Base Knowledge
Basic knowledge is acquired at the level of secondary education.
Teaching Methodologies
The teaching methodologies used in this course are:
1) Verbal Methodologies (say), making use of pedagogical resources: Exposition, Explanation, Dialogue and Interrogation;
2) Intuitive Methodologies (show), making use of pedagogical resources: Demonstration, Audiovisuals and Written Texts.
Learning Results
This curricular unit has as general objective to allow the student to master the principles, techniques and methodologies associated with discrete structure problems.
It is intended to provide the student with bases so that he/she is able to:
1. Recognize mathematical structures in discrete systems;
2. Manipulate discrete structures through specific techniques for each type of structure;
3. Prove properties of discrete structures;
4. Use discrete math as a problem-solving language.
5. Develop abstract reasoning, from a logical and mathematical point of view.
Program
Set theory: Sets: definition and representations; Subsets; Operations on sets: reunion, intersection and difference; Cardinality; Partitions and power of sets; Mathematical induction; Cartesian product of sets; Relations: definitions, representations and properties; Functions: definition, injectivity, superjectivity and inversion.
Logic and propositional calculus: Elementary logic propositions and operations; truth tables; Tautologies and contradictions; Equivalence; Algebra of propositions; Modus ponens and syllogisms.
Combinatorial Analysis and Probabilities: Introduction; Fundamental principles of counting; Permutations and combinations; Inclusion/Exclusion Principle; Combinatorial calculus; Pascal’s triangle.
Introduction to Graph Theory: Introduction; Basic definitions; Incidence and degree; Isomorphisms; Subgraphs; Tour, Route and Path; Connected Graph and Bipartite Graph; Digraphs: isomorphism and connectedness; Representation of graphs by matrices; Trees.
Curricular Unit Teachers
Grading Methods
- - Exam - 100.0%
- - Individual Written Exams and Individual Works - 100.0%
Internship(s)
NAO
Bibliography
Hunter, D. J. (2011). Fundamentos da Matemática Discreta. LTC.
Lipschutz, S.; Lipson, M. (2004) 2000 solved problems in discrete mathematics. McGraw-Hill.
Lipschutz, S.; Lipson, M. (2009) Discrete mathematics. McGraw-Hill.
Menezes, P. B. (2013) Matemática discreta para computação e informática. Bookman.
Perdicoúlis, T. P. C. A. (2005) Tópicos de Matemática Discreta. Edição UTAD.
Rosen, K. H. (2009) Matemática Discreta e suas Aplicações. McGraw-Hill.