The student is supposed acquire basic knowledge on Graph Theory, Set Theory and Number theory, in learning process, logical reasoning and critical mind are developed.
João Jorge Ribeiro Soares Gonçalves de Araújo
Weekly - 5
Total - 77
 R. Johnsonbaugh, Discrete Mathematics, Prentice Hall Inter., 1997
 T. S. Blyth e E. F. Robertson, Sets and Mappings, Chapman and Hall, 1986
 N. L. Biggs, Discrete Mathematics, Oxford Science Publ., 1994
 K. A. Ross e C. R. B. Wright, Discrete Mathematics, Prentice Hall Inter.,1999
 R. J. Wilson e J. J. Watkins , Graphs an Introductory Approach, Wiley, 1990
 S. Lipschutz, Set Theory and Related Topics, Mc Graw-Hill, 1964
 D.M. Cardoso, J. Szymanski e M. Rostami, Matemática Discreta, Escolar Editora, 2009
 A. J. Franco de Oliveira, Teoria de Conjuntos, Escolar Editora, 1989
 C. André e F. Ferreira, Matemática Finita, Universidade Aberta, 2000
Basic concepts will be introduced in lectures ("aulas teóricas") and problems will be solved in problem solving classes ("Aulas práticas").
There will be three test during the term and a final exam.
The students are required to subscribe to each test/exam, at the CLIP.
Part 1 - Sets, relations and functions
1. Sets: representations and basic operations; power set; cardinality
2. Binary relations
3. Functions: bijections; composition and inverse
Part 2 - Induction
1. Inductive definitions
2. Induction over natural numbers and structural induction
3. Complete induction and course-of-values induction
4. Recursive functions and proofs by induction
Part 3 - Graphs and applications
4. Euler graphs
5. Matrices and graphs
Programs where the course is taught: