Logic and Set Theory

Cod: 21079

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

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.

• 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.* Lógica e Teoria de Conjuntos* (2013/14) (available online).

Complementary readings:

Natural Deduction: An Introduction to Logic with Real Arguments, a Little History, and Some Humour.

Autor: Richard T.W. Arthur.

Editora: Broadview Press, 2011.

ISBN: 1770481974, 9781770481978.

E-learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).