### Sciences

## Subject: HISTORY OF MATHEMATICS (A.A. 2020/2021)

### master degree course in MATHEMATICS

Course year | 1 |
---|---|

CFU | 6 |

Teaching units |
Unit Storia della matematica
Related or Additional Studies (lesson)
- TAF: Supplementary compulsory subjects SSD: MAT/04 CFU: 6
Pietro MILICI |

Exam type | oral |

Evaluation | final vote |

Teaching language | Italiano |

### Teachers

### Overview

Foster students' historical perspective of some meaningful moments in the development of mathematics.

Describe the evolution of the main mathematical concepts, methods, and theories.

Promote the understanding of the epistemological difficulties and obstacles related to the evolution of mathematical concepts.

Develop critical skills in reading a mathematical text.

### Admission requirements

Basic knowledge of the topics of Mathematics at Scientific Postgraduate level.

### Course contents

Ancient mathematics. Numbering systems and arithmetic operations. Egyptian and Babylonian mathematics. Mathematical and philosophical schools in classical Greece. The contributions of Euclid, Archimedes, Apollonius. Mathematics in Alexandrian culture: Pappus and Diophantus of Alexandria.

Arab hegemony and al-Khuwarizmi algebra. The Liber abaci by Leonardo Pisano. Maestri e scuole d’abaco in Italy in the Middle Ages and Renaissance. The algebra in the sixteenth century. The solution formulas of the third and fourth order equations. The algebraic work of Viète. Napier and the invention of logarithms. Descartes et Fermat's contribution to the birth and development of analytic geometry.

Calculation of areas and volumes from antiquity to modern times. The "exhaustion method", the theory of the indivisible. The determination of the tangent line from antiquity to the modern era. The birth of infinitesimal analysis.

### Teaching methods

Lectures and group work on the historical texts. The activities will be carried out either in presence or in remote, depending on the evolution of the COVID19 situation.

### Assessment methods

Oral exams. The (optional) presentation of some topics during the lessons can be evaluated as a part of the oral exam according to the agreement with the teacher. The exams will be carried out either in presence or in remote, depending on the evolution of the COVID19 situation.

### Learning outcomes

Knowledge and comprehension:

Knowledge of the evolution of some mathematical concepts.

Knowledge of the methodologies of research in the history of mathematics.

Consciousness of epistemological issues related to teaching/learning problems of certain mathematical contents.

Application of knowledge and comprehension:

To express and make critical links on the topics of the course.

To deal with the study of mathematical concepts in a historical perspective.

Autonomy:

To evince (and eventually correct or complete) wrong or incomplete reasoning.

To work in autonomy, also taking care of scientific and organizational responsibilities.

To produce didactical text and/or multimedia.

Communication:

To expose and argue on the topics of the course.

Knowledge capabilities:

To chose autonomously how to deepen issues of the history of mathematics.

### Readings

Carl Boyer (1990). Storia della matematica. Oscar Mondadori.

Morris Kline (1991). Storia del pensiero matematico. Einaudi.

Articoli ed estratti di testi storici saranno forniti durante le lezioni.