2023
Introduction to Logic and Foundations of Mathematics
Name: Introduction to Logic and Foundations of Mathematics
Code: MAT14215L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Presentation
It is an initial discipline where students are expected to master the basic concepts of logic and the foundations of mathematics, and the practice of formal demonstration.
Sustainable Development Goals
Learning Goals
The main outcomes of the course are to acquire basic concepts logic and the foundations of mathematics, and the correct use of formal proofs. Students are expected to be able to use the various contents in order to use them skillfully and with critical sense in other areas of science, initiating them in mathematical reasoning and teaching them diverse methods of proof making.
Contents
Universe and language.
Axioms and set operations.
Relations and maps.
Equivalences and orders.
Well-ordered sets and ordinals.
Natural numbers and mathematical induction.
Axioms and set operations.
Relations and maps.
Equivalences and orders.
Well-ordered sets and ordinals.
Natural numbers and mathematical induction.
Teaching Methods
Problem-solving sessions, where students are invited to work on their own or in small groups, with some moments of exposition or discussion involving the whole class.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.
Teaching Staff
- Bruno Miguel Antunes Dinis [responsible]
