# 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

10971

9.0

##### Responsible teacher

Manuel Messias Rocha de Jesus

Weekly - 6

Total - 72

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).

## Programs

Programs where the course is taught: