67997 - Basic Geometry and Mathematics

Learning outcomes

Upon completion of the course, students will: - be able to determine the areas and volumes of basic figures, including through the use of their properties, the Pythagorean Theorem, and elementary constructions (e.g., solids of revolution); - be able to use equations of lines, angular coefficients, and basic formulas to solve problems of parallelism and perpendicularity between lines; - be able to determine the positions and relative distances of lines and points in the Cartesian coordinate system; - be able to recognize basic properties of plane figures. - be proficient in arithmetic tools (knowledge of number systems, ability to manipulate numbers using powers, roots, fractions, and decimals); - be able to use linear functions, including solving first-degree equations and systems; - be able to historically place the evolution of some of the main concepts regarding the development of number representation. - be able to apply basic notions of logic (statements, logical connectives); - calculate the probability of events in simple cases (e.g., in games involving dice rolls or number extractions).

Course contents

Euclidean Geometry:

Plane: Euclid's Postulates. Polygons. Triangles (equality criteria, Pythagorean Theory). Notable Quadrilaterals and their properties. Regular polygons. Circle. Isometries and similarities.

Space: Polyhedra and solids. Volumes and Surfaces.

Analytic Geometry:
Use of Cartesian Coordinates. Equations representing lines (Parallelism, Perpendicularity), graphs. Cartesian coordinates in space.

Arithmetic and Algebra:

Number aets (Whole numbers, Integer, Rational numbers, Real numbers): Representations, historical aspects, overview of constructions, elementary properties. Symbolic manipulation as a tool for proving in Arithmetic. Equations as a tool for solving problems.

Probability and Statistics:

Introduction to Probability. Applications and problem solving. Elements of combinatorics. Elements of Statistics.

Readings/Bibliography

• A.Gimigliano, L.Peggion: Elementi di Matematica, UTET Università
• M.I. Fandino Pinilla, S. Sbaragli: Matematica di base per insegnare nella scuola primaria, Bonomo editore

Teaching methods

The course consists of lectures, group discussions, and in-class problem-solving and exercises.

Assessment methods

The exam consists of a written test comprehending close and open-ended questions, administered via EOL virtual platform. Therefore, students must have their institutional login credentials available on the day of the exam. The exam will be held in person and students have two hours to complete it. Students may consult texts and notes. The final grade is expressed out of 30, and at least 18/30 is required.


To take the exam, students must register online (AlmaEsami website), adhering strictly to the established deadlines. It is not possible to change the assigned time slot.

Teaching tools

The e-learning space on the platform Virtual contains teaching materials

Office hours

See the website of Andrea Maffia