CODE 109049 ACADEMIC YEAR 2025/2026 CREDITS 12 cfu anno 1 MATEMATICA 11907 (LM-40 R) - GENOVA TEACHING LOCATION GENOVA MODULES Questo insegnamento è composto da: COMMUTATIVE ALGEBRA 1 ALGEBRA 3 MATHEMATICAL LOGIC ALGEBRAIC NUMBER THEORY CODING THEORY GALOIS THEORY OVERVIEW The course is made up of two modules, culturally connected but completely independent. Please consult the module data sheets for specific details. AIMS AND CONTENT LEARNING OUTCOMES The aim of the course is to introduce the basic tools for understanding first-order logical theories and their models, and the fundamental techniques related to algebra, mainly in the commutative setting, applied to both classical and foundational problems, as well as more modern and applied ones. In the logic module, the completeness and compactness theorems, as well as incompleteness theorems of arithmetic are covered. In the algebra modules, some basic notions are introduced, including localization, tensor product, and Krull dimension. Furthermore, the computational aspects of algebra are studied, such as Gröbner bases, as well as more applied aspects such as coding theory. PREREQUISITES Please consult the module data sheets for specific details. TEACHERS AND EXAM BOARD EMANUELA DE NEGRI Ricevimento: By appointment. STEFANO VIGNI ALESSANDRO DE STEFANI Ricevimento: By appointment ALDO CONCA Ricevimento: Office hours will be fixed at the beginning of the semester and comunicated via alulaweb. MATTEO VARBARO Ricevimento: The office hours will be ANNA MARIA BIGATTI Ricevimento: Reception hours: before and after lessons, or upon request by email/Teams. SARA NEGRI Ricevimento: By appointment FRANCESCO VENEZIANO Ricevimento: See Aulaweb EXAMS EXAM DESCRIPTION The final grade is given by the arithmetic mean (rounded up) of the exams of the two modules, which can be taken in any order and in a completely independent way. For the exam description of the two single modules, please see the specific teaching schedule of each module. Students with DSA certification ("Specific Learning Disorders"), disability or other special educational needs are advised to contact 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. Such aids will be defined according to specific needs, together with the Referent for the School of the Committe for the inclusion of Students with Disabilites and with SLD. Students in such conditions are invited to get in touch (via e-mail) with the Teacher at least 7 days before the examination. ASSESSMENT METHODS For the assesment method of the two single modules, please see the specific teaching schedule of each module. Agenda 2030 - Sustainable Development Goals Quality education Gender equality
