Elementary Mathematics from an Advanced Standpoint

Credits

Prerequisites

None.

Examination method

Passing an oral exam.

Learning
objectives

Review and contextualisation of the main mathematical topics relevant to school teaching in the light of the historical evolution of mathematics and its current disciplinary structure.

Origin of the various types of numbers and the main conceptual turning points in history. Historical and didactic motivations for the extensions of number systems. Real numbers. Algebraic and topological reasons for the passage from Q to R. Commensurability and incommensurability. Infinity in mathematics and at school. Potential and actual infinity. Infinity in geometry. Reflections on the meanings of algebra and on the transition from arithmetic to algebra: algebra as a “language”. Geometric transformations

Academic Year
2018/2019

Lecturer: Roberto TORTORA.

Semester: second.

Elementary Mathematics from an Advanced Standpoint