebra, Editori Riuniti Teachers will also provide written notes in italian via aula-web TEACHERS AND EXAM BOARD ALESSANDRO DE STEFANI Ricevimento: By appointment ALDO CONCA Ricevimento: To be decided later on when the general timetable will be fixed. Exam Board ALDO CONCA (President) MARIA EVELINA ROSSI ALESSANDRO DE STEFANI (President Substitute) 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 The exam consists of a written test and an oral exam. Exam schedule Data appello Orario Luogo Degree type Note 17/01/2023 09:00 GENOVA Scritto 19/01/2023 09:00 GENOVA Orale 14/02/2023 09:00 GENOVA Scritto 16/02/2023 09:00 GENOVA Orale 08/06/2023 09:00 GENOVA Scritto 09/06/2023 09:00 GENOVA Orale 03/07/2023 09:00 GENOVA Scritto 04/07/2023 09:00 GENOVA Orale 11/09/2023 09:00 GENOVA Scritto 12/09/2023 09:00 GENOVA Orale 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 !