SM/0127 - HISTORY AND EPISTEMOLOGY IN MATHEMATICAL EDUCATION 

Academic Year 2021/2022

Free text for the University

Objectives

The themes of the historical development of Mathematics with particular reference to the period from antiquity to the nineteenth century are introduced; it also deals with the basic themes of historical and epistemological reconstruction of the evolution of mathematical thought.
In particular, the student should acquire the following knowledge and skills.
To gain the main tools about the historical development of mathematics from the ancient mathematics untill the ninetheen century. To gain the basic tools of the historical reconstruction of the evolution of the mathematical thought.

Prerequisites

Knowledge of the the first degree in Mathematics

Contents

Chronological development of the history of mathematics (elements of the development of the arithmetics, geometry and elementary algebra). The pre-Hellenic mathematics. The first phase of Greek mathematics. Euclid. The twilight of the ancient mathematics. The arab mathematics. The development of the arab mathematics in Europe. The Renaissance mathematics. The mathematics from 1700 untill the first decades of 1900. Close examination of the evolution of the mathematical thought in the seventheen, eightheen and ninetheen century: the algebraic thought. The nature of objects and mathematical activity: Platonism, constructivists, neo-empiricists

Teaching Methods

Lectures and Interactive lessons - Guided Practice with a strong participation of the students;. Workshops involving one or several students. Tools: Blackboard, computer, web, Moodle.

Verification of learning

Spoken examination about the indivifual work (life and work of a mathematiciians, evolution of the mathematical thought in a given hystorical moment) and bout the arguments developed during the lectures. The written work has to be sent to the teacher by mail a week before the spoken examination.
The assessment criteria are the knowledge of the mathematical aspects of the courses; critical sensibility and originality of the individual work; clarity and accuracy of the spoken examination.

Texts

G.T. Bagni, 1996, Storia della matematica I - Dall’antichità al Rinascimento. II - Dal Rinascimento ad oggi, Pitagora, Bologna
Gabriele Lolli, 2002, La questione dei fondamenti tra matematica e filosofia. Panorama introduttivo, http://homepage.sns.it/lolli/articoli/QuestioneFondamenti.pdf
Consultation texts
1. C.B.Boyer, 1968, Storia della matematica, ristampa 2001 Oscar Saggi Mondadori.
2. Morris Kline, Storia del pensiero matematico, 2 voll., Einaudi, 1999.
3. Morris Kline, La matematica nella cultura occidentale, Feltrinelli, 1976.

Other materials
1. Documenti su brani di fonti originali tratti da A. Frajese, L. Maccioni, Gli Elementi di Euclide, UTET, Ristampa 1977, forniti durante il corso.
2. Documenti estratti da R.Netz, W. Noel, Il codice perduto di Archimede, Rizzoli, 2007, forniti durante il corso.
3. Documenti su brani di fonti originali tratti da “Bottazzini-Freguglia-Toti Rigatelli, Fonti per la Storia della Matematica, B.U.S.,1992 forniti durante il corso o pubblicati sul Corso Moodle.

More Information

Maria Polo – Tel. 0706758528 – 15.00/16.00- email: mpolo@unica.it

EXAM DATES: See website CdL and student's personal page; online registration - the examinations are held at the Department of Mathematics and Computer Science