First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCM0014410, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course First cycle degree in
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2017/18
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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 ALBERTO TONOLO MAT/02

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

Mode of delivery (when and how)
Period First semester
Year 3rd Year
Teaching method frontal

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

Start of activities 02/10/2017
End of activities 19/01/2018

Examination board
Board From To Members of the board
6 Teoria di Galois - 2017/2018 01/10/2017 30/09/2018 TONOLO ALBERTO (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
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