2020/2021

2020/2021

DM270

MAT/04 (COMPLEMENTARY MATHEMATICS)

DEPARTMENT OF PHYSICS

Didattica e storia della fisica

1°

1st semester (05/10/2020 - 20/01/2021)

6

48 lesson hours

Italian

WRITTEN AND ORAL TEST

MARACCI MIRKO (titolare) - 6 ECTS

Mathematical knowledge and compentencies developed in the upper secondary schools and in the "laurea triennale" in mathematics, with specific regard to: arithmetic, basic concepts of plane and space geometry, real numbers, real functions of one real variables, elementary probibility.

The course aims at introducing students to themes from diverse fields of mathematics (arithmetics, geometry, analysis and probability), chosen for their possible connections with the content tauhgt in secondary schools. The main objective is to provide tools for reflecting upon these themes in a critical way (even) from a didactical perspective.

Numeration systems.
Geometrical transformations of the Euclidean plane and space from a synthetic point of view.
(Depending on the time remaining and the interests of the students:
Introduction to iperreal numbers and non-standard analysis.
Different approaches to probability: classical, frequentist and subjectivist interpretation of probability.)

Interactive lessons, which will introduce the contents of the course and during which theoretical and meta-theoretical issuses will be discussed, and problem-solving sessions.

Didactical material made available by th teacher

Capelo, A.-C.; Ferrari, M. e Padovan, G. I sistemi di numerazione. CNR Quaderno n.7, Pavia, 1990.

Dedò, M. Trasformazioni geometriche. Decibel, Zanichelli, Bologna, 1996.

(possibly:
Kiesler, H.J. Foundations of infinitesimal calculus, 2007.)

The achievement of the learning objectives will be ascertained through a written and an oral examination. The written examination will include mathematical tasks and open questions. The examinations will aim at assessing the level of knowledge of the contents of the course and the ability to autonomously re-elaborate these contents.