Università degli Studi di Pavia

Dipartimento di Matematica ''F. Casorati''

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Complementary Mathematics

Professors:
Antonini Samuele
Year:
2015/2016
Course code:
500706
ECTS:
6
SSD:
MAT/04
DM:
270/04
Lessons:
48
Period:
I semester
Language:
Italian

Objectives

The course aims to introduce plane Euclidean geometry in the Euclid perspectives and in the modern Hilbert's view, to develop competences for problem solving and for an epistemological and didactical analysis of Euclidean plane geometry.

Teaching methods

Frontal lessons, discussions, problem solving.

Examination

Written and oral examination.

Prerequisites

Main concepts studied in Mathematics Bachelor Degree Courses.

Syllabus

Euclid plane geometry. Books I ? VI of Euclid's Elements. Common notions, postulates, definitions, propositions. The fifth postulate and the theory of parallel lines. Introduction to Non-Euclidean Geometries. Classical problems of compass and ruler constructions.
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.
The study will be combined with an analysis from epistemological, cognitive and didactical points of view.

Bibliography

Hilbert, D., Fondamenti della geometria, Feltrinelli, 1968
Agazzi E., Palladino, D., Le geometrie non euclidee e i fondamenti della geometria, ed. La Scuola 1998.
Gli Elementi di Euclide, a cura di A. Frajese e L. Maccioni, Torino, Utet, 1970
Teacher's notes.


Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602