Introduction to Logic and Elementary Mathematics
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.
Manuel Messias Rocha de Jesus
Weekly - 6
Total - 72
The student must be familiar with mathematics taught at pre-university level in Portugal (12nd level - science area).
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
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.
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.
1. Sentential and quantificational logic.
2. Basic operations on sets.
3. Proof strategies.
4. Relations: equivalence and order relations.
6. Mathematical induction and divisibility.
7. Finite and infinite sets.
8. Integers modulo n (optional).