2019/2020

2019/2020

DM270

MAT/04 (COMPLEMENTARY MATHEMATICS)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

1°

1st semester (30/09/2019 - 10/01/2020)

6

48 lesson hours

Italian

WRITTEN AND ORAL TEST

MARACCI MIRKO (titolare) - 6 ECTS

Mathematical knowledge and compentencies developed in the "laurea triennale" in mathematics.

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.

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.

Interactive lessons possibly with the use of dynamic geometry software, to introduce the contents of the course and discuss theoretical and meta-theoretical issues, and problem-solving sessions.

* "Gli Elementi di Euclide", edited by A. Frajese and L. Maccioni, Torino, Utet, 1970
* "The thirteen books of Euclid's Elements", edited by 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 achievement of the learning objectives will be ascertained through a written and an oral examination. The written examination will include mathematical tasks and open questions. The examinations will aim at assessing the level of knowledge of the contents of the course and the ability to autonomously re-relaborate these contents.