MATHEMATICS II - 139042-MOD1

courses
ID:
139042-MOD1
Dettaglio:
SSD: Complementary Mathematics Duration: 42 CFU: 7
Located in:
BERGAMO
Url:
PRIMARY TEACHER EDUCATION - 139-270/PERCORSO COMUNE Year: 2
Year:
2025
Course Catalogue:
https://unibg.coursecatalogue.cineca.it/af/2025?co...

Overview

Date/time interval

Secondo Semestre (16/02/2026 - 29/05/2026)

Syllabus

Course Objectives

• Stimulate and enhance the ability to observe, ask questions, formulate hypotheses and test them.
• Achieve a good mastery of the main arithmetic, algebraic and basic analytical concepts also through an adequate understanding of their theoretical foundations to overcome a mechanistic approach
• Through teaching labs learn how to identify mathematical models of real situations
• Know and use more and more rigorously the specific language of mathematics and its notation;
• Understand the value and scope of the deductive hypothetical method through some examples;
• Detect the value of inductive and abstraction processes and their scope in solving real problems;
• Obtaining analogies of structures between different domains;
• Critically review and logically master the acquired knowledge

Course Prerequisites

Foundational notions of geometry and manipulation of algebraic formulas at the high school level.
More specifically, students will take advantage of knowing:
1. Plane Euclidean geometry: in particular, triangle criteria for equality and similarity. Pythagoras theorem. Elementary properties of polygons and circles. One-to-one correspondence between real numbers and points on a line. Cartesian plane;
2. Powers with integer exponent, properties of powers, polynomials: divisibility, roots, factorization.
3. Equations and Inequalities of first and second degree.

Teaching Methods

This course consists of 42 hours of theoretical lectures and exercices solving. This course is associated to laboratory sessions for 2CFU that are described in a separate item.

Assessment Methods

The exam consists of a written test that aims at verifying the achievement by students of the educational objectives described above. In particular:
- Mastery of the methods and techniques developed
- Awareness of their theoretical foundations
- Appropriateness of the language used.
The test requires the resolution of some exercises and the presentation of some theoretical subjects. In general the tests consists of 7 questions and it lasts 2hours and a half.
After the exam is passed, up to 3 points will be added to the final mark for the fruitful attendance to the laboratory sessions.

Contents

1. Introduction to mathematical language (logic, sets, relations and functions)
2. The set of natural numbers also according to Peano's axiomatic theory. Sum and product with their properties.
3. Binary relations and functions.
4. Decimal positional notation of natural numbers: decomposition in base b.
5. Divisors and greatest common divisor.
6. Prime numbers and the unique factorization theorem.
7. Integers as a result of the extension of the natural numbers set.
8. Rational numbers as a result of the extension of integers. Decimal representation and fractions.
9. Countable and uncountable sets. Commensurable and incommensurable quantities. Outline of the set of real numbers.

Online Resources

More information

All the materials of the course will be posted on the Moodle web page Matematiche complementari a.a. 2023-2024. The students will be invited to join this web page in order to receive all the announcements about the course during the semester.

Degrees

Degrees

PRIMARY TEACHER EDUCATION - 139-270 
Single Cycle Master Degree 5 Years
5 years
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People

Other

Main module

MATHEMATICS II