ELEMENTARY MATHEMATICS FROM A HIGHER POINT OF VIEW
Academic year and teacher
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- Versione italiana
- Academic year
- 2017/2018
- 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 .
