# 67997 - Basic Geometry and Mathematics

• Campus: Bologna
• Corso: Single cycle degree programme (LMCU) in Primary teacher education (cod. 8540)

Also valid for Single cycle degree programme (LMCU) in Primary Teacher Education (cod. 5711)
• from Feb 12, 2024 to Apr 23, 2024

## Learning outcomes

At the end of the course every student should be able to work on problems about volumes and surfaces of the main objects of Euclidean Geometry (both in the plane and in space) and use simple construction (e.g. via Pythagoras' Theorem). In Analytic Geometry they should know how to use equations for lines and basic formulas for parallelism, orthogonality and distances. In Arithmetics they should be able to use elementary properties of operations, fractions, and decimals, give a historic picture of the development of the number system and compute probabilities (finite case) for games and simple events.

## Course contents

Euclidean Geometry :

In the plane. Euclid's axioms (Sketch), Polygons (Generalities, angles). Triangles (criteria for congruence, . Pythagoras' Theorem), 4-sided polygons and their properties. Regular Polygons. The Circle. In the space.: Polyhedra, Pyramids amd Prisms..Regular Polyhedra.. Solids of revolution.

Analitic Geometry:

The method of Cartesian coordinates on the line, in the plane and in 3-dimentional space. The Cartesian plane: equations for lines (parallel, perpendicular lines), graphs. Use of Cartesian coordinates in the space.

Other Geometries:

Sketch of Non-Euclidean Geometries and Topology.

Algebra e Arithmetics: Elements of set theory and logic. Numbers (naturals, integers): their history, Constructions, proprieties. Rational numbers, use and representation, proportionality. Highlights about real and complex numbers and their use.

Probability & Statistics: First elements of probability (finite case). Applications, problems. First notions of Statistics.

Textbook for the course: "A.Gimigliano, L.Peggion: Elementi di Matematica, UTET Università (Novara), 2022 (second Edition)".

This text follows the way arguments are proposed in the course, so its use is strongly recomended.

On the website "virtuale" of the University, exercises and texts from previous exams (with solutions) can be found.

The book: "Note di Geometria" ( by M.Idà, Pitagora Ed.) can be an auxilliary help.

## Teaching methods

The course is based on lectures in presence.

It is a particularly imperative necessity to be able to relate Math. knowledge and its use in real problems and situations; this will be taken care in exercise and examples.

For students whose first language is not Italian (as Erasmus students), there will be particular cure in having office ours where they can get info and explanations in English.  The written text for the final exam could be submitted also in English, SPanish or French.

## Assessment methods

The final test is made of a written exam about the program listed above. The exam will be "in presence" and the candidate will have three hours time. It will be possible to use notes, texts and written material, while the use of a calculator is not permitted. If the result of the written exam is sufficient, it can be registered. If the candidates want also to try an oral exam, this can be agreed upon on an individual basis.

The final mark is given as x/30; it is sufficient if x is at least 18. If the test is not sufficient, the candidate can try again at the following available test (Three possibilities in May-July; one in September, one in December, two in January) .

In order to take the written exam, one has to enlist on the website AlmaEsami. Whoever may not manage to do so for technical reasons, should contact the student's offices (within the deadline). The teacher could admit them to the test.

IMPORTANT NOTICE

Since 2020/21  OFA courses of Mathematics are part of the course  of Geometria e Matematica di base (prof. Gimigliano).

The exam of the course can be taken only after having passed the OFA test, for the students in need to do that.

The students with an OFA debt could follow the relative OFA course by prenotation on AlmaEsami since december. Such partecipation is advised for everyone with OFA debt.

The OFA debt in Mathematics is extint only when the exam of Geometria e Matematica di Base has been given with success.

https://corsi.unibo.it/magistralecu/ScienzeFormazionePrimaria/come-assolvere-ofa

## Teaching tools

The website "Virtuale"  ( https://virtuale.unibo.it) contains several exercises and old written test with answers.

The website:

http://progettomatematica.dm.unibo.it/

Contains notes and exercises on elementary
Algebra and Geometry