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University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

TEACHING MATHEMATICS
cod. 06187

borrowed from Corso di TIPO in CDS 0263 - MATEMATICHE COMPLEMENTARI II - cod. 04523
Academic year 2010/11
3° year of course - Second semester
Professor
Academic discipline
Matematiche complementari (MAT/04)
Field
A scelta dello studente
Type of training activity
Student's choice
60 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -
lectures timetable unavailable
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Learning objectives

To study in deep mathematical knowledge, also from historical and epistemological point of view.

Prerequisites

Basic concepts of Mathematics

Course unit content


The Babylonian and Egyptian mathematics.
The Greek mathematics: Thales, Pythagoras and his school, the crisis of incommensurables. Zeno's paradoxes.
The three famous problems of Greek antiquity: quadrature of the circle, duplication of the cube, trisection of angle. Hippocrates and the quadrature of lunula.
Plato: arithmetic and geometry, the platonics polyedra.
Numerics systems: natural, integer, rational, real, complex numbers. The fundamental theorem of Algebra.
Non-Euclidean geometries: hystorical and epistemological aspects, Poincaré's and Klein's models.
The Erlangen program and the transformations geometry: congruence, similarity, affinity, projectivity.
The geometrical transformations in Escher's works.
The geometrical transformations in the space.
The problem of foundations of Geometry: the Hilbert's axioms, indipendence, coherence, completeness.

Full programme

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Bibliography

E. Agazzi, D. Palladino, Le geometrie non euclidee e i fondamenti della geometria dal punto di vista elementare, La Scuola Editrice, Brescia, 1998.
C.B.Boyer, Storia della Matematica, Mondadori, Milano, 1980.
M. Dedò, Trasformazioni geometriche (con un’introduzione al modello di Poincaré), Decibel, Zanichelli, Bologna, 1996.
F. Speranza, Scritti di Epistemologia della Matematica, Pitagora, Bologna, 1997.

Teaching methods

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Assessment methods and criteria

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Other information

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