Discrete Mathematics


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.

General characterization





Responsible teacher

João Jorge Ribeiro Soares Gonçalves de Araújo


Weekly - 5

Total - 77

Teaching language






[1] R. Johnsonbaugh, Discrete Mathematics, Prentice Hall Inter., 1997

[2] T. S. Blyth e E. F. Robertson, Sets and Mappings, Chapman and Hall, 1986

[3] N. L. Biggs, Discrete Mathematics, Oxford Science Publ., 1994

[4] K. A. Ross e C. R. B. Wright, Discrete Mathematics, Prentice Hall Inter.,1999

[5] R. J. Wilson e J. J. Watkins , Graphs an Introductory Approach, Wiley, 1990

[6] S. Lipschutz, Set Theory and Related Topics, Mc Graw-Hill, 1964

[7] D.M. Cardoso, J. Szymanski e M. Rostami, Matemática Discreta, Escolar Editora, 2009

[8] A. J. Franco de Oliveira, Teoria de Conjuntos, Escolar Editora, 1989

[9] C. André e F. Ferreira, Matemática Finita, Universidade Aberta, 2000


Teaching method

Basic concepts will be introduced in lectures ("aulas teóricas") and problems will be solved in problem solving classes ("Aulas práticas").

Evaluation method

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. 

Subject matter

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

1. Introduction

2. Connexity

3. Trees

4. Euler graphs

5. Matrices and graphs


Programs where the course is taught: