# Discrete Mathematics

3629

### Department

Departamento de Matemática

6.0

### Teacher in charge

Maria de Fátima Vale de Gato Santos Rodrigues

5

77

Português

### 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.

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### 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

### Bibliography

Bibliografia

[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. In order to be aproved at the UC, students must attend to at least 2/3 or the given problem-solving sessions.

Tests are graded from 0 to 20 points.  A minimal grade of 6 points in the 3rd test is required. Whenever the requirements are fulfilled, the final grade corresponding to the (round up of the)  arithmetic sum of the grades of the three tests will be atributed. 10 points or more lead to approval.

Those students that fail the evaluation by tests, but fulfill the formal requirements, may go to the final exam.

Whenever the grade (of tests or exam) is more or equal than 18 points, an extra examination might be required. If the student declines it, the final grade of 17 points will be given.