# Introduction to Logic and Elementary Mathematics

## Objectives

Use of logical operations on propositions, conditions and sets to decide if a proposition is true or false and to prove theorems.

Use of elementary concepts of Set Theory, namely basic set operations, equivalence relations and order relations.

## General characterization

##### Code

10971

##### Credits

9.0

##### Responsible teacher

Manuel Messias Rocha de Jesus

##### Hours

Weekly - 6

Total - 72

##### Teaching language

Português

### Prerequisites

The student must be familiar with mathematics taught at pre-university level in Portugal (12nd level - science area).

### Bibliography

Bibliography:

1. Ferreira, J.C., *Elementos de Lógica Matemática e Teoria dos Conjuntos*, 2001

2. Guerreiro, J.S., *Curso de Matemáticas Gerais*, vol 1, Livraria Escolar Editora, 1973

3. Johnson, D. L., *Elements of Logic via Numbers and Sets*, Springer Undergraduate Mathematics Series, 1998

4. Krantz, S. G., *The elements of advanced Mathematics*, CRC Press, 1995

5. Sebastião e Silva, J., *Compêndio de Matemàtica*, Curso Complementar do Ensino Secundário, 1º volume, 1º tomo, GAP-MEC 1995

6. Velleman, D. J., *How to prove it*, Cambridge University Press, 1994

### Teaching method

In theoretical sessions the contents of the course are exposed and illustrated with examples. In problem-solving sessions students will be asked to solve problems and elaborate demonstrations of some of the results presented.

Any questions/doubts are clarified during classes or tutorial sessions or even in extra sessions combined directly between student and teacher.

### Evaluation method

Students must attend, at least, 2/3 of problem-solving classes.

Each student will be evaluated by two tests or an exam. More details in the portuguese version.

## Subject matter

1. Sentential and quantificational logic.

2. Basic operations on sets.

3. Proof strategies.

4. Relations: equivalence and order relations.

5. Functions.

6. Mathematical induction and divisibility.

7. Finite and infinite sets.

8. Integers modulo n (optional).