Matematica | HISTORY OF MATHEMATICS

cod. 0512300024

HISTORY OF MATHEMATICS

	0512300024
	DIPARTIMENTO DI MATEMATICA

	MATHEMATICS
	2015/2016

CURRICULUM MATEMATICA AD INDIRIZZO GENERALE-DIDATTICO Cohort 2013/2014

	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2010
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/04	6	48	LESSONS	OPTIONAL SUBJECTS

	Objectives
	1. THE STUDENT IS REQUIRED TO KNOW 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. THE STUDENT IS ABLE TO ASSESS CRITICALLY HISTORIOGRAPHICAL DIFFERENT APPROACHES AND EVENTUALLY TO MAKE RESEARCHES IN HISTORY OF MATHEMATICS. 4. THE STUDENT IS ABLE TO EXPOSE CRITICALLY ALL MATHEMATICAL THEORIES LEARNED. 5. THE STUDENT IS ABLE TO MAKE A HISTORICO-MATHEMATICAL RESEARCH AND TO BUILD AN HISTORICAL-DIDACTICAL PATH.

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

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

5. 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.

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 AND SEMINARS GIVEN BY STUDENTS

	Verification of learning
	THE ASSESSMENT WILL BE CARRIED OUT BY MEANS OF ORAL EXHAMINATION AND A SEMINAR. 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. DOCUMENTS AND PAPERS PROVIDED BY THE TEACHER.