Module page

Algebra II

academic year:	2013/2014
instructor:	Valentina Barucci
degree course:	Mathematics - DM 270/04 (triennale), II year
type of training activity:	caratterizzante
credits:	9 (72 class hours)
scientific sector:	MAT/02 Algebra
teaching language:	italiano
period:	II sem (03/03/2014 - 13/06/2014)

Lecture meeting time and location

Presence: highly recommended

Module aims: Il corso descrive le proprietà elementari dei gruppi finiti e delle loro azioni su insiemi e la teoria delle estensioni algebriche di campi. In particolare:

Principali teoremi elementari di per i gruppi finiti, inclusi i teoremi di Sylow;
Elementi algebrici e trascendenti;
Classificazione dei campi finiti;
Corrispondenza di Galois;
Costruibilità con riga e compasso;
Risolubilità delle equazioni polinomiali.

Module subject:

Groups.
Group actions and symmetries.
Finite groups and Sylow theorems.
Field theory
Galois Theory

Detailed module subject: Diario delle lezioni

Suggested reading:
Michael Artin, "Algebra", Boringhieri, 1997.
Giulia Maria Piacentini Cattaneo, Algebra, un approccio algoritmico, Zanichelli 1996.
G. Campanella, "Appunti di Algebra 2" ed esercizi, http://campanelgiu.altervista.org/

Type of course: standard

Exercises:

Examination tests:

Knowledge and understanding: Knowledge and understanding
Successful students will be able to remember the main concepts and technical tools of the course. They will know elementary examples of finite groups , in particular groups of symmetries. They will understand how to treat some classical mathematical problems with tools from algebra and from field theory.

Skills and attributes:
Successful students will be able to solve problems concerning finite groups, field extensions, splitting field of a polynomial and to calculate the Galois group of some classes of polynomials.

Personal study: the percentage of personal study required by this course is the 65% of the total.

Statistical data on examinations