| Code |
14334
|
| Year |
1
|
| Semester |
S2
|
| ECTS Credits |
6
|
| Workload |
TP(60H)
|
| Scientific area |
Mathematics
|
|
Entry requirements |
This curricular unit don´t have entry requirements. Mathematical maturity at the level of Calculus I is recommended, but not mandatory.
|
|
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.
|
|
Teaching Methodologies and Assessment Criteria |
All classes are Theoretical-Practical.
The Teaching-Learning assessment consists of three tests (T1, T2 and T3) all evaluated for 20 points.
The student with a grade lower than 2.5 in any of the tests (T1, T2 or T3) is Not Admitted.
The student with worker-student status is admitted to the TL assessment, respecting the following conditions.
The final classification of the Teaching-Learning assessment is given by the formula: TL=0.35*(T1+T3)+0.30*T2
Students with an TL classification above 17 points are invited to take a supplementary test to defend their grade; In case of no-show, the final classification will be 17 points.
Article 134 of the UBI General Regulations will be applied to students who commit fraud or attempted fraud.
|
|
Language |
Portuguese. Tutorial support is available in English.
|