| 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-practical. After the subject is presented, duly illustrated with examples, by the teacher, students are invited to apply their knowledge in solving proposed exercises.
The teaching-learning assessment consists of three tests.
The student who does not obtain a classification of 2,5 values in each of the tests is rejected.
The student who has at least 2,5 values in each of the tests is Admitted to the Exam with the classification in Teaching-Learning given by the formula EA=T1*0.36+T2*.28+T3*.36.
To pass the teaching-learning period, the student must obtain an EA rating equal to or greater than 9.5 values.
All Finalist students or Student Workers (recommended by the Academic Services) are Admitted to the Examination.
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Language |
Portuguese. Tutorial support is available in English.
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