# Discrete Mathematics

## Objectives

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

3629

6.0

##### Responsible teacher

João Jorge Ribeiro Soares Gonçalves de Araújo

##### Hours

Weekly - 5

Total - Available soon

Português

Available soon

### Bibliography

[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, OxfordScience 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 two 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

Programs where the course is taught: