| Code |
14334
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| Year |
1
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| Semester |
S2
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
This curricular unit don´t have entry requirements. Mathematical maturity at the level of Calculus I is recommended, but not mandatory.
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Mode of delivery |
Face-to-face.
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Work placements |
Non applicable.
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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
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Syllabus |
1- Set theory.
2- Relations, equivalence relations, functions, order relations, Boole algebras.
3- Mathematical induction.
4- Counting principles.
5- Graph theory.
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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.
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Teaching Methodologies and Assessment Criteria |
978 / 5,000
All classes are theoretical and practical.
The teaching-learning assessment consists of three exams.
1st Exam - 6:00 pm on Tuesday, March 25, 2025.
2nd Exam - 6:00 pm on Tuesday, April 29, 2025.
3rd Exam - 6:00 pm on Thursday, June 5, 2025.
Each exam is worth 20 points and each exam has a minimum grade of 2.5 points.
The final grade for continuous assessment Nf will be given by Nf = 0.35*F1 +0.3*F2+ 0.35*F3, where each Fi is the grade for each exam i.
If a student does not reach the minimum grade, he or she will not be admitted to the exam. Final year students and student workers are excluded from this rule. If the final grade for continuous assessment Nf is strictly higher than 17 points, the student must also take an oral exam to maintain the grade. If, in this situation, the student does not take this exam, the final grade drops to 17 points. Also note that after this exam the final grade may be lower than the grade obtained by attendance.
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Language |
Portuguese. Tutorial support is available in English.
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