Algebra I
Code
10977
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
9.0
Teacher in charge
Maria de Fátima Vale de Gato Santos Rodrigues
Weekly hours
5
Total hours
70
Teaching language
Português
Objectives
The student is supposed to learn about fundamental aspects of groups and rings.
Prerequisites
None.
Subject matter
I. Groups
1. Basics.
2. Subgroups.
3. Cyclic groups.
4. Cosets. Index of a subgroup.
5. Congruence relations. Quotient groups. Normal subgroups.
6. Morphisms.
7. Canonical decomposition and Homomorphism Theorem.
8. Isomorphism theorems.
9. Symmetric Group.
II. Rings
1. Basics.
2. Zero divisors. Integral domains. Division rings.
3. Characteristic of a ring.
4. Subrings.
5. Congruence relations. Quotient rings. Ideals.
6. Morphisms.
7. Canonical decomposition and Homomorphism Theorem.
8. Isomorphism theorems.
Bibliography
1. J. Durbin, Modern Algebra, John Wiley & Sons, Inc.
2. N. Jacobson, Basic Algebra I, W. H. Freeman and Company.
3. S. Lang, Algebra, Addison-Wesley Publishing Company, Inc.
4. A. J. Monteiro and I. T. Matos, Álgebra, um primeiro curso, Escolar Editora.
5. M. Sobral, Álgebra, Universidade Aberta.
Teaching method
Lectures + problem-solving sessions (5h00).
Evaluation method
Students must attend, at least, 2/3 of the classes taught.
There are three mid-term tests. These tests can substitute the final exam if the student has grade, at least, 6.5 in the third one and CT is, at least, 9.5. CT is the arithmetic mean of the non-rounded grades of the tests.
If the student satisfies the conditions above with CT (rounded to units) greater than 17, he may choose between having 17 as final grade or undertake a complementary assessment.
To be approved in final exam, the student must have a minimum grade of 9.5 in it. Again, for grades (rounded to units) greater than 17, the student must undertake a complementary assessment, otherwise his final grade will be 17.
More detailed rules are available in the portuguese version.