# Matematica | COMPLEMENTARY MATHEMATICS

## Matematica COMPLEMENTARY MATHEMATICS

 0512300044 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2021/2022

 YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2018 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/04 6 48 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 FRANCESCO SAVERIO TORTORIELLO T
Objectives
THE COURSE HAS THE OBJECTIVE OF REVIEWING THE BASIC CONCEPTS OF MATHEMATICS IN A CRITICAL MANNER.
KNOWLEDGE AND UNDERSTANDING: KNOWING THE REASONS WHICH HAVE LED TO THE BIRTH AND DEVELOPMENT OF NOTIONS WHICH ARE AT THE BASE OF MATHEMATICS. IN PARTICULAR, THE ROLE OF MATHEMATICS IS ANALYZED AS A GLUE AMONG THE TWO CULTURES
Prerequisites
KNOWLEDGE OF THE BASIC NOTIONS IN ALGEBRA, ANALYSIS AND GEOMETRY
Contents
GENERAL FRAMEWORK OF GREEK GEOMETRY. THE PROBLEM OF INCOMMENSURABILITY. THE ELEMENTS OF EUCLID. GENERAL TEXT TEXT AND CONTENT OF THIRTEEN BOOKS. ANALYSIS OF DEFINITIONS, POSTULATIONS AND COMMON NOTIONS OF THE BOOK I. DEMONSTRATIONS IN THE EUCLIDEA THEORY. THE CANONICAL STRUCTURE ACCORDING TO PROCLO (PROTASI, ECTESI, DIORISMO). FROM I.47 TO RETURN IN BOOK I: I.4, I.8, I.31, I.35. THE V POSTULATE: ANALYSIS OF THE ANOMALIES. PROPOSALS I.16 AND I.17 (VERIFIES THAT I.17 IS THE INVERSE OF THE POSTULATE. THE THEORY OF PARALLEL NETWORKS IN BOOK I: PROPEP. I.27, I.28, I.29, I.31 AND I.32 LOGICAL EQUIVALENCE BETWEEN POSTULATE, POSTULATE OF UNICITY AND POSTULATE OF THE OBLIGATION, THE FORMULATION OF PARALLELISM GIVEN BY POSIDONY AND QUADRILATER OF SACCHERS WHAT IS LOGIC? BRIEF HISTORICAL INTRODUCTION AND INTRODUCTION TO THE BASIC PRINCIPLES OF LOGIC CLASSIC, MODERN LOGIC
RELATIONSHIP BETWEEN THE TWO CULTURES: MATHEMATICS AND LITERATURE:
ARCHIMEDE AND THE LATIN POETRY OF I A. C .: CATULLO, VIRGILIO, ORAZIO, STRUCTURAL SYMMETRIES IN THE POETIC COMPOSITIONS OF VIRGILIO, THE GREEK MYTHS ON THE INVENTION OF NUMBERS, THE ROLE OF MATHEMATICS IN THE ANCIENT GREEK THEATER
BIRTH OF THE SONG AND ITS METRIC STRUCTURE, MATHEMATICS IN DANTE AND PETRARCA. SHAKESPEARE AND THE INFINITE OF BRUNO
GALILEO WRITER, THE MATHEMATICS IN DOSTOEVSKI ,, NOVALIS, GOETHE, CHLEBNIKOV AND FLORENSKIJ, LEOPARDS AND THE MATHEMATICAL INFINITE, THE FUTURISM: MARINETTI, PIRANDELLO AND THE NON-EUCLIDEAN GEOMETRIES, THE ISSUE OF DEDEKIND AND ZERMELO IN KAFKA AND MUSIL , BORGES AND MATHEMATICAL INFINITY
MATHEMATICS AND HISTORY
THE BIRTH OF SCIENTIFIC CULTURE, USE OF GEOMETRY FOR THE ART OF ORATORY. THE BIRTH OF THE ALGEBRA AND ITS DIFFUSION IN THE WEST, FROM AL-KHWRIZM TO THE LATIN TRANSLATIONS, THE LIBER ABACI DI FIBONACCI: THE COMMERCIAL DEVELOPMENTS INTRODUCED BY THE ARAB SERIES. MATHEMATICS AND NAPOLEON. THE GREAT SCIENTIFIC INSTITUTIONS AND THE REFORM OF THE INTELLECTUAL INSTITUTIONS THE ROLE OF RESEARCH IN THE NEW INSTITUTIONAL SYSTEM. MATHEMATICS AND FASCISM, THE ROLE OF MATHEMATICS IN THE HISTORY OF THE SECOND WORLD WAR: TURING AND MILITARY STRATEGIES

MATHEMATICS AND PHILOSOPHY
FREGE; RUSSELL AND LOGICISM, POINCARÉ: CONSTRUCTIVE AND CONVENTIONAL THEORIES OF MATHEMATICS, FROM BROUWER TO DUMMET: INTUITIONALISM AND THE PROBLEM OF THE THIRD EXCLUDED, HILBERT: FORMALISM, GOEDEL: THE PROBLEM OF COMPLETENESS, WITTGENSTEIN: MATHEMATICS WITHOUT FOUNDATIONS
MATHEMATICS AND ART
THE BIRTH OF THE PERSPECTIVE: GIOTTO, BRUNELLESCHI, PIER DELLA FRANCESCA AND ALBERTI, MATHEMATICS IN DURER: FROM GEOMETRIC LETTERS TO MELANCONIA, KANDISKY AND EUCLIDEA GEOMETRY, PAINTING AND THE FOURTH DIMENSION (DALI ALSO PICASSO), THE ANALYTICAL LINE AND THE CRISIS OF FOUNDATIONS IN MATHEMATICS: MAGRITTE, MONDRIAN. ART AND FRACTALS, DE CHIRICO AND MATHEMATICS
Teaching Methods
THE COURSE IS DIVIDED IN FRONTAL LESSONS HELD BY THE TEACHER (2 CFU), PRESENTATION OF SHORT SEMINARS HELD BY STUDENTS ON THEMES AGREED WITH THE TEACHER (3 CFU), CREATION OF WORKING GROUPS THAT DEVELOP AND ARTICULATE SEMINARS TO BE PROPOSED IN THE DIFFERENT CONFERENCES "MATHEMATICS AND.." AND .. WHICH ARE CARRIED OUT AT THE MATHEMATICS DEPARTMENT EVERY YEAR (1 CFU).
Verification of learning
THE ASSESSMENT WILL BE CARRIED OUT BY MEANS OF AN ORAL EXHAMINATION. DURING THE EXAMINATION, KNOWLEDGE OF THE MATHEMATICAL CONTENT OF THE ARGUMENTS, CAPABILITY TO EXPOSE THEM IN A CRITICAL MANNER AND TO CONTEXTUALIZE THEM IN THE HISTORICAL DEVELOPMENT WILL BE EVALUATED.
Texts
G.GERLA, TENTATIVI DI FONDARE LA MATEMATICA, VOLUME 1.
A CURA DI MAROSCIA, C. TOFFALORI, F.S. TORTORIELLO, G. VINCENZI, MATEMATICA E LETTERATURA: ANALOGIE E CONVERGENZE. UTET, 2016
PIRO F. SFIDE DIDATTICHE. IL PENSIERO CRITICO NELLA SCUOLA E NELL'UNIVERSITÀ EDITORIALE SCIENTIFICA
More Information
FOR FURTHER INFORMATION, PLEASE CONTACT THE TEACHER.
EMAIL: fstortoriello@unisa.it
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