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ELEMENTARY MATHEMATICS

Academic year and teacher
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Versione italiana
Academic year
2021/2022
Teacher
VALTER ROSELLI
Credits
6
Didactic period
Secondo Semestre
SSD
MAT/04

Training objectives

The main objective of the course is to provide students with advanced knowledge on topics of elementary geometry, number theory and analysis , relating to items on the " course content" .
At the end of the course students will know solve problems on the geometry of the triangle , the numerical congruences and the maximum and minimum in elementary way and will have the capacity to recognize and then solve a problem of one of these types .
The course also aims to provide students with tools to design and develop mathematics teaching methodologies.

Prerequisites

Elementary algebra . Elements of Euclidean geometry of the plane . Elements of trigonometry . Elements of analytic geometry . First elements of mathematical logic: concepts of definition , theorem , demonstration, role of examples and counterexamples .

Course programme

The course includes 48 hours of teaching between lessons and exercises.The topics covered in the course are the following .

Geometry of the triangle (4h) . Theorem of Ceva (2h) . Triangle Center (2h) . Euler line (2h ). Nine-point circle (2h) . Morley's Theorem (2h). Butterfly theorem (1h) . Fibonacci numbers (5h). Numbers of Lucas (2h) . Congruences (3h) . Chinese remainder theorem (2h) . Maximum and minimum from an elementary point of view (6h) . Various demonstrations of the Pythagorean theorem (2h) . Using geometric transformations to address some maximum and minimum problems (4h) . Menelaus theorem and van Aubel . Applications (4h). Some trigonometric inequalities (2h). Regular polygons inscribed and circumscribed to a circumference (3h).

Didactic methods

Lectures to introduce the theoretical concepts . Exercises relating to the application of these concepts. Also receiving students for questions and clarifications.

Learning assessment procedures

The goal of the exam test is to verify the level of achievement of learning objectives previously indicated .
The exam consists of a written test in five questions : three theoretical on the course subjects and two exercises that require the application of the various arguments put forward in the course .
The maximum score for each exercise is 6 points and then the maximum final grade will be 30 that will be able to be confirmed by the praise , depending on the level of accuracy of the performance of individual exercises .

Reference texts

Lecture notes .