# 67997 - Basic Geometry and Mathematics

## 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.

Algebra e Arithmetics: Elements of set theory and logic. Numbers (natural, integer): 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), 2018",

On the website:  http://campus.cib.unibo.it  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 the classroom.

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.

## Assessment methods

The final test is aimed to verify whether a student is able to work on problems about volumes and surfaces of the main objects in Euclidean Geometry (both in the plane and in space), also via  simple constructions (e.g. via Pythagoras' Theorem). In Analytic Geometry in the plane the candidate should know how to use equation for lines and basic formulas for parallelism, orthogonality and distances. In Arithmetics She/He 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.

The final test is made of a written  exam about the program listed above. The candidate will have three hours time and can 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.

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.

## Teaching tools

On the web site:
http://www.dm.unibo.it/matematica/
One can find notes and interactive exercises of Algebra and Geometry.