Unit HISTORY OF MATHEMATICS I
- Course
- Mathematics
- Study-unit Code
- 55A00102
- Curriculum
- Didattico-generale
- Teacher
- Daniele Bartoli
- Teachers
-
- Daniele Bartoli
- Hours
- 42 ore - Daniele Bartoli
- CFU
- 6
- Course Regulation
- Coorte 2024
- Offered
- 2024/25
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/04
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- italiano
- Contents
- History of Infinitesimal Calculus. History of Non-Euclidean Geometries. Crisis in the Foundations during the nineteenth century.
- Reference texts
- Gli Elementi di Euclide-edizione U.T.E.T.
La Geometria di Cartesio-edizione U.T.E.T.
C. B. Boyer Storia delle matematiche, Mondadori. Varie edizioni in italiano.
Morris Kline, Storia del pensiero matematico, Einuadi Editore, 1991. - Educational objectives
- The course aims to facilitate the acquisition of a historical vision of some significant moments in the development of mathematics. The evolution of some of the main concepts, methods and theories is presented. As didactic purpose, we propose to educate to the identification and understanding of epistemological obstacles emerged in the arrangement of some mathematical concepts over the centuries, providing adequate tools to overcome them.
- Prerequisites
- no particular prerequisites
- Teaching methods
- Frontal lessons, use of original texts
- Other information
- Further materials and references will be provided during the lessons and made available on Unistudium
- Learning verification modality
- Oral exam on the whole program of the course.
The duration of the interview can vary between about 30 and 45 minutes. See also http://www.unipg.it/disabilita-e-dsa - Extended program
- Ancient, Classical, and Hellenistic Mathematics: Pythagoras, Plato, Aristotle.
History of Euclidean and Non-Euclidean Geometry: Euclid, Proclus, Saccheri, Gauss, Lobachevsky, Riemann.
History of Infinitesimal Calculus: Eudoxus, Archimedes, Galileo and his school, Descartes, Newton, Leibniz, Cauchy, Riemann, and Lebesgue.
Logic between the 19th and 20th centuries: Propositional Logic, Predicate Logic, Intuitionistic Logic, Set Theory, Tarski.
The problems of the foundations of mathematics: 19th-century reductionism, the axiomatization of mathematics, Frege, Russell, Poincaré, Brouwer, Hilbert.
Modern Geometry: Hilbert and the Foundations of Geometry, Enriques, Linear Algebra, Geometric Calculus.
Main currents in the philosophy of mathematics: Traditional analysis of knowledge, Premodern mathematical philosophy (Plato and Platonism, Kant, Mill’s Empiricism), The second half of the 20th century (Neologicism, Platonism, Implicationalism, Structuralism, Fictionalism, Internalism, Constructivism, Conjecturalism, Empiricism, Cognitivism). - Obiettivi Agenda 2030 per lo sviluppo sostenibile
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