Introduction to Logic and Elementary Mathematics
Code
10971
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
9.0
Teacher in charge
Vitor Hugo Bento Dias Fernandes
Weekly hours
6
Total hours
84
Teaching language
Português
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.
Prerequisites
The student must be familiar with mathematics taught at pre-university level in Portugal (12nd level - science area).
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. Integers modulo n.
8. Finite and infinite sets.
Bibliography
Bibliography:
1. Guerreiro, J.S., Curso de Matemáticas Gerais, vol 1, Livraria Escolar Editora, 1973
2. Johnson,D. L., Elements of Logic via Numbers and Sets, Springer Undergraduate Mathematics Series, 1998
3. Krantz, S. G., The elements of advanced Mathematics, CRC Press, 1995
4. Sebastião e Silva, J., Compêndio de Matemàtica, Curso Complementar do Ensino Secundário, !º volume, 1º tomo, GAP-MEC 1995
5. Velleman, D. J., How to prove it, Cambridge University Press, 1994
Teaching method
Classes consist on an oral explanation of the theory which is illustrated by examples and the resolution of some exercises.
Evaluation method
First inscription students may miss classes 3 times maximum; the others must attend, at least, 2/3 of classes.
Each student will be evaluated by 2 tests and at least 2 mini-tests or an exam. More details in the portuguese version.