CODE 108961 ACADEMIC YEAR 2022/2023 CREDITS 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/01 TEACHING LOCATION GENOVA SEMESTER 2° Semester TEACHING MATERIALS AULAWEB OVERVIEW The course introduce set theory as foundational theory for mathematics. Then it presents some subjects peculiar to the theory, like ordinal and cardinal arithmetic, and provides some applications of them to algebra, topology, and analysis. AIMS AND CONTENT LEARNING OUTCOMES Main goal of the course is the study of set theoretic constructions and their mathematical applications. AIMS AND LEARNING OUTCOMES At the end of the course, students will be able to deal with basic set theoretic operations, recognise the applicazions of set theoretic principles like the axiom of choince, be familiar with the concepts of order type of a well order and cardinality, and apply set-theoretic methods to various mathematical problems. PREREQUISITES Familiarity with basic mathematical notions from algebra, analysis, and topology. TEACHING METHODS Class lectures. SYLLABUS/CONTENT 1. Review of the notion of a set and of basic set theoretic operations 2. Construction of number sets 3. The axiomatisation of set theory 4. The axiom of choice and its equivalents 5. Ordinals, cardinals, and their arithmetic 6. Descriptive set theory 7. Applications RECOMMENDED READING/BIBLIOGRAPHY The instructor notes will be available. Other useful references are: D.W. Cunningham, Set theory, Cambridge University Press 2016. K. Hrbacek, T. Jech, Introduction to set theory, Dekker 1999. A.S. Kechris, Classical descriptive set theory, Springer 1995. TEACHERS AND EXAM BOARD RICCARDO CAMERLO Ricevimento: By appointment. Exam Board RICCARDO CAMERLO (President) SARA NEGRI GIUSEPPE ROSOLINI (President Substitute) LESSONS Class schedule L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy. EXAMS EXAM DESCRIPTION Written exam. The written exam can be partially or totally replace by exercises proposed during lectures. Students with DSA certification («specific learning disabilities»), disability or other special educational needs are advised to contact the teacher at the beginning of the course to establish on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools. ASSESSMENT METHODS The evaluation of the written test or the exercises takes into account the correctedness of the solution, the clarity of the exposition, and the rigour of the arguments.