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TEORIA ELEMENTARE DEGLI INSIEMI

CODE 108961
ACADEMIC YEAR 2023/2024
CREDITS
  • 6 cfu during the 3nd year of 8760 MATEMATICA (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 to introduce and analyse the 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.

    D. Goldrei, Classic set theory, Chapman & Hall 1996.

    TEACHERS AND EXAM BOARD

    Exam Board

    RICCARDO CAMERLO (President)

    GIUSEPPE ROSOLINI (President)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    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.