| Code |
16669
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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 |
All classes are theoretical and practical. After the teacher has presented the material, duly illustrated with examples, students are invited to apply their knowledge to solve the proposed exercises.
The teaching-learning assessment consists of three moments: two mini-tests and a final test.
The Teaching-Learning (EA) grade is given by the sum of the results obtained in the three assessment moments.
Students who do not obtain a minimum of 5.5 points in the Teaching-Learning grade are Not Admitted.
To pass the teaching-learning period, students must obtain an EA grade equal to or higher than 9.5 points.
All Final Year students or student workers (indicated by the Academic Services) are Admitted to the Exam.
The exam is rated at 20 points.
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Language |
Portuguese. Tutorial support is available in English.
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