# Matematica | HISTORY OF MATHEMATICS

## Matematica HISTORY OF MATHEMATICS

 0512300024 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2013/2014

 YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2010 PRIMO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/04 6 48 LESSONS OPTIONAL SUBJECTS
 VERONICA GAVAGNA T
Objectives
1. IT IS REQUIRED THAT THE STUDENT KNOWS THE FUNDAMENTAL PROBLEMS AT THE ORIGIN OF THE DIFFERENTIAL CALCULUS, AND IS ABLE TO DESCRIBE THE MAIN PHASES OF THE DEVELOPMENT OF ANALYSIS FROM THE SEVENTEENTH CENTURY UNTIL THE EARLY TWENTIETH CENTURY, IDENTIFYING ALSO THE CONTRIBUTIONS OF THE MOST IMPORTANT MATHEMATICIANS.

2. THE STUDENT MUST BE ABLE TO INTERPRET AND CONTEXTUALIZE THE MOST IMPORTANT SOURCES (ORIGINAL OR IN TRANSLATION), AND MUST ACQUIRE THE BASIC TOOLS OF THE METHOD OF HISTORICAL RESEARCH,

3. IT IS REQUIRED THE STUDENT IS ABLE TO ASSESS CRITICALLY HISTORIOGRAPHICAL DIFFERENT APPROACHES AND EVENTUALLY TO MAKE RESEARCHES IN HISTORY OF MATHEMATICS.

4.IT IS REQUIRED THAT THE STUDENT IS ABLE TO EXPOSE CRITICALLY ALL MATHEMATICAL THEORIES LEARNED.

5. IT IS REQUIRED THAT THE STUDENT IS ABLE TO MAKE A HISTORICO-MATHEMATICAL RESEARCH AND TO BUILD AN HISTORICAL-DIDACTICAL PATH.
Prerequisites
BASIC KNOWLEDGE OF ANALYSIS AND GEOMETRY.
Contents
QUADRATURES AND TANGENTS IN GREEK MATHEMATICS: EUCLID, ARCHIMEDES, APOLLONIUS. INFINITESIMAL METHODS IN THE RENAISSANCE CENTROBARYCA: COMMANDINO AND CALERIO. CAVALIERI, TORRICELLI AND THE THEORY OF INDIVISIBLES. DESCARTES AND FERMAT’S METHODS FOR TANGENTS AND THEIR FOLLOWERS DE BEAUNE, DE SLUSE, HUDDE. LEIBNIZ AND HIS NOVA METHODUS. NEWTON AND THE METHOD OF FLUXIONS. EULER AND HIS INTRODUCTIO IN ANALISYN INFINITORUM. LAGRANGE’S PROGRAM OF ALGEBRAIC ANALYSIS. CAUCHY AND HIS COURS D’ANALYSE. RIEMANN AND WEIERSTRASS’ SCIENTIFIC WORK AND ITS INFLUENCE ON THE ITALIAN SCHOOL OF ANALYSIS.
Teaching Methods
FRONTAL LESSONS
Verification of learning
THE ASSESSMENT WILL BE CARRIED OUT BY MEANS OF ORAL EXHAMINATION. DURING THE EXAMINATION WILL BE EVALUATED: KNOWLEDGE OF THE MATHEMATICAL CONTENT OF THE ARGUMENTS, CAPABILITY TO EXPOSE THEM IN A CRITICAL MANNER AND TO CONTEXTUALIZE THEM IN THE FIELD OF TEACHING MATHEMATICS.
Texts
C.BOYER, STORIA DEL CALCOLO E IL SUO SVILUPPO CONCETTUALE, BRUNO MONDADORI, MILANO 2007
E. GIUSTI, PICCOLA STORIA DEL CALCOLO INFINITESIMALE DALL’ANTICHITÀ AL NOVECENTO, IST. EDITORIALI E POLIGRAFICI, PISA 2007.
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DOCUMENTS AND PAPERS PROVIDED BY THE TEACHER.