Academic year: 2024-25
Course: Foundation Course Science
Credits: 3
Period: Second semester
Number of hours: 24
Teacher(s): Roberto Bruni (roberto.bruni@unipi.it)
Language of instruction: English
Learning outcomes
Knowledge
Students will learn the syntax and some basic aspects of the semantics of Set Theory, Propositional Calculus and First-Order Logic. They will also learn simple but formal techniques applicable to the three formalisms to state some properties and to prove them.
Assessment criteria of knowledge
Oral exam at the end of the course.
Skills
Students will learn how to use logic formulas to formalize simple propositions in the natural language. They will also learn how to use formal proof techniques to prove (or disprove) equivalences among sets, and among propositional or first-order formulas.
Assessment criteria of skills
Continuous evaluation based on on-line tests along the course.
Behaviors
The students will be encouraged to transfer the acquired knowledge to other contexts.
Assessment criteria of behaviors
Classroom discussion of examples and exercises.
Prerequisites
None
Co-requisites
None
Prerequisites for further study
None
Teaching methods
Learning activities:
attending lectures
participation in discussions
home assignments, to be solved together in the next lecture
individual study
Attendance: Advised
Teaching methods:
Lectures
Self-assesment tests
Recommended readings
Syllabus
Introduction: relevance of the Mathematical Language in Science.
Examples of discursive and formal proofs of algebraic identities.
Notations for sets, comparing sets, composing sets: some laws.
Discursive, graphical and formal proofs of set equalities.
Syntax and semantics of Propositional Calculus.
Syntax and basics of semantics of First Order Logic.
Formalization of natural language statements and formal proofs of logical equivalence.
Bibliography
Teaching material (in English) will be distributed at the beginning of the course.
Non-attending students info
Recorded streaming of lectures will be available upon request
Assessment methods
Online tests during the course, and oral exam.
Work placement
None
Class web page
Additional web pages
None
Notes
None