Università di Pavia - Offerta formativa

ELEMENTARY MATHEMATICS

Enrollment year

2020/2021

Academic year

2020/2021

Regulations

DM270

Academic discipline

MAT/04 (COMPLEMENTARY MATHEMATICS)

Department

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

Course

MATHEMATICS

Curriculum

PERCORSO COMUNE

Year of study

1°

Period

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

ECTS

6

Lesson hours

48 lesson hours

Language

Italian

Activity type

WRITTEN AND ORAL TEST

Teacher

MARACCI MIRKO (titolare) - 6 ECTS

Prerequisites

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.

Learning outcomes

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.

Course contents

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.)

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.)

Teaching methods

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.

Reccomended or required readings

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.

DedÃ², M. Trasformazioni geometriche. Decibel, Zanichelli, Bologna, 1996.

(possibly:

Kiesler, H.J. Foundations of infinitesimal calculus, 2007.)

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

DedÃ², M. Trasformazioni geometriche. Decibel, Zanichelli, Bologna, 1996.

(possibly:

Kiesler, H.J. Foundations of infinitesimal calculus, 2007.)

Assessment methods

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.

Further information

Sustainable development goals - Agenda 2030