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ALGEBRA 3

CODE 90694
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 3nd year of 8760 MATEMATICA (L-35) - GENOVA
  • 7 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA
  • 6 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA
  • 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/02
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    Language: English

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The goal of the course is to introduce fundamental and computational aspect of  commutative algebra.

    AIMS AND LEARNING OUTCOMES

    The aim is to introduce the basic notions of commutative algebra as, e.g., noethrerian ringsand modules, and their computational aspects via the introduction of Groebner bases. 

    PREREQUISITES

    Basic algegra (groups and rings).

    TEACHING METHODS

    Teaching style: In presence+computational sections with the use of symbolic computation packages.

    SYLLABUS/CONTENT

    1) - Rings, ideals and modules. Noetherian rings and the Hilbert basis theorem. Polynomials: The ring K [x_1, ..., x_n] of polynomials with coefficientsin a field.

    2) Grobner Bases  and the Buchberger algorithm. Systems of polynomial equations and elimination theory. Syzygies and intersection of ideals.

    3) Computations with system of Symbolic computations.

     

    RECOMMENDED READING/BIBLIOGRAPHY

    Computational Commutative Algebra, Kreuzer, Robbiano, Springer, 2004.

    TEACHERS AND EXAM BOARD

    Exam Board

    ALDO CONCA (President)

    FRANCESCO VENEZIANO

    ANNA MARIA BIGATTI (President Substitute)

    EMANUELA DE NEGRI (President Substitute)

    ALESSANDRO DE STEFANI (President Substitute)

    MARIA EVELINA ROSSI (President Substitute)

    MATTEO VARBARO (President Substitute)

    LESSONS

    LESSONS START

    The class will start according to the academic calendar.

    Class schedule

    ALGEBRA 3

    EXAMS

    EXAM DESCRIPTION

    Oral exam and computer algebra  project

    ASSESSMENT METHODS

    Discussion concerning the theoretical results and the algorithms presented. The student is expected to be able to reproduce the proofs of the main results discussed. 

    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 !