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
Herberto de Jesus da Silva
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. Finite and infinite sets.
Bibliography
Oliveira, Augusto J. Franco; Lógica & Aritmética, gradiva, 2010.
Pommersheim, J. E.; Marks, T. K.; Flapan, E. L; Number Theory, John Wiley & Sons, Inc., 2010.
Sebastião e Silva, J.; Compêndio de Matemática, 1.º Vol., 1º Tomo, GEP-MEC, Lisboa, 1975.
Vellement, D. J.; How To Prove It, A Structured Approach, 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
There are three tests that can substitute the final exam in case of approval. Otherwise the student must succeed the final exam. Detailed rules are available in the portuguese version.