Foundations of Mathematics I
A.Y. 2024/2025
Learning objectives
The course aims at providing the students with a deep knowledge of some, modern
axiomatic theories. The main topic of the course is given by a detailed analysis
of the first example of modern, axiomatic theory, the foundations of geometry
according to Hilbert's approach. In addition, the elements of Veblen's and Tarski's system of axioms for geometry are presented as well as the foundations of non-Euclidean geometries, including the hyperbolic geometry in particular. The concluding part of the course is devoted to the axiomatic set theory (ZF) and the axiomatic theory of natural numbers.
axiomatic theories. The main topic of the course is given by a detailed analysis
of the first example of modern, axiomatic theory, the foundations of geometry
according to Hilbert's approach. In addition, the elements of Veblen's and Tarski's system of axioms for geometry are presented as well as the foundations of non-Euclidean geometries, including the hyperbolic geometry in particular. The concluding part of the course is devoted to the axiomatic set theory (ZF) and the axiomatic theory of natural numbers.
Expected learning outcomes
Undefined
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Lessons: 42 hours
Professors:
Branchetti Laura, Mantovani Sandra
Shifts:
Professor(s)
Reception:
By appointment
Online, Microsoft Teams
Reception:
Thursday 12.45-14.15, by appointment
Studio 1019, I Floor, Dipartimento di Matematica, Via Saldini, 50