| Código |
14334
|
| Ano |
1
|
| Semestre |
S2
|
| Créditos ECTS |
6
|
| Carga Horária |
TP(60H)
|
| Área Científica |
Matemática
|
|
Mode of delivery |
Face-to-face.
|
|
Work placements |
Non applicable.
|
|
Learning outcomes |
This Curricular Unit aims to give an introduction to several themes of Discrete Mathematics: set theory, relations, equivalence relations, functions, order relations, Boole algebras, mathematical induction, counting principles and graph theory.
In the end of this Curricular Unit the student should be able to:
- discern the different types of proofs
- compute small theoretical proofs within the scope of the subjects covered in the discipline
- compute the partition induced by an equivalence relation and vice versa
- compute the transitive closure of a relation
- represent graphically order relations
- compute proofs using mathematical induction
- resolve counting problems
- manipulate binomial coefficients
- compute an Euler circuit using the Fleury algorithm
- compute a minimal generator tree using Kruskal's algorithm
- estimate the chromatic number of a graph
|
|
Syllabus |
1- Set theory.
2- Relations, equivalence relations, functions, order relations, Boole algebras.
3- Mathematical induction.
4- Counting principles.
5- Graph theory.
|
|
Main Bibliography |
- Discrete Mathematics and Its Applications 7th edition. Rosen, Kenneth.
- Apontamentos de Matemática Discreta. Cruz, Henrique & Rosa, Silvério.
- Notes on Combinatorics. Cameroon, Peter.
- Ten Chapters of the Algebraical Art. Cameron, Peter.
|
| Language |
Portuguese. Tutorial support is available in English.
|