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Second cycle
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School of Science
Course unit
SCM0014410, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2019/20
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Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination GALOIS THEORY
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge RICCARDO COLPI MAT/02

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/02 Algebra 7.0

Course unit organization
Period First semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 3.0 24 51.0 No turn
Lecture 4.0 32 68.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2008 course timetable

Examination board
Board From To Members of the board
8 Teoria di Galois - a.a. 2019/2020 01/10/2019 30/09/2020 COLPI RICCARDO (Presidente)
LUCCHINI ANDREA (Membro Effettivo)

Prerequisites: Algebra and Geometry courses of the first and second years: in particular groups, rings fields and linear algebra.
Target skills and knowledge: The classical theory of the fields and the theory of Galois will be presented. In particular: ruler and compass constructions, solubility for radicals of
algebraic equations, field extensions, normality, separability.
Examination methods: Written and oral exams. In the written exam, the student must demonstrate to be able to solve exercises of the Galois theory. The oral exam, in which the vote is decided, is dedicated to verify the knowledge of the definitions and the results (and their proofs), encountered in the course.
Assessment criteria: The knowledge and the ability to apply the notions and results seen during the course will be evaluated.
Course unit contents: Polynomials and their roots. Artin theorem on simple extensions. Separable and purely inseparable extensions of fields. Splitting fields. Algebraic closure of a field. Galois extensions. Cyclotomic Extensions. Jordan Holder Theorem. Soluble groups. Fundamental theorem of algebra. Resolubility for radicals. Galois Theorem. Berlekamp algorithm. Cyclic extensions. Dedekind's theorem. Ruler and compass constructions. Galois groups of polynomials up to the fourth degree.
Planned learning activities and teaching methods: Frontal lessons, using a tablet.
Additional notes about suggested reading: The study material is made up of suggested text books, lesson notes, and any other notes that will be made available on the course website.
Textbooks (and optional supplementary readings)
  • D.J.H. Garling, A course in Galois Theory. --: Cambridge University Press 1986, --. Cerca nel catalogo
  • J.S. Milne, Fields and Galois Theory. --: (note disponibili in rete), --.
  • I. Martin Isaacs, Algebra, a graduate course. --: AMS, --. Cerca nel catalogo