Elementos de Álgebra
Cod: 21133
Department: DCET
Department: DCET
ECTS: 6
Scientific area: Mathematics
Scientific area: Mathematics
Total working hours: 156
Total contact time: 26
Total contact time: 26
In this course unit students are introduced to some algebra structures such as groups, rings and fields. In particular, it is also important the study of polynomials and irreducibility criteria
- Groups
- Rings
- Fields
At the end of this course, students are expected to be able to deal with fundamental concepts and techniques concerning groups, rings and fields.
1) Groups: subgroups; normal subgroups, quotient groups; homomorphism of groups; cyclic groups; direct products, finite abelian groups; finite groups.
2) Rings: subrings, ideals, quotient rings; homomorphism of rings; polynomials; principal ideal domains, euclidean domains; zeros of polynomials
3) Fields: prime fields; extension of fields; splitting fields; finite fields.
2) Rings: subrings, ideals, quotient rings; homomorphism of rings; polynomials; principal ideal domains, euclidean domains; zeros of polynomials
3) Fields: prime fields; extension of fields; splitting fields; finite fields.
SOBRAL, Manuela, Álgebra, Universidade Aberta, 1998.
Complementary
1) RUI LOJA FERNANDES, MANUEL RICOU, Introdução à Álgebra,
ISTPRESS
2) MONTEIRO, António; MATOS, Isabel Teixeira, Álgebra - Um Primeiro Curso,
Escolar Editora, 1995
E-learning.
Continuous assessment is privileged: 2 digital written documents (e-folios) during the semester (40%) and a final digital test, Global e-folio (e-folio G) at the end of the semester (60%). In due time, students can alternatively choose to perform one final exam (100%).