Elementary mathematics from a higher standpoint
- Professors:
- Maracci Mirko
- Year:
- 2017/2018
- Course code:
- 500707
- ECTS:
- 6
- SSD:
- MAT/04
- DM:
- 270/04
- Lessons:
- 48
- Period:
- I semester
- Language:
- Italian
Objectives
The course aims at analysing and comparing different axiomatic approaches to elementary geometry with a specific focus on the classical Euclidean presentation and the modern Hilbert's one.
Teaching methods
Lectures
Examination
Written and oral examination.
Prerequisites
Main concepts studied in Mathematics Bachelor Degree Courses.
Syllabus
Euclidean plane and solid geometry. Common notions, postulates, definitions, propositions. The fifth postulate and the theory of parallel lines. Classical problems of compass and ruler constructions.
Geometry as formal system: Hilbert's axioms. The problems of continuity and completeness of line. Issues of consistency, independence and categoricity. Introduction to Non-Euclidean Geometries.
Choquet's and Prodi's axioms. Geometry as the study of invariants: the Erlangen Program.
Geometry as formal system: Hilbert's axioms. The problems of continuity and completeness of line. Issues of consistency, independence and categoricity. Introduction to Non-Euclidean Geometries.
Choquet's and Prodi's axioms. Geometry as the study of invariants: the Erlangen Program.
Bibliography
Gli Elementi di Euclide, a cura di A. Frajese e L. Maccioni, Torino, Utet, 1970
The thirteen books of Euclid's Elements, a cura di T.S.Heath, Dover Publications
Hilbert, D., Fondamenti della geometria, Feltrinelli, 1968
Choquet G., L’insegnamento della geometria, Feltrinelli, 1967.
Volumi del progetto Matematica come scoperta di G.Prodi.
Agazzi E., Palladino, D., Le geometrie non euclidee e i fondamenti della geometria, ed. La Scuola 1998.
Materiale didattico fornito dal docente.
The thirteen books of Euclid's Elements, a cura di T.S.Heath, Dover Publications
Hilbert, D., Fondamenti della geometria, Feltrinelli, 1968
Choquet G., L’insegnamento della geometria, Feltrinelli, 1967.
Volumi del progetto Matematica come scoperta di G.Prodi.
Agazzi E., Palladino, D., Le geometrie non euclidee e i fondamenti della geometria, ed. La Scuola 1998.
Materiale didattico fornito dal docente.
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602