Scheda programma d'esame
ALGEBRA 1
GIOVANNI GAIFFI
Anno accademico2016/17
CdSMATEMATICA
Codice037AA
CFU6
PeriodoPrimo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
ALGEBRA 1MAT/02LEZIONI60
FILIPPO GIANLUCA CALLEGARO unimap
GIOVANNI GAIFFI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The students are expected to deal with the basic algebraic structures like groups, rings, fields and with an introduction to the Galois theory. They will be tested on the basis of various exercises and examples.
Assessment criteria of knowledge
The students is asked to solve a number of problems in the written exam and to give proofs and examples relative to the matter of the course.

Methods:

  • Final oral exam
  • Final written exam
  • Periodic written tests

Further information:
No special weighting, but roughly 50% is assigned to the written exam and roughly 50% to the oral exam.

Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • individual study
  • group work

Attendance: Advised

Teaching methods:

  • Lectures
  • Task-based learning/problem-based learning/inquiry-based learning

Syllabus
Theory of groups : subgroups and normal subgroups, homomorphisms, quotients. Authomorphims, conjugacy classes, class formula, permutations, finite abelian groups. Theory of rings: domains, zero divisors, units, ideals, quotients, homomorphisms. Special rings: euclidean domanins, principal ideal domains, unique factorization domains. Extensions of fields, splitting field of a polynomial, finite Galois theory.
Bibliography
Recommended readings include the following books: S. Lang, Undergraduate Algebra 2nd Ed., Springer-Verlag. N. Herstein, Algebra, Editori Riuniti. M. Artin, Algebra, Bollati Boringhieri.
Ultimo aggiornamento 14/11/2016 17:27