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

COMPLEMENTARY MATHEMATICS II
cod. 04523

Academic year 2009/10
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: PARMA
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

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

Prerequisites

<p>Basic concepts of Mathematics</p>

Course unit content

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

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. <br />
C.B.Boyer, Storia della Matematica, Mondadori, Milano, 1980. <br />
M. Dedò, Trasformazioni geometriche (con un’introduzione al modello di Poincaré), Decibel, Zanichelli, Bologna, 1996. <br />
F. Speranza, Scritti di Epistemologia della Matematica, Pitagora, Bologna, 1997.<br />

Teaching methods

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Assessment methods and criteria

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Other information

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