| 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 |
Teaching Methodology:
All classes are theoretical-practical. After presenting the subject, duly illustrated with examples, by the teacher, students are invited to apply the knowledge in solving proposed exercises.
Assessment criteria
To obtain approval in the discipline in the teaching-learning period, the student must:
-get final grade equal or superior to 10.
In case the teaching-learning classification is higher than 17, the student must take an oral test.
In case of fraud at any time of assessment, the student is excluded from the assessment process.
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Language |
Portuguese. Tutorial support is available in English.
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