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 equation 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:: Uss 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:  First elements of probability (finite case).  Applications, problems.

Readings/Bibliography

Notes of the course. (files PDF on line on the website ALMA DL). Book: "Note di Geometria", by M.Idà, Pitagora Ed.

Teaching methods

It is a particularly stressed request 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 finial test is made of a written  exam plus an oral one, if requested by the student or needed to reach a sufficient mark.

Links to further information

http://www.dm.unibo.it/~gimiglia/

Office hours

See the website of Alessandro Gimigliano