OVERVIEW

The lecture course presents the basic theories of mathematics (geometry, arithmetic, calculus, set theory) within the perspective of present day mathematics, with the intent to highlight the technical points which must be known by the lecturer to give a clear presentation of such disciplines to a lay audiience. In particulare basic tools will be offered for the preparation of didactic activities and the discussion with students.

AIMS AND CONTENT

LEARNING OUTCOMES

To focus on some foundational problems relating to the main mathematical areas addressed in upper secondary education and their connection with the cultural and pedagogical choices that a teacher must face in setting up and developing his own teaching activity.

AIMS AND LEARNING OUTCOMES

Study of the basic theories from the expert's point of view, to analyze didactic issues and research questions.

PREREQUISITES

None. Standard mathematical practice may be useful.

TEACHING METHODS

Teaching style: In presence

SYLLABUS/CONTENT

Historical setting for the basic mathematical theories: Euclidean geometry, non-Euclidean geometries, arithmetic, real analysis, set theory. Review of the basics of mathematical logic and first order theories related to the basic mathematical theories.

Applications and experiments in didactics: Pythagora's theorem; Euler's line; Ceva's theorem; angles in a triangle; parallel lines; Fibonacci's sequence; Pascal's triangle; Matijasevic-Robinson theorem; algorithms for elementary operations.

RECOMMENDED READING/BIBLIOGRAPHY

Course notes and slides presented during the lectures will be available on aulaweb, complemented by other material. Notes taken at the lectures and the material on aulaweb are enough in preparation for the exam. The books listed below are good references.

Mendelson, E. Introduzione alla logica matematica. Boringhieri

Prodi, Analisi matematica, Boringhieri

Russo, Il primo libro degli elementi di Euclide, Carocci

TEACHERS AND EXAM BOARD

Exam Board

GIUSEPPE ROSOLINI (President)

JACOPO EMMENEGGER

FRANCESCA MORSELLI (President Substitute)

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written essay and of an oral examination which can be taken in either order. The written essay is on the arguments of the lecture course and asks for the presentation of particular subjects taught in the course. The oral examination is a presentation and an open discussion of subjects in the syllabus. The final mark determines how the two tests complement each other. The oral examination can be taken in itinere.

ASSESSMENT METHODS

The written essay verifies the actual acquisition of the mathematical knowledge of the basic mathematical theories. The oral examination consists mainly in a presentation of some part of the syllabus and aims at evaluating that the student has acquired an appropriate level of knowledge and analytical skills about the mathematical theories.

Students with DSA  (=Specific Learning Disabilities) certification, disability or other special educational needs are advised to contact the teacher at the beginning of the course to establish on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

Exam schedule