Base Knowledge
N/A
Teaching Methodologies
Not available
Learning Results
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; Study of algorithms.
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.