Insegnamento mutuato da: B018783 - STORIA DELLA MATEMATICA Corso di Laurea Magistrale in MATEMATICA Curricula DIDATTICO
A few notes on ancient mathematics. Mathematics in Italy: XIII-XVI century. The work of Viète. Descartes's Géométrie. Methods of squaring: XVI-XVII century. First developments of Calculus. The subjects are examined from a historic and didactic point of view through a critical analysis of the principal research methods in the teaching of the history of mathematics, and with reference to the conceptual, epistemological and didactic issues of the teaching and learning of this discipline.
Boyer C. B., Storia della Matematica, Milano, Mondadori, 2009.
Franci R., Toti Rigatelli L., Storia della teoria delle equazioni algebriche, Milano, Mursia, 1979.
Freguglia P., La geometria fra tradizione e innovazione, Torino, Bollati Boringhieri, 1999.
Giacardi L., Roero C.S., La matematica delle Civiltà arcaiche: Egitto, Mesopotamia, Grecia, Torino, Università Popolare di Torino, Editore, 2010 (I ed. 1979).
Giusti E., Piccola storia del Calcolo infinitesimale dall'antichità al Novecento, Pisa-Roma, 2007.
Maracchia S., Storia dell'algebra, Napoli, Liguori Srl, 2005.
Itinera Mathematica. Studi in onore di G. Arrighi per il suo 90° compleanno. A cura di R. Franci, P. Pagli, L. Toti Rigatelli. Centro Studi sulla Matematica Medioevale. Università di Siena, 1996.
Un ponte sul Mediterraneo. Leonardo Pisano, la scienza araba e la rinascita della matematica in Occidente, a cura di E. Giusti e con la collaborazione di R. Petti, Firenze, 2002 .
Ulivi E. Dispense del Corso di Storia della Matematica.
Rudiments of the History of Mathematics from Antiquity to the first half of 18th century
General picture of developments in arithmetic, algebra and geometry, with particular reference to the 13th to 17th centuries, of broad use also in teaching
Skills acquired (at the end of the course):
Capacity for direct analysis of ancient mathematics texts, bibliographical research and coordination of the theoretical aspects of mathematics with its teaching and related historic developments. For this purpose, students are invited to identify and use appropriate online sites where, with a view of scientific research and didactic application, they can find and consult ancient books in digital format, bibliographic material, texts of conferences presented in conventions and seminars on the teaching of history of mathematics in secondary schools. Still in this view, the course ends with a visit to the ancient library of the Department of Mathematics, where various ancient texts belonging to the Department are displayed. The exhibition was presented to secondary school teachers in 2016.
Courses to be used as requirements (required and/or recommended): none
Courses required: none
Courses recommended: none
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Hours reserved to private study and other indivual formative activities: 153
Hours for lectures: 72
Hours for laboratory: 0
Hours for laboratory-field/practice: 0
Seminars (hours): 10
Stages (hours): 0
Intermediate examinations (hours): 0
Attendance of lectures, practice and lab:
Computer and projector
Egyptians, Babylonians and Greeks:
Numbering systems and arithmetic operations. First-degree equations in Egyptian mathematics. First-, second- and third-degree equations and systems in Babylonian mathematics. The problems of "application of areas" in Greek mathematics and second-degree equations. Classical problems ascribable to third-degree equations. Notes on Diophantus's Arithmetica.
Indians and Arabs:
Numbering systems and arithmetic operations. First-, second-, third- and fourth-degree equations and systems in Indian mathematics: Aryabhata, Brahmagupta and Bhaskara. Importance and influence of Arab culture in the West. First-, second- and higher-degree equations in Arab mathematics: al-Khwarizmi, Abu Kamil, al-Karaji, al-Khayyam, al-Kashi.
Arithmetic in the Middle Ages and Its Teaching:
Severino Boezio and the De institutione arithmetica, Aurelio Cassiodoro, Isidoro of Seville, Beda, Alcuino of York, Gerberto d'Aurillac.
Leonardo Fibonacci and the Mathematics of the Abacus:
Life and works of Fibonacci. Analysis of the fifteen chapters of the Liber abaci. Abacus teachers and schools in Italy in the Middle Ages and Renaissance. The mathematics of the abacus and treatises dealing with it. Operations with integers and fractions: various methods of multiplication and division, multiple fractions and unitary fractions, approximation of roots. The methods of simple and double false position. Problems of mercantile arithmetic: barter, coins, companies. Recreational mathematics. Algebra. Analysis of the algebraic problems in chapter XV of the Liber abaci. First-, second- and higher-degree equations in the mathematics of the abacus: Jacopo da Firenze, Paolo Gherardi, Dardi of Pisa, Antonio Mazzinghi, Piero della Francesca; Benedetto da Firenze and the great "encyclopedias" of the 15th century.
The figure and work of Pacioli: the Summa de arithmetica, geometria, proportioni et proportionalità and the mathematics of the abacus, the De viribus quantitatis and the Divina proportione.
Developments in Algebra in the 16th Century:
Invention of formulae for the solution of the third- and fourth-degree equations: Scipione Dal Ferro, Nicolò Tartaglia, Gerolamo Cardano and Ludovico Ferrari. Raffaele Bombelli's Algebra: relations between algebra and geometry; the irreducible case of the third-degree equation and complex numbers.
The Algebraic Work of François Viète:
Life and works of Viète. The Isagoge and Viète's method of analysis; the "logistica speciosa" or new algebra using letters. Summary of the contents of the Notae priores and the Zeteticorum libri quinque. The De aequationum recognitione et emendatione tractatus duo: zetetic analysis, plasma, sincrisis and the "remedia" for the reduction of an equation to canonical form. Algebraic solution of third- and fourth-degree equations. The Canonica recensio and the Supplementum geometriae in reference to the geometric solution of second- and third-degree equations.
Life and works of Descartes. Analysis of the three books of Géométrie.
The "exhaustion" method. Archimedes and the Method: sphere, cylinder and cone. The volume of the sphere according to Al-Haytham. The revival of the Archimedean studies in the Renaissance: Luca Valerio. Bonaventura Cavalieri and the
Theory of Indivisibles. The infinite hyperboloid of Evangelista Torricelli: curved indivisibles. The indivisibles after Cavalieri: observations.
The birth of the calculus:
The Nova methodus of Leibniz; Newton's method; the dispute on the calculus. I nod to the spread of calculus in Europe.