# HISTORY OF MATHEMATICS

## Learning outcomes of the course unit

After completing the course the student will have an overview of mathematical thinking with particular reference to the theory of algebraic equations and development of symbolism. The course also allows students to reflect on the difficulties relating to the learning of mathematical concepts and to interpret the "obstacles" epistemological while providing historical instruments to be used as educational material for teaching.

## Prerequisites

Algebra, Mathematical Analysis 1, Geometry 1

## Course contents summary

History of documents and history of ideas. History of Algebra, from the ancient times to Galois. Algebraic equations of 1st , 2nd, 3rd and 4th degree. Geometrical Algebra in Euclid and in the subsequent epochs.

## Course contents

Ancient civilizations: the Egyptian and Mesopotamian numbering systems and the origins of algebra. Greek mathematics: the numbering system, Euclid and the structure of the Elements (definitions, axioms and common notions) the geometric algebra, Diophantus. The Chinese numerals and algebra in China and India. The algebra in Arabic mathematics. The methods of false position and the abacus treaties. Algebraists Italian Renaissance (Cardano, Tartaglia, Bombelli, Ferrari), Viète, Descartes. The transforms of Tschirhaus and Lagrange. Gauss, Ruffini, Galois. From algebra of equations to abstract algebra. Short history of the analysis.

## Recommended readings

Boyer, C.B., Storia della Matematica, 1980, Mondadori

Kline, M., Storia del pensiero matematico, 1972, Giulio Einaudi Editore

Franci, R., Toti Rigatelli,L, Storia della teoria delle equazioni algebriche, 1979, Mursia

D.Medici -appunti di storia della Matematica

## Teaching methods

Lectures will be mainly in transmissive style, but with a steady dialogue with students which can be called to the blackboard for discussing problems, or for showing their understanding of and taking part to the course.

## Assessment methods and criteria

Oral examination

## Other informations

The course will contribute to the knowledge of relevant historic times of the mathematical thought, by a direct and/or mediate use of original texts. In this way it is possible to follow the evolution of concepts in times