Logic and Set Theory
The goal of this course is to: familiarize the students with the process of formalizing mathematical reasoning; introduce the standard concepts and results of Mathematical Logic (on propositional calculus, predicate calculus and set theory) – including the study of the advantages and limitations of the formalization process.
1. Proposicional calculus
2. Predicate calculus
3. Set theory
It is intended that at the end of this Course, students should be able to:
• Recognize the usefulness of the formal reasoning, especially of mathematical reasoning.
• Apply the key techniques of propositional calculus, predicate calculus and set theory.
Propositional calculus:
• The language of propositional calculus.
• The semantics of propositional calculus.
• The proofs in propositional calculus.
Predicate Calculus:
• The first-order languages.
• The semantics of predicate calculus.
• The proofs in predicate calculus.
Set theory:
• The nature of definitions.
• A subsystem of axioms to set theory.
• Operations on sets.
• Relations and functions.
Main
M. J. Edmundo, G. Ferreira e J. Gaspar, Introdução à Lógica Matemática (available online).
Complementary readings:
- M. S. Lourenço, Teoria Clássica da Dedução, Assirio & Alvim 1991.
- Richard T. W. Arthur, Natural Deduction: An Introduction to Logic with Real Arguments, a Little History, and Some Humour, Broadview Press, 2011.
E-learning.
Continuous assessment is privileged: 2 digital written documents (e-folios) during the semester (40%) and a final digital test, Global e-folio (e-folio G) at the end of the semester (60%). In due time, students can alternatively choose to perform one final exam (100%).